Saturday, 28 January 2023

Reviews of the Star Trek movies from 2009, 2013 and 2016

(Originally posted on Saturday, 28 January 2023)

The reviews are in the point 8 (and its sub-points), but the previous points are important to understand my ratings.

1. Long perspective.

When I was a teenager I used to watch the series Star Trek Next Generation. To me some things were cool but overall I wasn’t really impressed. I can’t remember if I ever watched a “full” Star Trek movie, which proves that I wasn’t a true fan of this franchise.

2. Off-putting images of the villains.

I know that many people claim that the best Star Trek movie is The Wrath of Khan (1982), but I wouldn’t be able to watch a movie happening in space with characters dressed like barbarians with bare chests. This image is so ridiculous that I am personally sure that it was just a trick to make the main villain appear even more villainous. I know that this trick is used also in some other movies, also in some other Star Trek movies. I hate this kind of screenwriting – I strongly prefer villains who are villainous only by their behavior, not by their looks.

3. The catalyst: The Big Bang Theory and J. J. Abrams.

This conversation between Sheldon and Leonard, seen by me for the umpteenth time, made me finally read about the Star Trek franchise in general:

Sheldon: Next question: Kirk or Picard?
Leonard: Oh, that's tricky. Original Series over Next Generation, but Picard over Kirk.
Sheldon: Correct.



Reading about the Original Series vs. the Next Generation made me read about the Star Trek franchise in general and by the way I found out that it was brought back to life by J. J. Abrams. I wondered why I missed it, but I realized that it was in 2009, several years BEFORE The Force Awakens, so at that time I had no idea who J. J. Abrams was, so I ignored the Star Trek (2009) movie then.

I loved the way J. J. Abrams brought Star Wars back to life with the movie The Force Awakens. I also loved the way he saved Star Wars from collapsing with the movie The Rise of Skywalker, after Rian Johnson almost ruined the franchise with the movie The Last Jedi (I HATE Rian Johnson for what he did in that movie).

The main difference is that as far as Star Trek is concerned J. J. Abrams didn't write any scripts – he only directed and co-produced the movies Star Trek (2009) and Star Trek Into Darkness and only co-produced the movie Star Trek Beyond (without even directing it). But is was enough for me to buy the whole Kelvin trilogy.

Please notice that any plot flaws of the movies shouldn't be blamed on J. J. Abrams because he didn't write the scripts! I have no idea why some people hate him, but his story for The Force Awakens was quite good, especially when compared to the terrible story for the Star Trek (2009) that was wrote by other people – see my review in point 8.1.

4. No attachments.

As I already wrote I had never been a Star Trek fan (even though I used to watch the series Next Generation) and I can’t imagine watching the original series from 1960s, nor The Wrath of Khan (1982). In fact I don't intend to watch ANY Star Trek movies other than the Kelvin trilogy. So, in all my reviews I judge the movies without any attachments to any previous Star Trek movies/series. Some fans seem to be overreacting, but some other are more objective – see the screenshots farther down below.

I have to point out that in the Kelvin trilogy there is no continuity from earlier movies/series, because it’s an alternative time-line, so it’s UNLIKE the latest Star Wars trilogy. It means that in the Kelvin trilogy the Star Trek characters may be a little different, the story may be a little different and the whole concept may be a little different. No problems there at all, especially to me.

5. Science-fiction and the limits of the suspension of disbelief.

A part of a science-fiction movie is some fiction about science, obviously. It means that such a movie requires some sort of suspension of disbelief. However, to me there are limits of the suspension of disbelief and anything beyond these limits is a clear flaw of a movie.

Here are example of things that to me are within the limits of the suspension of disbelief:
5.1. Fast travel in space.
In reality a journey to a relatively close star system would take YEARS, even when traveling with a speed close to the speed of light (the maximum theoretical speed). Very long journeys would take thousands of years. Obviously that would make any movie about space exploration only a “one-way track” (which would be cool, actually).
5.2. Fast travel in space and passing of time.
This is connected with the point 1, but I have to point out that in reality for objects that travel almost with the speed of light from their point of view the time almost stops. In other reference frames (for example looking from a particular planet) the time of travel of the spaceship would be equal to the time needed to reach a particular point by an object traveling with almost the speed of light, so a time dilation would still apply to such travels. Such travels (almost at the speed of light) would be like traveling in time, but it would be again only a “one-way track” (into the future).
5.3. Instant long distance communication.
Any signal can’t exceed the speed of light either, so communication with a relatively close star system would also take YEARS.
5.4. Abilities of spaceships/weapons/devices/medicines.
I don’t mind such things under the condition that their properties “work”/are used in a consistent way.
5.5. Basic teleportation (beaming) technology.
Teleportation (beaming) technology is one of the most iconic features of Star Trek, but I can accept it only in a basic form – teleporting (beaming) small stationary objects, especially on short distances.

6. Coincidences and stupid behaviors of characters.

I hate when very important things are too unlikely/coincidental. I also hate when some actions of characters are based on stupid/illogical assumptions or conclusions. Sometimes I can accept/ignore some other illogicalities, but never when character's motives are concerned.

7. Imagination and your own explanations for some plot details.

This is actually a very important aspect when I judge a movie (of ANY kind). Quite often I can see a plot flaw, but I instantly realize that it could be easily explained/avoided by a slight change in the plot. Sometimes a one proerly phrased sentence would be enough. Such an avoidable plot flaw is not important to me at all.

8. The reviews.

There are so many misleading reviews of the movies that I have to address the most outrageous ones, but I will try to avoid significant spoilers (unlike the misleading reviews).

Minor spoilers ahead! (But everything is taken out of context, so the spoilers are not that bad.)

8.1. Star Trek (2009).

My rating: 6.5/10

There are some cool things happening, but there are also some things that are very poor as far as the story is concerned.

The cool things are the characters, especially that they are all very strong minded and are not afraid to speak their minds. I love especially Spock and his story, but sometimes he is too emotional, even from a human perspective.

Many people claim that the plot is very good, but to me such opinions are like jokes. The bad things about the plot are very striking and numerous.

Most notably in the movie it's possible to create a black hole from a drop of some red liquid! Outrageously ridiculous! A similar “black hole” creation was used in order to try to stop a “supernova explosion wave”. OMG! Such a black hole can destroy a planet, but can also move a spaceship back in time. WHAT?! The travel back in time actually leads to an alternative time-line. Why? Usually changing past leads to an alternative time-line, but in this movie the time-line is changed right away without any explanation!

The four things above are the base for the whole plot and this is why I think the plot is simply terrible overall. But that's not all!

Other annoying things are: The main villain's motives are completely illogical because people actually tried to help his planet. The main villain is supposed to lead a MINER spaceship but its weapons and overall combat abilities are much better than they should be. Another minor flaw is the fact that the miner spaceship can drill a hole to the core of a planet from an orbit, which is ridiculous on its own.

Other than that: One of the main characters is punished by being dropped onto an icy planet in a small capsule without any guidance, so it looks practically like a death sentence that is a total overreaction and doesn't fit the character who ordered this punishment. What’s worse it leads to an extremely unlikely meeting with another character that is followed closely by yet another extremely unlikely meeting with yet another character. What a fucking mess!

On top of that: Two characters are teleported/beamed to a spaceship that is moving extremely fast through WARP space! At another moment two characters are teleported/beamed to a spaceship when they are themselves moving very fast (falling down). There is more hand-to-hand combat than combat with using weapons. Lastly, a spaceship can destroy a swarm of missiles fired by the “bad guys”, but earlier the same “bad guys” were able to destroy SEVERAL similar spaceships! Couldn't the spaceships protect each other in the same way?

All the flaws above either cross my limits of the suspension of disbelief or are too unlikely/coincidental or the character's behaviors/motives are illogical. They can't be explain with just a tad of imagination – the plot is unsalvageable.

Some people claim that this movie has a better plot than the next movie, but this is a total bullshit. It’s a mindlessly fun reboot, but the plot is definitely its weakest part. A very weak part, actually. After watching this move only once I feel no inclination to watch it again in the foreseeable future, mostly because of the plot flaws I described above.

8.2. Star Trek Into Darkness (2013)

My rating: 9.0/10

Star Trek Into Darkness is a GREAT movie! It's DEFINITELY better than the first movie! I can't believe that some people claim that it's the worst Star Trek movie ever, when the previous movie was so terrible as far as plot was concerned!

Before watching the movie I had read various reviews/opinions and lots of people complained about some particular things, giving heavy spoilers by the way. After watching the movie I have to say that I was shocked how misleading most of the negative reviews/opinions were – they were mostly half-truths or complete untruths. I will address them to some extent, but I will try to AVOID significant spoilers.

The very start of the movie is strongly criticized by some people, but it's actually not that bad – two characters create a diversion to lure away some primitive people from a volcano, so a “freezing bomb” can be safely detonated to prevent a huge eruption of the volcano. The only true flaw in this opening is a spaceship being “parked” underwater, but it's a kind of joke – after the spaceship lifts out of the water with the primitive people watching, it is later pictured by the primitive people like some kind of god. It cracked a smile on my face!

Here's a screenshot of a very good comment I found on the net – click to enlarge:

The opening scene may not be perfect, but it’s very important for two later scenes that are simply great (in one of them Spock is talking about his own emotions and the other scene is towards the end of the movie, so I can’t explain it without significant spoilers).

The “proper” start of the movie (the action on the Earth) is gripping right from the start and the plot is very interesting because it’s quite mysterious. Most importantly it's a very COHERENT plot! The main plot revolves around the villain, so I will address the misleading opinions about him first.

Some people complain about the villain just because he's similar to a villain from an old Star Trek movie (Khan), but to me this is complaining just for the sake of complaining. The villain in Star Trek Into Darkness is simply fantastic! He’s extremely intelligent, extremely strong, extremely durable, extremely cunning and extremely deceitful, all the time looking (and dressing) extremely normal. This is the kind of villain I like – his looks is NOT used to make him appear more villainous. Perfect!

Here's a screenshot of another very good comment I found on the net – click to enlarge:

The only thing I don’t really like about the villain is a minor thing that can be EASILY “replaced” by my own imagination – I don’t like the fact that he had been frozen for hundreds of years. The same ridiculous plot idea actually happened in the original Star Trek series and to me it seems silly either way. My own version is much better – the villain was not unfrozen, but he has been recently created by illegal genetic modifications done by the people who wanted to use him. I can’t explain for what they wanted to use him without spoilers, but it fits the fact that they trained him the way they did.

It’s not really important if the villain was unfrozen or recently created because everything still holds up if you can understand what happened off-screen. I understand it this way: After some time (after being unfrozen/created) the villain realized that he was much better than future/normal humans and started to plan his “grand escape”, all the time pretending that he could still be manipulated. The people who unfroze/created the villain also understood his power, so they prevented other genetically modified superhumans from being unfrozen/trained. When the villain escaped, the people who unfroze/created him panicked and they wanted him dead at all costs. It explains basically every “plot hole” about the villain that those stupid negative reviews were claiming. I have no idea why some people claim the opposite, but to me the plot of Into Darkness is simply fantastic!

Some people also complain about a SINGLE case of instant teleportation/beaming to another planet. In this case it can be EASILY explained within the limits of suspension of disbelief. The main villain helped the people who unfroze/created him invent a long distance device-to-device teleportation/beaming that was already functional and was already being tried out – one device was on the Earth (later stolen/taken over forcefully by the villain) and the other was already on the other planet, secretly transported by a small smuggler spaceship (which fits perfectly to the plans of the people who unfroze/created the villain). When the villain escaped to the other planet he destroyed the device that was there, so nobody could teleport/beam there from the Earth after him. A fantastic plot idea that wasn’t actually phrased/shown in the movie, but it holds up with the rest of the movie! It holds up perfectly!

Some people also complain about the gravity on a spaceship that is falling down, but it can also be EASILY explained by using just a tad of imagination. The spaceship was badly damaged, so there was malfunction of the artificial gravity on the spaceship and the gravity kept changing direction – the artificial gravity didn’t disappear (it was working on minimal emergency power supply), but it was simply working incorrectly. And everything holds up again!

Some people also complain about the end fight between the villain and one of the main characters, but this fight is perfectly CORRECT, considering who could face a genetically modified superhuman. Actually there is a fantastic scene earlier in the movie showing how it looked like when another character tried to beat the villain with bare hands. Hilarious!

What a GREAT movie! I love it! I fucking LOVE it!

Some more screenshots of opinions similar to mine – click to enlarge:





8.2. Star Trek Beyond (2016)

I will update this post after I watch the Star Trek Beyond, but from what I've read on the net I'm afraid that this movie is overrated, exactly like the first one. I'll see.

Saturday, 21 January 2023

The Banshees of Inisherin – what a sick movie!

(Originally posted on Wednesday, 21 January 2023)

My rating: 2/10

I can believe I got tricked and wasted my money and my time to watch the movie The Banshees of Inisherin. What a sick movie!

It was advertised as a black comedy, but it's not funny AT ALL in the second half of the movie. It's also extremely illogical. The ending is even more illogical. It's definitely not a happy ending and not even a positive ending. The sick movie just ends. The end.

A movie about a mentally ill guy who hurts himself and takes away from himself his only joy of life, that is playing violin, is not remarkable at all. Such a behavior makes absolutely no sense and such ill people, when they overcome a difficult mental period, are sorry for they have done because they can't take it back.

Wednesday, 18 January 2023

How and WHEN to find the comet C/2022 E3 ZTF at relatively high northern latitudes

(Originally posted on Wednesday, 18 January 2023)

I feel the need to describe how and WHEN to find the comet C/2022 E3 ZTF (with binoculars) at relatively high northern latitudes, because most Internet sites write about times “between midnight and dawn”. At high northern latitudes it’s actually possible to find the comet already in the evening.

Moreover, some Internet sites give info about this comet in a very unhelpful way – by writing about many different constellations (over many different days). In or near big cities most of the constellations are hard to locate and/or identify because there are too few stars visible with the naked eye, so total newcomers should concentrate on the North Star and later on the constellation Orion.

To identify the North Star (also called Polaris) you need to find only one mini-constellation (precisely speaking an asterism) that is fortunately very bright – the Big Dipper, also called the Big Wagon or the Plough.

All the screenshots below were taken while using the site stellarium-web.org set for the latitude 52 degrees north (local times may vary).

Starting from now (18 January 2023), for the next several days it will be possible to see the comet in the early evening almost exactly below the North Star, so almost directly to the north. First the comet will be very low above the horizon (which is bad for observations), but with every passing day it will be higher and higher.


The back of the Big Dipper/Big Wagon/Plough points at the North Star – the distance is about five times the height of the back of the Big Dipper/Big Wagon/Plough. The North Star is actually a part of another mini-constellation (precisely speaking an asterism) that is harder to see in significant light pollution – the Little Dipper, also called the Little Wagon. But all that matters is the North Star.

Please notice that in big light pollution the skies will look much differently – something like this (or even worse):

On 27 January 2023 the comet will be already as high as the Little Dipper/Little Wagon, while the Moon will be still not too bright (it will be getting brighter and brighter with every passing day):

In the evening of 31 January 2023 the comet will be higher than the North Star (and a little to the right), but the Moon will be already very bright.

On this night the comet should be at its brightest, so it will be best to observe the comet several hours later when the Moon will be already below the horizon – in the morning of 1 February 2023. The comet will be on the other side of the North Star because of the Earth rotation around its own axis of rotation (the rotation that will happened between the evening and the morning):

For the next several days the comet will be still very bright, but the Moon will be at its brightest, so it will spoil the observations of the comet. Another problem will be the fact that the comet will be moving away from the North Star (more to the west) and the time of observations will be moving closer and closer to the middle of the night (less and less past midnight).

Starting from 8 February 2023 BEFORE MIDNIGHT the comet will be quite close to the planet Mars – just before midnight they will be in the west direction. In binoculars the planet looks just like a very bright red-orange star (actually much brighter than any star on the night-sky), quite similar in color to the nearby star Aldebaran. They will be both able to be identified by the proximity of the very bright constellation Orion.

You can find all those night-sky objects earlier in the evening, but they will be much higher above the horizon, with the comet being the highest, so it will be very uncomfortable to point binoculars in its direction (looking at the angle of 70 degrees feels like looking straight up – it’s much more difficult than I had imagined without trying).

Several days later, on 14 February 2023 in the evening the comet will be very close to the star Aldebaran (and the nearby open star cluster Hyades) – significantly lower above the horizon, so it will be easier to find relatively early (it will be much more to the south rather than west):

In the following weeks the comet will be moving very slowly (as seen on the night sky from the Earth) along the right side of the constellation Orion, but its brightness will be fading rapidly.

At least for once I feel that my high northern latitude of 52 degrees is better than a lower one – I will be able to hunt the comet in the early evening at a much earlier date than people living at lower latitudes (because the comet, like everything else to the north, is higher in the sky and also because the night is longer, so it gets dark at an earlier hour) and later my observing angles will be better (higher in the morning on 1 February 2023 and lower in the evenings past 8 February 2023).

Clear skies!

Sunday, 15 January 2023

Do you think that modern communism would be much different than this?

(Originally posted on Saturday, 9 October 2021)

Do you think that modern communism would be much different than this?


Easy astronomy for total amateurs

(Originally posted on Friday, 26 March 2021; updated most recently on 15 January 2023)

The update from 15 January 2023 was BIG! I changed some parts significantly and I added/changed lots of my own pictures. I also made lots of little changes that are not overwhelmingly important, so I wrote UPDATE only at the crucial parts.

INTRODUCTION

I am a total amateur as far as astronomy is concerned, but I have already learned many things about astronomy anyway, so there is LOTS of info on various topics in this post.

I am a pure enthusiast who concentrates on positive things, instead of complaining about negative ones, so I truly enjoy watching the night sky through a small telescope from a balcony in a city with big light pollution. By the way: light pollution is all about the night sky being brighter near human settlements than at remote locations (more on that later).

The brighter the night sky (because of light pollution) the less night-sky objects you can see, both with the naked eye and through any observing equipment, however there are ALWAYS some very interesting things to be seen even in a small telescope.

At the time I finally bought my first telescope I was 43 years old and I have to say one thing: I wish I had done it earlier!

ATTENTION!
I constantly refer to small telescopes, but I do NOT recommend ANY small telescope. I recommend a small telescope that is SLOW (“lean”) – a small telescope that is “long enough”. Why? Because in a slow telescope light rays are less bent, which minimizes potential problems with aberrations, false colors, coma and things like that. As far as inexpensive telescopes are concerned buying a slow one (f/10 in case of refractors or f/8 in case of reflectors) is like taking a sure shot. More on that later.

UPDATE (all the way to the end of the Introduction):

Some of the examples below are actually my own photos or videos that I I took/recorded with just a hand-held smartphone (without an adapter) gently pressed against a telescope eyepiece. Obviously astrophotography with a smartphone is very limited, so in reality everything looks clearly better than on a single picture, BUT some stacked (more on that later – in the point I.1.2.) and processed smartphone pictures look almost as good as visually. Even some smartphone videos of the Moon and the planet Saturn (without any processing) look simply fantastic!

Nowadays I always take same pictures AND record some videos, to have fun stacking and processing them later, when there are clouds in the skies and I can't use a telescope. They also remind me how some of the objects look in a small telescope when it's a different season and they hide behind the Sun.

As far as normal (daytime) pictures are concerned the standard Camera app in my smartphone works great, but it doesn't have manual focus (even in the “pro” mode), so I had to install another one. Well, I installed several free apps, but the one that worked for me was Lumio Cam. Here's a screenshot from a video I found on the net:

The app Lumio Cam also has a GREAT setting that allows taking a series of photos with one press of a button! The symbol of this setting is three rectangles overlapping each other. This symbol replaces the single rectangle that can be seen on the picture above – second from the right at the bottom. Simply press this symbol to change the setting.

I always set the manual focus at “Far”, but not at maximum (not focus at infinity – some smartphones/apps apparently allow focus “beyond infinity” and it messes things up). I also manually set ISO and shutter, but the settings vary from photo to photo.

Typical settings for smartphone pictures/photos:
1) the Moon: ISO-200, shutter-250 (which means 1/250th of a second)
2) Jupiter belts: ISO-400, shutter-120
3) Saturn with rings: ISO-400, shutter-60
4) Jupiter with moons: ISO-2500, shutter-25
5) relatively weak stars: ISO-3200, shutter-8 (which means 1/8th of a second)

Any shutter setting longer than 1/8th of a second makes my pictures blurred because my hand-held smartphone shakes a little. Some of my pictures of stars taken with the setting shutter-8 are blurred too.

The same settings are important when recording a video. In general videos yield surprisingly similar results to pictures, but the size/resolution is smaller, so some details may be lost OR some very close stars are not properly separated on a video. On the other hand it seems that there is a little less noise in videos, especially in the background (probably some different kind of processing is used from the one for taking pictures), so they often look better than single pictures. Not to miss anything I always take some pictures AND record some videos of the same object.

All of my best pictures and videos (some of them below) were taken/recorded with my 114/900 Dobson simply because its base is more sturdy and there is less shaking when I press my smartphone against a telescope eyepiece. My other telescope (that I had bought as my first telescope) is an inexpensive 70/700 refractor on a light tripod, so any vibrations are stronger by definition. It's not really important for visual use because you don't touch a telescope eyepiece with your own eye, so the view is perfectly steady then.

Please notice that it's actually good to use a little digital zoom while taking/recording pictures/videos of the planets (or even of the stars), so they appear slightly bigger (or more separated in case of close stars). Generally all the objects, except for the Moon, look quite small in a small telescope.


I. What can be seen from a city with big light pollution.

Please notice that when I write about seeing a particular night-sky object I mean seeing it “with your own eyes”, so seeing the light that travelled a HUGE distance through space. When you see a picture of the object displayed on a computer screen you see only the light generated by the computer screen. When you see a picture of the object printed on a piece of paper you see only the light generated by the Sun or by a lamp, reflected from the picture.

Please notice that when I write about binoculars I mean hand-held binoculars. There are also some binoculars that are very big and heavy, but they are very expensive by definition – in binoculars all the elements, including the prisms, are doubled. Moreover when you have to use a tripod to be able to use big and heavy binoculars you might as well use a tripod with a small telescope. I own 12x60 binoculars and I can use them only for several minutes before my arms get too tired. This is why I consider such binoculars as the upper limit of hand-held binoculars and I DON'T recommend them at all!

I.1. What can be seen in a small telescope, but not in binoculars:

I.1.1. The rings of Saturn (seen as one big ring).

To me seeing the rings of Saturn was like a dream come true! The view was simply hypnotizing!

UPDATE:

Saturn is the best object in a small telescope for recording a video with a smartphone – it's fantastic on its own (without any stacking or processing), but it's good to crop it later (only crop, not resize), so the object appears bigger, especially in the full screen mode.


I.1.2. The darkest belt(s) of Jupiter.

Seeing darkest belt(s) of Jupiter means that you can actually see something on a surface of another planet! Incredible! Please notice that the belts of Jupiter (their size and their colors) change over time and sometimes they even disappear.

UPDATE:

It's hard to show you how Jupiter looks in a small telescope because it's not about shape of the planet, but about small details. Here's the main part of a smartphone photo:


Now, this is not really impressive because there is lots of noise on the photo, BUT you can still see the belt(s) AND you can see a SHADOW of Ganymede (the biggest moon of Jupiter) cast on the surface of the planet!

I toyed with the free program GIMP (GNU Image Manipulation Program) combined with the free plug-in G'MIC (GREYC's Magic for Image Computing) and made an average of five different photos (the one above was the best):

Averaging just five photos already gave impressive results! But it's still worse than what I could see with my own eyes.

Please, notice that all the photos that are to be average/stacked in the program GIMP/G'MIC have to be taken AT THE SAME ANGLE! When you move your hands, even slightly, between photos then a planet/belt may get a little tilted, so averaging such pictures would produce a mess. This is why it's good to take a series of photos with one press of a button.

By the way: averaging many different photos is the main part of what some people call “stacking”, but the number of averaged/stacked pictures should be MUCH higher, which is impossible to obtain with a hand-held smartphone. HOWEVER there is a way to stack hundreds of VIDEO FRAMES from a single video recorded with a hand-held smartphone.

For example this is the final “picture” created from a video recorded on a different occasion (an eyepiece was combined with my favourite color filter for visual use – green/light green filter #56) – the number of stacked video frames was 300:

The processing tools, especially the sharpening tool, in RegiStax 6 are simply fantastic, but this program is a little unpredictable. When everything works then the end result is like magic! Here's a video showing how I obtain the above “picture”:


Please, notice that most of the beautiful photos of night-sky objects which you can find on the Internet are not really “true photos” but they are in fact hundreds or even thousands of different photos taken with a long exposure time and then averaged/stacked together. There is NO WAY to see anything like this with your own eyes even in a big telescope.

I.1.3. Relatively small details of the Moon.

There is no comparison between the amount of detail that you can see in a small telescope and in binoculars. Here's a picture I took with a smartphone by hand (without an adapter) at the magnification of 50x (the Moon is especially fun when only half of its disk is visible). Click to enlarge!

I.1.4. Shape and details of the Orion Nebula.

The Orion Nebula can be seen in light-polluted areas even in binoculars and it’s a fascinating sight indeed! The glowing middle of the Orion Sword is simply beautiful! However in binoculars you can’t see the shape of the nebula, nor some details hidden inside.

UPDATE:

In a small telescope the nebula is “less glowing” when compared to binoculars (because bigger magnification makes such diffuse objects dimmer), but it appears much larger and you can see its shape (or rather it's brightest part). Moreover inside the nebula you can see 4 stars that are very close to each other – these stars as a whole are called the Trapezium.


To create the above “image” I had to put lots of work – the only way to achieve decent results was to stack screenshots of MP4 video frames. More on that in this Youtube video (and in the detailed comments to this video), but please notice that in the video I processed the picture slightly differently (the above final picture is a little brighter):


I.1.5. The brightest moons of Jupiter even when they appear very close to the planet.

It's not about the brightness of the moons, but about the apparent separation of the moons from the planet (about the angular distance between the moons and the planet). The moons can be seen even in 8x42 binoculars, but only when they appear far enough from the planet. In a small telescope the magnification is much bigger, so the moons can appear much closer to the planet (and much closer to each other) and still be discernible.

Here's the main part of a smartphone photo (ISO-2500; Shutter-25, which means 1/25th of a second) taken probably at magnification 90x (it's a photo taken on a different night than the ones above):

All four Galilean Moons were visible in my small telescope, but only 2 of them were visible in my 8x42 binoculars. Please notice that Jupiter is overexposed because I had to make the moons visible and this is why the belts are not visible at all (I could see 2 belts on that night). Again: astrophotography with a smartphone is very limited.

Here's a site where you can identify all the moons at any chosen time:
https://stellarium-web.org

Here's a screenshot for the time I took the picture above:

I.1.6. The brightest moon of Saturn.

It looks like a relatively weak star, but it's clearly visible (unless it hides behind the planet).

I.1.7. Relatively bright stars that are very close to each other.

Some relatively bright stars appear very close to each other, so they can be separated/split only at a big magnification (otherwise they appear as a single star). From my own experience I can say that it's extremely cool to “discover” a double star by sheer accident. Simply unforgettable!

UPDATE:

There are also multiple stars appearing as one star! The most famous example is the Trapezium I mentioned (and pictured) together with the Orion Nebula. Another great multiple star is Sigma Orionis – just below the Orion Belt on the left. There are 4 main stars, but one of them is clearly weaker than the rest, so it can get drowned in the light of the nearby star:

The Sigma Orionis is in the middle, but as you can see there is another double star nearby (HD 294272).

I.1.8. Relatively weak stars.

Increasing magnification makes more stars visible, especially in big light-pollution, so under equal skies a small telescope will always show more stars than binoculars, just because the magnification is much bigger (more on that later – in the part about contrast).

I.1.9. Most of the “doable” galaxies.

A galaxy “doable” under light-polluted skies has to be very bright at its core – what you can (barely) see is only that central part of the galaxy.

There is actually one galaxy (M31 – the Andromeda Galaxy) that I saw even in my 8x42 binoculars, but all the other galaxies that I have seen from my light-polluted city (4 of them so far: M64, M81, M82 and M94) were visible only in my small telescope. Either way they look extremely unimpressive – like a small cloud of light. The Andromeda Galaxy looks more or less like this:

It's not important how well you can see a galaxy, but what it means that you can see it at all. Galaxies are typically millions of light-years away – for example the Andromeda Galaxy is around 2.5 million light years away. It means that the light that you can see travelled for 2.5 million years before it reached your eyes! My personal best is seeing light that travelled for around 16 million years (from the M94).

I.1.10. Most of the “doable” globular star clusters.

A globular star cluster “doable” under light-polluted skies has to be “rich” enough – when there are too few stars the core of the cluster is not bright enough to be seen.

There is actually one globular star cluster (M13 – the Hercules Globular Cluster) that I saw even in my 8x42 binoculars, but all the other globular star clusters that I have seen from my light-polluted city (six of them so far: M3, M5, M9, M10, M12 and M53) were visible only in my small telescope. Either way they look almost as unimpressive as galaxies – like a small cloud of light, but the cloud is more concentrated, so it's a little easier to see.

Please notice that globular star clusters are typically tens of thousand of light-years away. Maybe it's not as impressive as in case of galaxies, but it's still very far! For example I have seen light that travelled from the M53 for 58 thousand years!

I.1.11. More open star clusters.

There are many open star clusters that can be seen in binoculars, but in a telescope you can see MUCH more such clusters overall. This is not about seeing more stars in a cluster, but seeing a whole new cluster! There are many open star clusters that consists ONLY of very weak stars that can't be seen in binoculars at all.

I.2. In what regard are binoculars better than a small telescope?

I.2.1. Looking at big night-sky objects.

The best thing about hand-held binoculars is that the filed of view (FOV) is clearly larger than in any telescope, so you can see much more of the night sky at a particular moment. Some of the biggest night-sky objects (as far as their angular size on the night sky is concerned) can fit into the view ONLY in binoculars, but there are very few such objects and many of them can't be seen in light-polluted areas at all.

I.2.2. Easier identification.

Thanks to a bigger FOV you can find/identify a particular place on the night sky much easier simply because you see more stars at the same time. This fact makes binoculars a perfect complement to a small telescope. I often look through binoculars first to see stars than are invisible to the naked eye, which helps me point my telescope in a preferable direction.

I.2.3. Quicker scanning of the night sky.

In a span of several seconds I can switch from the Orion's Sword (the area with the Orion Nebula in the middle) up to the Orion's Belt, then right to the star Aldebaran and the nearby open star cluster Hyades and then farther right to the open star cluster Pleiades. This sequence is truly spectacular and you can't do something like this (so quickly) in a telescope. But it actually makes binoculars kind of boring – when you find what you are looking for almost instantly then you can run out of targets pretty quickly, especially in light-polluted areas.

I.2.4. Portability and instant use.

Hand-held binoculars are much smaller and much more portable than a small telescope. Moreover you can use them instantly – the preparation time with any telescope, even a small one, is clearly longer. However, extreme portability and extremely short preparation time should be considered the least important things in astronomy. The visual side of astronomy is much more important.

I.3. A small telescope vs. binoculars – summary.

To me a small telescope is definitely better than a pair of 12x60 binoculars – there is absolutely no comparison as far as magnification is concerned. To me relatively high magnification is the most important thing because it shows details/new things that are simply too small at low magnification.

I actually regret buying 12x60 binoculars after reading some opinions like “It’s better to buy a pair of binoculars instead of a small telescope”. Based on my experience, I now find such opinions controversial, to say the least.

I would say that if you can afford it then you should buy BOTH a small telescope and a pair of 8x42 binoculars. They complement each other perfectly and I use them alternately. Moreover, a small telescope comes with a toy-like finder scope that is useless when looking from my balcony. Thanks to binoculars it’s easier to find crucial night-sky objects.

I own three pairs of binoculars (all of them porro binoculars): 12x60, 8x42 and 8x30:

I compared different types of binoculars in detail here:
Most universal types of binoculars


II. General info.

II.1. Celestial sphere and other basic terminology.

All the night-sky objects from outside of the Solar System are so far away from the Earth that they appear almost completely stationary in reference to each other. The Earth rotates around its own axis of rotation, so (almost) all night-sky objects seem to be moving through the night sky, but the distances between them on the night sky don't change.

Some tiny movements of the closest stars, that can actually be measured when the Earth circles the Sun, are not important from the point of view of amateur astronomy. Search the net for “Stellar parallax” if you’re interested – basically it “works” like this:

The Earth is round, so a person standing at the North Pole will see almost completely different night sky than a person standing at the South Pole. For example the North Star (also called Polaris), that is often used to find a northern direction, can be seen only from the Northern Hemisphere (and from a latitude of less than 1 degree south, to be precise):

When looking from the Southern Hemisphere the Earth itself obscures the North Star. On the other hand at the North Pole the North Star is (almost exactly) at zenith – it’s (almost exactly) overhead.

So, the night sky is actually seen not as a flat surface, but as a sphere. And this sphere is called a celestial sphere. The crucial parts of the celestial sphere are named according to the names used when describing the Earth – there are: the north celestial pole (overhead the North Pole), the south celestial pole (overhead the South Pole), the celestial equator (overhead the Equator), the northern celestial hemisphere (overhead the Northern Hemisphere) and the southern celestial hemisphere (overhead the Southern Hemisphere).

II.2. Observing possibilities – latitude and declination.

A person at the North Pole (a latitude of 90 degrees north) can see only the northern celestial hemisphere and a person at the South Pole (a latitude of 90 degrees south) can see only the southern celestial hemisphere. A person standing at the Equator (a latitude of 0 degrees) can see the WHOLE celestial sphere (not on every night, but throughout a year).

However, there is a big problem with observing night-sky objects that are very low over the horizon – there is simply too much air/atmosphere in the way, so they are much less visible then. A relatively good minimum threshold is around 20 degrees above the horizon, so you have to discard some parts of the celestial hemisphere.

At the Equator you have to discard 40 degrees in total (20 degrees above the northern horizon and 20 degrees above the souther horizon), so you are still left with a view of 140 degrees: from a declination of +70 degrees to a declination of -70 degrees.

Please notice that a declination for the celestial sphere “works” exactly the same way as a latitude for the Earth – a positive value means “north” on the celestial sphere and a negative value means “south” on the celestial sphere. In other words a positive declination points at the northern celestial hemisphere and a negative declination points at the southern celestial hemisphere.


At the North Pole there is only one horizon – the southern horizon (interestingly there are no directions north, east or west at the North Pole), so you have to discard only 20 degrees, BUT because you can see only the northern celestial hemisphere from there you are left with only 70 degrees of view (from a declination of +90 degrees to a declination of +20 degrees).

Please, notice that at the North Pole during the times when the Sun stays below the horizon all through the day, the night-sky objects just move around in full circles and no “extra” night-sky objects are visible then. The lower a latitude is the smaller circles around a celestial north pole can be seen in full. At the Equator you can see all the night-sky objects moving in celestial half-circles (the one directly above the Equator actually looks like a straight line).

Most astronomers agree that the best latitude is actually a little below the Equator because the southern celestial hemisphere is generally more interesting. Unfortunately most people in the world can’t change their latitude in any significant way, so we have to live with a particular night sky.

TRIVIA: The stars that are close to the celestial equator can be seen both from the Northern Hemisphere and from the Southern Hemisphere, but they are upside-down on the opposite Hemishpere (their “left-right” and “up-down” directions are reversed). Here's a picture of the constellation Orion seen from the Northern Hemisphere:

Here's a picture of the constellation Orion seen from the Southern Hemisphere:

Please notice that the Earth rotates around its own axis of rotation, so when you look from the Southern Hemisphere in the north direction the Sun and all the night-sky objects move from right to left – in opposite direction than on the Northern Hemisphere when looking south. The reason is the same – a person standing on the Southern Hemisphere is upside-down when compared to the person standing at the Northern Hemisphere.

II.3. Degrees above the horizon.

Forget about a declination for a minute and look again at the first picture in the previous point (the example about declination – please, open it in a new tab) – it's a very good example how different angles “work” in a sphere. Imagine that you are standing in the middle of this sphere and when you look at the horizon the angle is 0 degrees. When you look at an object at 20 degrees above the horizon (a relatively good minimum threshold) it's already relatively far from the horizon and an object at 45 degrees is suddenly very high in the sky! It means that the amount of air/atmosphere in the way when looking at an object at 45 degrees (or more) is already very small (it doesn't get much better than this).

Interestingly, looking at an object at 70 degrees above the horizon feels almost like looking exactly straight up! In fact aiming ANY telescope at objects at an angle of 65 degrees (or more) is quite troublesome and is not really recommended for newcomers. Even more experience astronomers avoid aiming at objects above 70 degrees. I had no idea that looking almost straight up can be so troublesome!

II.4. Observing possibilities – calculating possible declination from latitude.

Let’s focus on the Northern Hemisphere and calculate what can be seen from there. If your latitude is at least 20 degrees north then you can see the North Star at least 20 degrees above the horizon, which is good enough. A latitude of more than 20 degrees north doesn't really improve anything as far as the northern celestial hemisphere is concerned.

The crucial question is this: “How far south can I see?” It’s very easy to calculate: take your latitude and subtract 90 degrees for the objects seen at the horizon or 70 degrees for the objects seen at 20 degrees above the horizon. I live at a latitude of 52 degrees north, but the view from my balcony is blocked by a nearby apartment building (around 10 degrees from the horizon), so I subtract 80 degrees for what I can see at all (I get a declination of -28 degrees) or 70 degrees for what I can see at 20 degrees above the horizon (I get a declination of -18 degrees). Pretty weak.

II.5. Observing possibilities – seasons.

The Earth not only circles the Sun, but it also rotates around its own axis of rotation that is tilted in reference to the Earth’s orbital plane:


First of all, there are some objects that can’t be seen for some part of the year – they either “hide” behind the Sun or are too close to the Sun, so they are (in)visible only during days. Half a year later the Earth is on the other side of the Sun and such objects can be seen during the night.

Second of all, the bigger a latitude the shorter/longer the nights are (depending on the season). At the Equator the night is (almost exactly) 12 hours long throughout a year:

At latitudes that are “too far” north during late spring and early summer the night sky is never truly dark because the Sun is too little below the horizon. so you miss additional part of the southern celestial hemisphere. Interesting at the North Pole you don't actually miss anything when there are white nights because you can see only the northern celestial hemisphere from there anyway.

II.6. Direction of an observing site.

Some observing sites, like a lawn next to a detached house, allow observing practically in any direction, but some other, like a balcony or a place near big apartment buildings, have some directions blocked.

Generally the best observing direction on the Northern Hemisphere is to the south because it maximizes the number of night-sky objects you can see throughout the year. The worst direction is to the north, but even the directions to the northeast or to the northwest are not good enough as far as the Moon and the planets are concerned. The only way to observe these objects is to find a place facing more to the south.

III. Light pollution and urban astronomy.

Nowadays it's a real problem to find a dark location that is relatively close to your home because even small cities produce significant amount of artificial light that “spills” over large areas around them. When you go out of a city to a place with significantly lower light pollution then you are stunned by how many stars you can see even with the naked eye. In such places you can see much more stars with any observing tool, but such voyages are quite rare and somewhat problematic.

Please notice that a modest amount of light pollution degrades diffuse objects such as galaxies, nebulas and comets far more than stars. On the other hand the Moon, the planets and brightest stars are generally IMMUNE to light pollution. Basically, there is always something interesting to look at even from a balcony, unless you have some unrealistic expectations.

III.1. Confusion about the Bortle scale.

The Bortle scale is a scale describing different levels of light pollution as seen with the naked eye, but there is LOTS of confusion about this scale. Some people use it in a totally indiscriminate way – they mix it up with bad transparency (bad clarity of the atmosphere) and/or bad seeing (big atmospheric turbulence) and/or artificial lights that make your eye pupils constrict (for example street lamps).

Bortle himself wrote about light pollution in reference to SKY conditions as far as their DARKNESS is concerned. Bortle also wrote that he hoped that his scale “would provide a consistent standard for comparing observations with light pollution”. You can’t achieve consistency in comparing light pollution when other important factors don’t remain equal.

When seeing and/or transparency is bad then your observations will be obviously worse, but NOT because of light pollution! Please notice that transparency and/or seeing can be bad even at remote locations, where there is hardly any light pollution by definition. Even in a city it would be silly to accept an idea that light pollution changes from night to night, depending on current transparency and/or current seeing.

The main problem with the Bortle scale is that it is based on naked eye observations, so If you assess the sky conditions while being directly blinded by nearby street lamps and/or by other relatively bright objects (including objects that only reflect light) you will definitely misjudge what you could see through a telescope. An objective lens/mirror of a telescope doesn't constrict due to bright light, unlike the human eye pupil does during naked-eye observations. In other words: judging the Bortle class from a balcony in a city is practically impossible, but a telescope is immune (more or less) to direct light and what really counts is only the sky-glow.

Fortuantely you don't have to judge the Bortle class of your location yourself and you can use an online map. I prefer this site:
https://www.lightpollutionmap.info
with the overlay “World Atlas 2015” active – when you click at a particular place a description pops up, where you are given also the Bortle class of the chosen place. It may be not perfectly up to date, but the other overlays are very poor at showing truly dark locations and they don't state the Bortle class of a particular place at all.

III.2. Light pollution vs. the full Moon.

The full Moon (or close to the full Moon) has a similar effect to light pollution – it degrades diffuse objects such as galaxies, nebulas and comets far more than stars. It's true even at remote dark locations and some people don't go to such places when there is the full Moon (or close to the full Moon).

Some people add the effect of the full Moon to light pollution itself, but to me it's again incorrect. It would actually be totally silly to say something like this: “We're in the middle of a desert, very far from human settlements, but there is the full Moon, so the middle of the desert is full of light pollution.” To me light pollution is all about artificial lights produced by human settlements and the moonlight is not artificial. Moreover, the light pollution map I mentioned above does NOT change according to the phases of the Moon, so it treats light pollution as something totally independent from the Moon light. Exactly like I do.

Anyway, when you look at the night sky from a place with a particular light pollution (for example a balcony in a particular city) and there is also the full Moon then the effect is even worse – the night sky is even brighter and even less night-sky objects can be seen, both with the naked eye and through any observing equipment.

III.3. Dark adaptation on a balcony.

The difference between looking at the night sky while being directly blinded by nearby street lamps and looking at the same night sky “from a covered place” is HUGE! The first time I tried to find the Hercules Globular Cluster (M13) from my balcony I couldn't see it in my 8x42 binoculars, but I was doing it while standing up, so the nearby street lamps were blinding me. The next time I looked at the M13 from my balcony I saw it even in my 8x42 binoculars, but I was doing it while half-lying on a portable reclining chair, so I was shielded from the nearby street lamps by a cover on my balcony guardrail.

It actually proves that the street lamps make your eye pupils constrict in a significant way, which is totally independent from light pollution of the night sky (from the sky-glow). Unfortunately you can't lie down when looking through a telescope, but there are some things hat can help you even on a balcony.

My dark adaptation is always very weak because when I look at the night sky from my balcony there are several street lamps close by that are blinding me directly (more or less), even when I shield my eyes with my hands. Here’s a picture taken from my balcony:

I took the picture in the “night-mode” (the time of exposure was relatively long), so the planets Jupiter (on the left) and Saturn (above the Moon) would be visible (they were visible with the naked eye), but it made everything else (especially the street lamps and the apartment buildings) a little brighter that in reality.

As you can see there are lots of nearby street lamps, so “my balcony astronomical observatory” is simply terrible to the naked eye. When I look into a telescope eyepiece at particular angles (at some positions of my telescope) the street lights are especially annoying. I planned to buy some kind of movable cover, but this site (with all those pictures) inspired me to use a kind of hood instead:
https://www.cloudynights.com/topic/446598-in-praise-of-dark-skies-apparels-observing-hoods/

And here's my hood:

My hood is actually a piece of black cloth folded in half (100cm x 144cm folded into 100cm x 72cm). Why folded in half? Because one layer of the cloth still lets some light through while two layers of the cloth block practically all light.

Interestingly the cloth is folded in such a way that its “good side” is inside and what you can see is actually the “wrong side”. Why? Because the “wrong side” of the cloth is more slippery, so it shouldn't drag my telescope by accident.

Additional advantage of my hood is that I can use it together with ANY kind of clothing, from a T-shirt to a winter jacket.

When I tested my hood I realised it was perfect in two different ways! The main goal was to block light from nearby street lights and it was pretty straight-forward. However another unforeseen problem arrived – my balcony floor was so bright (mostly because of the street lights) that it was blinding me on its own. My hood “rose to the challenge” and I was able to wrap it around my head also from below. I had to hold it with one hand, but my whole head was like in a mini darkroom and I could have my both eyes open. Fantastic feeling in the middle of a city.

The only problem was that my hood touched a part of the focuser that was greased. Now I know I have to be more careful how I wrap my hood around my head.

III.4. Good sides of balcony astronomy.

When you look at the night sky from your own balcony you can do it relatively often and together with your little children! There are also some other HUGE practical advantages of using a telescope on a balcony – you can keep all the little things inside your home, you can put a normal (relatively heavy, but comfortable) chair next to your telescope AND you can always wash your hands in your bathroom when you accidentally touch a telescope element that is greased. You can't do such things “in the wild”.

Over time I noticed an additional advantage of balcony astronomy – easy access to a computer and very good online star maps. When I am star-hopping from an easy night-sky target to a more difficult one I usually go in and out of my apartment several times, checking my current “night-sky position” on the computer and planning the next “hop” one at a time. I wouldn't find some object at all if I tried to do it without a computer star map (free smartphone star maps are much worse).


IV. Types of telescopes.

There are basically two kinds of telescopes: refractors and reflectors. Before I show you some simplified examples how they work I have to point out one very important thing – any observing equipment works in a very counter-intuitive way. Here's an example for a telescope (I think), but binoculars generate image in a similar way:

Totally mind-blowing! Please notice that every point at the exit pupil contains light rays coming from ALL the objects in view! You can verify this fact by looking through any kind of binoculars while covering half of the objective lenses – you will still see the whole view (NOT half of it), but the whole view will be half as bright. Here is a fascinating discussion on this topic:
https://www.cloudynights.com/topic/603397-a-basic-exit-pupil-question/

This quote is awesome: “And on your part, I want to thank you for your honest and concerted effort to understand this confusing issue. I can tell you in the Astromart thread I referenced earlier, members whose names are well known here gave Alan French quite a battle before they finally grasped the concept. At the time, I was merely a bystander...”

Farther down below there are some examples for different types of telescopes, but they are greatly simplified and may be misleading unless you remember the example above.

By the way: here's a picture of what happens when light rays enter human eye:

So, ALL light coming from a particular star is concentrated on the retina, where an upside-down image is formed (and then reversed by the brain).

If the eye has a vision defect all light from a particular star is concentrated at the wrong place, so the star gets blurred (more or less, depending on the severity of the vision defect):

IV.1. Refractors.

A refracting telescope uses a lens as its objective to form an image:

The objective lens is mounted in a fixed way, so it doesn't need any adjustments later. This is why a refractor is totally unproblematic as far as maintenance is concerned. It's very similar to binoculars in this regard – just take it out and watch the night sky.

Please notice that the mirror on the other end of a refractor is theoretically not needed, but it helps to look at the night sky at a more convenient angle. If there were no mirror diagonal then you would have to literally lie under the telescope when it would be pointing straight up. By the way: the mirror in the diagonal is mounted in a fixed way too (it's more than big enough).

IV.2. Reflectors.

A reflecting telescope uses one or more curved mirrors to form an image:


The first reflector above (the simple one) is called a Newtonian telescope (or simply a Newton), just because it was invented by Newton (the famous scientist) himself. By the way: a Dobsonian telescope (also called a Dobson) is a Newtonian telescope with a simplified mount – perfect for newcomers (exactly like a small refractor on a simple tripod).

As you can see the secondary mirror is “obstructing the view”, but it blocks only several percent of the incoming light (it's the area of the central obstruction that counts, not the diameter – see the next point) and sometimes it causes diffraction spikes (see the following point).

IV.3. Practical differences between small refractors and small reflectors.

IV.3.1. Light gathering abilities.

Generally for the same price the reflectors are brighter (better as far as light gathering abilities are concerned) than refractors because the objective mirrors in reflectors are significantly less expensive to produce than the objective lenses in refractors. In other words: for the same price you get a mirror that is clearly bigger than a prism.

It doesn't even matter that in a reflector a secondary mirror is “obstructing the view” because it blocks only several percent of the incoming light. It's nothing! For example when the central obstruction is 25% of aperture (objective diameter) then the AREA of the central obstruction is only 6.25% (I omitted some elements from the formula for the area because they get reduced anyway):
(0.25*A)^2 / (A)^2 = (0.25)^2 / 1^2 = 0.0625 = 6.25%

The difference due to ANY central obstruction (even a much bigger one) is NOT noticeable AT ALL. A noticeable difference in aperture area requires around 50% increase (or 33% decrease). A significant difference in brightness requires around 100% increase (or 50% decrease). A HUGE central obstruction of 50% of aperture blocks “only” 25% of the incoming light.

Please, notice that for the reasons above I ignore the central obstruction of the Dobson completely throughout this post.

IV.3.2. Diffraction spikes and “less pin-point” stars in reflectors.

There is one main downside of the central obstruction – the diffraction spikes. The secondary mirror has to be held in place somehow, so there are some tiny spider vanes that make very bright stars appear not quite realistic (not as points). ONLY the brightest stars – the vast majority of stars appear in a normal way (as points). Some purist may be annoyed by the diffraction spikes, but I like them myself. They are very rare (in a small telescope) and they make a single bright star look very interesting. Here's my own picture of the star Betelgeuse (that was stacked and resized):

Pleas notice that there are different types of spider vanes, but in small Newtonian telescopes the typical type is the “cross” – second to last on this picture:

UPDATE:

When I compared my 70/700 refractor with my 114/900 Dobson side-by-side I realized that in the refractor stars were “slightly more pin-point”, but barely. The difference was very small and without the side-by-side comparison I wouldn't even notice it. I noticed something similar when looking at Jupiter at high magnification – the edge of the planet looked slightly smoother in the refractor, but barely. For a total amateur like me the differences were too small to be of any importance, so the Dobson is definitely better because it gathers more light.

IV.3.3. Cool-down times.

A reflecting telescope takes longer to cool down, which is important when there is a significant difference in temperatures between indoors and outdoors. It's all about air shimmering around warmer surface when it's cooling down – the moving air spoils the view. On the net I found this quote:

“In general, small refractors cool quickly. Unless the temperature differential is large, a refractor is ready for use within a few minutes after it is set up. A 6” to 10” Newtonian reflector (such as a Dob) may require 30–60 minutes to cool down, depending on the temperature differential, and less if fans are used to expedite cooling.”

Using my Dobson is hilariously enjoyable – I just grab it by the handle, place it on my balcony and go back to my apartment. While the Dobson is cooling down I do whatever I want (usually I eat supper). By the way, a small Dobson doesn't take very long to cool down (around 25 minutes).

IV.3.4. Collimation of reflectors.

Mirrors in a reflecting telescope are NOT mounted in a fixed way. It doesn't matter why, it matters that they are mounted in an adjustable way and from time to time you need to align the mirrors again. This process is called collimation.

For a total newcomer collimation may look like a very troublesome thing. Well, in some cases it is a very troublesome thing – there are LOTS of topics on various astronomy forums where people tell some “hair-raising stories” about collimation. HOWEVER it turns out that collimating a slow (“lean”) Newtonian telescope is much easier than collimating a “fast” one (more on that later), just because the room for error is much bigger.

In fact I had wanted to keep everything as easy as possible, so originally I avoided collimation issues by buying a refractor, but when I finally found the crucial info about easier collimation of a small slow reflector I instantly bought such a telescope myself.

I own a small reflecting telescope (Orion SkyQuest XT4.5 Classic Dobsonian Telescope) which comes with a spherical primary mirror that is criticized by some people, but some other people claim that in a small SLOW reflector it’s not important at all. To me the views are great, but it's not the point.

The point is that the collimation of a small slow reflecting telescope with a spherical mirror is the least problematic. Why? Because in a slow telescope the room for error is much bigger AND because a spherical mirror reflects light rays always in the same way, no matter if it's a little skewed or not. On the other hand in a fast telescope the room for error is much smaller AND the parabolic mirror has to be aligned/collimated very carefully, which is more difficult by definition.

Here are examples of spherical and parabolic mirrors that are exaggerated from the point of view of telescopes:


To me it's enough when I see (during the collimation process) the whole primary mirror reflected in the secondary mirror – otherwise some light would be lost. So far I haven't even touched the secondary mirror and I only collimated the primary mirror, which was a piece of cake (and actually quite fun). I didn't notice anything negative in my views.

IV.3.5. Upside-down vs mirrored views.

Another difference is that in my reflector the view is upside-down (each direction is reversed: left-right and up-down), while in my refractor the view is mirrored (the direction left-right is reversed, but the direction up-down is correct).

As far as astronomy is concerned the view upside-down is actually better! Why? Because when I look at a star map all I have to do is to turn my head upside-down and I see what I can see in the telescope. In the mirrored view I can't use this “trick” and I have to use my imagination to “reverse back” the right-left view.

IV.3.6. Mount of a telescope.

There are basically two kinds of mounts of a telescope: alt-azimuth (altitude-azimuth) mount and equatorial (or parallactic) mount. A Dobsonian mount is a kind of alt-azimuth (altitude-azimuth) but instead of a tripod it uses a kind of wooden base:

The alt-azimuth mount on a tripod is light and easy to assemble and operate – there are independent movements up-down and left-right that don't require complex mechanisms or any geographical alignments. The Dobsonian mount is equally easy to operate, but assembling it requires some time and effort. The bright side is that it needs to assembled ONCE and later you don't have to do it at all.

On the other hand, the equatorial mount (always on a tripod) allows you to move your telescope according to the movements of the night-sky objects, BUT it's definitely more difficult to assemble and operate. Moreover the mechanism is much heavier because there has to be a counterweight attached.

No contest – the alt-azimuth mount is MUCH better for a total amateur. Please notice that the equatorial mount with a proper setup allows also the alt-azimuth type of movements, but what would be the point of using such a mount with such a setup? Making the whole setup heavier?

IV.3.7. Height at which the focuser/eyepiece is.

The height of a refractor on a tripod can be adjusted in an easy way. On the other hand a small Dobson is too low for any comfortable seeing, even while sitting on a normal chair. I had to buy some kind of platform to raise my Dobson off the ground.



I had had one folding step in my apartment already, so I had to buy only two more. This solution woks perfectly well for me – I can look into the eyepiece while sitting on a normal chair, no matter which direction my telescope is pointing at.

IV.3.7.2. Looking almost straight up vs. looking almost horizontally.

I can place my Dobson right next to my balcony guardrail, so I am able to look almost straight up. With a refractor I couldn't do it because the legs of the tripod “pushed” the refractor away from the guardrail.

On the other hand looking almost horizontally through my Dobson is a problem because a balcony guardrail is the way. Even when I place it on the above platform the balcony guardrail still forces me to discard all the night-sky objects that are rather low above the horizon (less then 20 degrees). Well, it has an upside too – I save some time and avoid possible disappointments (when night-sky objects are very low over the horizon – there is simply too much air/atmosphere in the way, so they are much less visible then).

UPDATE:

The Dobson is much more versatile as far as eyepiece placement is concerned – no matter which way I point it I can sit on the same chair. Please, just look at these pictures that I took inside my home:



On the second picture I added a normal chair that I use on my balcony. As you can see the Dobson can be used on any target (quite low and quite high over the horizon) with the same chair, while the refractor can't. If I set the tripod for the refractor high enough to sit on the chair while looking at a target that is quite high over the horizon then if I changed for a target that is quite low over the horizon I would have to stand.

My Dobson, being a small one, is UNIVERSAL in this regard, unlike the refractor. Usually people complain about Dobsons, but such complaints are true only for big Dobsons – apparently it's the price you have to pay for having a telescope with huge aperture.


V. Telescopes numbers.

You can describe a particular telescope in several different ways, so it's important to understand some basic terms.

V.1. Aperture = objective lens/mirror diameter.

Aperture describes in a simplified way the light gathering abilities of a telescope (or binoculars), HOWEVER what really matters is the AREA of aperture. Generally the bigger the aperture (area) the better/brighter the telescope.

You can compare different aperture in a very easy way when you ignore some elements from the formula for the area that get reduced anyway:
(A1/A2)^2

For example let's compare aperture of my two telescopes (a 114/900 Dobson and a 70/700 refractor) one way and then the opposite way:
(114/70)^2 = 2.652
(70/114)^2 = 0.377 (= 1/2.652)

The first value means that (at the same magnification) the area of the bigger aperture is 2.652 times bigger than the area of the smaller aperture, which means that it's bigger BY 165.2%. The second value means that (at the same magnification) the area of smaller aperture is 37.7% of the area of the bigger aperture, which means that the area of smaller aperture is smaller by 62.3% (1-0.377 = 0.623).

If you’re interested the math behind this “conversion” is this:
1.652/(1+1.652) = 0.623 (rounded)
0.623/(1-0.623) = 1.653 (rounded)

Please notice that the assumption about he same magnification is very important because brightness would be otherwise different (more on that later – in the part about the exit pupil).

V.2. Focal length = distance from the objective lens/mirror to a place where all light rays come together.

In a refractor or in a Newton it's basically the length of the telescope.


V.3. Focal ratio = focal length / aperture.

I prefer to describe my telescopes as “Aperture/Focal length” given in millimeters, for example 70/700 or 114/900. Unfortunately many astronomers describe their telescopes using Aperture and Focal ratio. What's worse some of them, especially in the US, give the Aperture in inches instead of millimeters. Even worse, the notation of the focal ratio is always “inverted” (f/…), which makes it even more confusing.

Please notice that it's all about proportions – for example two different telescopes (70/700 and 100/1000) have the same focal ratio of 10 (700/70 = 1000/100 = 10), which is written as “f/10”. I hate this “inverted focal ratio notation” with all my passion.

Another thing connected with the focal ratio that annoys me very much is the fact that it is common to describe some telescopes as “slow” (f/8 and “above”, so f/9, f10 and so on) or “fast” (f/5 and “below”, so f/4, f/3 and so on).

Here's a description that I found on the net:

“The terms fast and slow in reference to focal length come from photography and make more intuitive sense when applied to telescopes used for astrophotography. To take an image of the night sky, your DSLR or CCD collects photons of light. The trick to good astrophotography is to catch as many photons as you can as quickly as possible. Speed is important because longer exposures increase the risk of noise in the image sensor and your telescope drifting off target.”

I don't really care about the reference to photography and from my point of view the focal ratio basically tells me if the telescope is “fat” (fast) or “lean” (slow). The only things I have found really useful about the focal ratio are these (I already mentioned them):
1) in a slow (“lean”) telescope light rays are less bent, which minimizes potential problems with aberrations, false colors, coma and things like that,
2) collimating a slow (“lean”) Newtonian telescope is much easier than collimating a fast one, just because the room for error is much bigger.

These are all the numbers that describe a telescope alone. Please notice that things like magnification, exit pupil and field of view don't come from a telescope alone, but from a combination of a telescope and an eyepiece. More on that later – in the part about eyepieces.


VI. Telescopes + eyepieces = more numbers.

An eyepiece looks like a small tube with a couple of lenses (in fact there are more than two lenses inside) that you insert into the part of a telescope that is called focuser or focus tube.

One telescope can be used with many different eyepieces, which means that you can achieve many different results with the same telescope. A particular eyepieces combined with a telescope is responsible for magnification, which influences both the field of view and the exit pupil. These three things should be ALWAYS analysed together!

A quote comes to my mind: “It was my understanding that there would be no math”.



VI.1. Magnification.

Magnification = focal length of the telescope / focal length of the eyepieces

The shorter the eyepiece the bigger the magnification. For example my 70/700 refractor came with two different eyepieces:
1) a 25mm eyepiece that gives the magnification 28x (700/25),
2) a 10mm eyepiece that gives the magnification 70x (700/10).

The same eyepieces give different magnifications with a different telescope. For example in a 114/900 Dobson:
1) a 25mm eyepiece gives the magnification 36x (900/25),
2) a 10mm eyepiece gives the magnification 90x (900/10).

As you can see, the “longer” the telescope the bigger the magnifications with the same eyepieces.

I have to repeat some things that I already mentioned in the point I (in all the sub-points):
1) at higher magnification the moons of Jupiter can appear much closer to the planet (and much closer to each other) and still be discernible,
2) increasing magnification makes more stars visible,
3) some relatively bright stars appear very close to each other, so they can be separated only at high magnification (otherwise they appear as a single star),
4) the higher the magnification the more details of the Moon you can see.

I used to think that magnification is almost exactly like shortening the distance to a particular object, HOWEVER after I saw the pictures below I realised that this is NOT the case.


So, the amount of light rays entering a telescope does NOT depend on magnification because the real distance doesn't change. Pretty obvious, isn't it? Yes, it is, but it's not obvious why higher magnification makes more stars visible. More on that later – in the part about contrast.

VI.2. Field of view (FOV)

Field of view (FOV) = apparent field of view of the eyepiece (AFOV) / magnification

Both my small telescopes use 1.25-inch eyepieces and standard such eyepieces have the AFOV of around 52 degrees:
1) magnification 28x gives the FOV of 1.86 degree (52/28),
2) magnification 36x gives the FOV of 1.44 degree (52/36),
3) magnification 70x gives the FOV of 0.74 degree (52/70),
4) magnification 90x gives the FOV of 0.58 degree (52/90).

Obviously the bigger the magnification the smaller the field of view. It's actually quite natural – when you use bigger magnification you see a smaller part of the whole picture, so you look through a narrower path, hence narrower field of view. As simple as that. This general rule can be slightly “bent” by using wide-view eyepieces (eyepieces with bigger apparent field of view).

Interestingly it's easier to understand and explain narrow-view optics, so wide-view optics are simply a “reversed” case. To generate examples I used this awesome site:
https://www.stelvision.com/en/telescope-simulator/

I simulated what can be seen in a 70/700 telescope. The second picture in the first example is only theoretical because there is no narrow-view 25mm eyepiece available, but it greatly helps to explain the concept.

Please, remember that you can open all the pictures in different tabs and switch between the tabs to see the differences better.

1. The same magnification, but different optics.

Normal-view (AFOV 52 degrees) 25mm eyepiece (magnification: 28x)

NARROW-view (AFOV 43 degrees) 25mm eyepiece (magnification: 28x)

UPDATE:

It's like looking at the same picture, but in the narrow-view you are looking through some kind of tube/tunnel (the example pictures are exaggerated in this regard). Some people claim that this “looking through a tunnel” effect is annoying to them, but I myself bought a 40mm eyepiece with apparent field of view of just 43 degrees (after hesitating for several months) and I don't see this "tunnel" effect AT ALL, probably because the field of view is overall very big (for a telescope).

In fact in some cheap SHORT NORMAL-VIEW (AFOV 52 degrees) eyepieces I do have a problem of "tunnel" effect, but for a whole different reason – I can't see the whole theoretically possible field of view simply because the eye relief is too short. It annoys me VERY much because I feel that I'm loosing something (that is theoretically possible) and this is the main reason why I stopped using a 10mm eyepiece completely (nowadays I use a 15mm or a 20mm wide-view eyepiece combined with a Barlow lens – more on that later).

When the idea is reversed the second picture could be considered as the normal-view and the first picture could be considered as the wide-view. So, a wide-view is like looking through a shorter tube/tunnel (the example pictures above are exaggerated in this regard), which in practice means that you can see a bigger picture. A daytime example would be like this:

In this example you can see that everything is of the same size, so the magnification in wide-view optics is the same, but you can see a little more. In telescopes it's really important only at high magnifications, when the field of view is really small.

2. Different magnifications, but the same optics.

Normal-view (AFOV 52 degrees) 25mm eyepiece (magnification: 28x)

Normal-view (AFOV 52 degrees) 32mm eyepiece (magnification: 22x)

It's like looking at similar pictures, but taken with different zooms – on the picture taken with less zoom everything is smaller, but you can also see some additional things on the sides of the picture. Pretty natural concept, right?

3. Different magnifications and different optics + wider FOV.

Normal-view (AFOV 52 degrees) 25mm eyepiece (magnification: 28x)

NARROW-view (AFOV 43 degrees) 40mm eyepiece (magnification: 17.5x)

It's like looking at similar pictures, but taken with different zooms AND in the narrow-view you are looking through some kind of tube/tunnel (the example pictures are exaggerated in this regard). In THIS combination on the second picture you can still see some additional things on the sides of the picture, but everything is smaller.

4. Different magnifications and different optics + the same FOV (more or less).

Normal-view (AFOV 52 degrees) 32mm eyepiece (magnification: 22x)

NARROW-view (AFOV 43 degrees) 40mm eyepiece (magnification: 17.5x)

Again it's like looking at similar pictures, but taken with different zooms AND in the narrow-view you are looking through some kind of tube/tunnel (the example pictures are exaggerated in this regard). However in THIS combination it's almost like looking at the same picture (the field of view is almost equal) but the in narrow-view the picture is held farther away from your eyes, so the picture and everything on the picture looks smaller. Strange, isn't it?

So, what's the point of using the narrow-view 40mm eyepiece instead of normal 32mm eyepiece? The difference lies in the exit pupil – in the narrow-view 40mm eyepiece the exit pupil is bigger (the view is brighter) because the magnification is smaller (see the next point).

UPDATE:

Theoretically the usefulness of this “move” is very limited in light-polluted areas because magnification is generally more important then, HOWEVER when I bought a 40mm eyepiece with apparent field of view of just 43 degrees (after hesitating for several months) and I compared it to my 32mm eyepiece side-by-side (or rather one after another) I realized that in my 114/900 Dobson I actually prefer the 40mm eyepiece because for some reason it's easier to maintain a proper eye placement. In case of my 70/700 refractor the 32mm eyepiece is a little better because the background is visibly darker (I'm not quite sure why this effect is much smaller in my Dobson – the background is already “dark enough” in the 40mm eyepiece).


VI.3. Exit pupil and eye relief.

Exit pupil = aperture / magnification

The meaning of the exit pupil is by far the most difficult thing to grasp and to explain, so please concentrate.

Basically the exit pupil is a diameter of a “beam of light” that exits a telescope (or binoculars). This “beam of light” enters a human eye pupil, so when the beam is very narrow then the view is very dark. The broader the beam the brighter the view (because more light enters the human eye pupil), BUT there is an upper limit (the size of the human eye pupil). Please notice that this “beam of light” concept is actually a simplification.

Let's refresh the example how the exit pupil works – I will repeat everything that I wrote at the start of the point IV:

Totally mind-blowing! Please notice that every point at the exit pupil contains light rays coming from ALL the objects in view! You can verify this fact by looking through any kind of binoculars while covering half of the objective lenses – you will still see the whole view (NOT half of it), but the whole view will be half as bright. Here is a fascinating discussion on this topic:
https://www.cloudynights.com/topic/603397-a-basic-exit-pupil-question/

This quote is awesome: “And on your part, I want to thank you for your honest and concerted effort to understand this confusing issue. I can tell you in the Astromart thread I referenced earlier, members whose names are well known here gave Alan French quite a battle before they finally grasped the concept. At the time, I was merely a bystander...”

There is another cool “experiment” that you can do with a pair of binoculars to further understand the concept of exit pupil and by the way to understand the importance of big eye relief.

Please, slowly move your eyes away from your binoculars (or move your binoculars away from your eyes/head). The view will NOT get dimmer AT ALL (quite surprising), BUT the field of view will get smaller and smaller (kind of natural).

All the examples are for a telescope (I think), but binoculars “handle” light rays in a similar way. The main difference is that in some telescopes the view is upside-down – in the examples the “red light rays” go into the objective lens “from above”, but the same light rays go into the exit pupil “from below”.


The correct distance at which the human eye pupil should be places is called eye relief – you can see all of the “available” field of view ONLY from there. With a yellow line I marked a human eye pupil that is placed incorrectly (very far away from the eye relief).

As you can see when you move your eye very far away from your telescope eyepiece (or from your binoculars) without any up or down movements then you can see ONLY the “green light rays” coming from objects that are straight ahead (this is why the field of view is very narrow then), BUT you can see ALL of the “green light rays” (this is why what you can still see is as bright as possible).

The next step in this “experiment” is to move your eyes (head) upwards – the narrow field of view will shift downwards (in case of binoculars) or “upwards while the view is upside down” (in case of some telescopes):

In such case you can see ONLY the “red light rays” coming from objects that are up (this is why the field of view is still very narrow then), BUT you can see ALL of the “red light rays” (this is why what you can still see is as bright as possible). Please notice that the “red objects” (that are up) in such case “appear from the bottom” (because the view is upside-down – this is why I numbered the “red light rays”).

VI.3.1. Comparing exit pupils = comparing brightness.

ATTENTION! Comparing brightness is all about comparing objects that are more or less diffuse. Comparing brightness is NOT about point-like objects like stars, small planets or moons of the planets (except for “our” Moon), BUT the brightness of the background is connected with the concept of contrast (more on that later).

Comparing exit pupils (precisely speaking: comparing their areas) is like comparing brightness. This is another thing that is a little counter-intuitive about binoculars and telescopes. Some people think that when aperture is bigger then the view is always brighter, but this is NOT true!

There is a “very good” argument that “much bigger aperture gathers much more light rays, so the view should be always brighter”. This is true ONLY at the same magnification, but when magnification is bigger then the view gets darker. Why? Because at bigger magnification any diffuse object looks bigger, so it looks more “stretched”. When an objects looks more stretched all the light rays that come from the object are more “spread out”, so the object looks dimmer.

If you don't believe me then look at a diffuse object with a long eyepiece (small magnification) and then change the eyepiece for a much shorter one (much bigger magnification). The object will definitely look dimmer, which is actually good for very bright objects like the Moon or the planet Jupiter.

Let's repeat the formula for exit pupil:

Exit pupil = aperture / magnification

It's actually a little time consuming to first calculate two different exit pupils and then to compare their areas, but there is a much easier way to compare brightness of equipment (even between telescopes and binoculars):

EBC – equipment brightness comparison
M – magnification
A – aperture

EBC(M1xA1; M2xA2) = (M2/M1)^2 * (A1/A2)^2

I used the notation MxA just like it is used in binoculars (for example 12x60). My formula works also for telescopes because it’s just a different (greatly simplified) way of comparing exit pupil areas. I described it in detail here:
Binoculars and spotting scopes brightness comparison

VI.3.2. Different exit pupils (different brightness) at THE SAME magnification.

Something like this is possible ONLY when you compare telescopes with different aperture:
Exit pupil = aperture / magnification

Let's compare a 70/700 refractor combined with a 14mm eyepiece (magnification 50x) to a 114/900 Dobson combined with an 18mm eyepiece (also magnification 50x):
1) in a 70/700 refractor magnification 50x gives the exit pupil of 1.4mm (700/50),
2) in a 114/900 Dobson magnification 50x gives the exit pupil of 2.28mm (114/50).

What really counts is the AREA of the exit pupil, but you can compare different areas in a very easy way when you ignore some elements from the formula for the area that get reduced anyway:
(2.28mm/1.4mm)^2 = 2.652
(1.4mm/2.28mm)^2 = 0.377 (= 1/2.652)

It may seem easy, but it still required two steps – calculating exit pupils and then comparing their areas. In this case my formula is much quicker! When magnifications are the same (M1=M2) then you have to calculate only the second part of my formula:
EBC(50x114; 50x70) = 1^2 * (114/70)^2 = 2.652
EBC(50x70; 50x114) = 1^2 * (70/114)^2 = 0.377 (= 1/2.652)

The calculations and the results are exactly the same as in the point V.1., when we were comparing only apertures (at the same magnification).

I will rephrase what I wrote in the point V.1. (instead of aperture I now simply write brightness):
The first value means that (at the same magnification) the brightness of a 114/900 Dobson is 2.652 times bigger than the brightness of a 70/700 refractor, which means that it's bigger BY 165.2%. The second value means that (at the same magnification) the brightness of a 70/700 refractor is 37.7% of the brightness of a 114/900 Dobson, which means that the brightness of a 70/700 refractor is smaller by 62.3% (1-0.377 = 0.623).

If you’re interested the math behind this “conversion” is this:
1.652/(1+1.652) = 0.623 (rounded)
0.623/(1-0.623) = 1.653 (rounded)

From this topic:
https://www.cloudynights.com/topic/579795-how-much-increase-in-aperture-to-see-a-difference/
you can learn that a noticeable difference (due to a change in aperture) requires around 50% increase (1.5) or 33% decrease (0.67 = 1/1.5) and a significant difference requires around 100% increase (2.0) or 50% decrease (0.5 = 1/2.0).

VI.3.3. Exit pupils at DIFFERENT magnifications.

By using different magnifications/eyepieces you can achieve all kinds of combinations:

VI.3.3.1. The views in a single telescope can be of different brightness.

For example in a 70/700 refractor:
1) 25mm eyepiece (magnification 28x) gives the exit pupil of 2.5mm (70/28),
2) a 10mm eyepiece (magnification 70x) gives the exit pupil of 1.0mm (70/70).

Comparing areas of the exit pupils:
(2.5mm/1.0mm)^2 = 6.25
(1.0mm/2.5mm)^2 = 0.16 (= 1/6.25)

In this case my formula is again much quicker! When you compare only eyepieces combined with the same telescope the aperture stays the same (A1=A2), so you have to calculate only the first part of my formula:
EBC(28x70; 70x70) = (70/28)^2 * 1^2 = 6.25

EBC(70x70; 28x70) = (28/70)^2 * 1^2 = 0.16 (= 1/6.25)

By the way: the value 6.25 means that in a 70/700 refractor the view at magnification 28x is over SIX times brighter than at the magnification 70x! And the value 0.16 means that the drop in brightness caused by the change in the magnification form 28x to 70x is 84%!

Please notice that when you compare different eyepieces in a particular Dobson you can ignore the central obstruction of the Dobson simply because it stays the same, not because it's so small that it can be ignored (see the point IV.3.1.).

VI.3.3.2. The views in two telescopes with different apertures can be equally bright.

For example (ignoring the central obstruction of the Dobson – see the point IV.3.1.):
1) in a 70/700 refractor a 25mm eyepiece (magnification 28x) gives the exit pupil of 2.5mm (70/28),
2) in a 114/900 Dobson a 20mm eyepiece (magnification 45x) also gives the exit pupil of 2.53mm (114/45).

The exit pupils are (almost exactly) the same, so their areas are also (almost exactly) the same – no need for more calculations here.

Let's see how my formula works in this case:
EBC(28x70; 45x114) = (45/28)^2 * (70/114)^2 = 0.974
EBC(45x114; 28x70) = (28/45)^2 * (114/70)^2 = 1.027 (= 1/0.974)

A value close to 1 means that the brightness is practically the same.

Please notice that the difference between the magnifications at the same brightness is significant (45x vs. 28x), so the Dobson is clearly better. The same conclusion is when you simply compare apertures (114mm vs 70mm), but it's the higher magnification that makes more stars/details visible.

VI.3.3.3. The view in a telescope with big aperture can be DARKER than the view in a telescope with small aperture.

For example (ignoring the central obstruction of the Dobson – see the point IV.3.1.):
1) in a 70/700 refractor a 20mm eyepiece (magnification 35x) gives the exit pupil of 2.0mm (70/35),
2) in a 114/900 Dobson a 10mm eyepiece (magnification 90x) gives the exit pupil of 1.27mm (rounded from 1.267 = 114/90).

Comparing areas of the exit pupils:
(2.0mm/1.27mm)^2 = 2.48
(1.27mm/2.0mm)^2 = 0.403 (= 1/2.48)

I strongly prefer my straightforward formula:
EBC(35x70; 90x114) = (90/35)^2 * (70/114)^2 = 2.493
EBC(90x114; 35x70) = (35/90)^2 * (114/70)^2 = 0.401 (= 1/2.493)

The slight differences come from rounding the values.

VI.4. Contrast.

The meaning of contrast is my newest “discovery” as far as astronomy is concerned. It explains why increasing magnification makes more stars visible, but why it works is not really obvious.

I will start with some things that you can verify yourself, even in a city with big light pollution. For example the brightest planets and the brightest stars can be seen even around sunset when the sky (background) is still relatively bright. The same stars (and some other too) can be seen in the middle of the night even in biggest cities, simply because they are so bright they stood out from the relatively bright light-polluted night-sky (background).

It's all about contrast – the brighter a planet/star the easier it can be seen. It works also the other way round – the weaker a planet/star the more difficult it is to spot it. When the brightness of a star is the same as the brightness of the background you cant's see it at all because it can't be “singled out” from the background.

The crucial thing to realise is that the background of the night-sky is never completely black, even in space. There are always some light rays that come from stars, galaxies or other space objects that are very far away, so they can't be seen individually. Let's refresh these two pictures:


Human eye can't see a particular star when there are too few light rays from the star going into the eye. It's true both while looking at the night-sky with the naked eye and while using a telescope. When you increase ONLY magnification (in a telescope) then the amount of light rays coming from a particular star stays the same, so you can't see it individually IF it's very far away, no matter how “powerful” it is.

Even though very distant stars can't be see on their own, their light rays accumulate to some extent. A perfect example is the Milky Way, understood not as our whole galaxy but as a patch of light on the night sky. Unfortunately it can't be seen from light-polluted cities, so I have to show you a picture:

This patch of light is actually a central part of our galaxy that is very far away, so individual stars can't be seen. But you can see the accumulated light coming from millions or maybe even billions of stars that are there.

By the way: I think that naming our galaxy as the Milky Way was a moronic idea because now we have two different things that are called exactly the same way. One thing is the patch of light on the night-sky (the original meaning of the phrase Milky Way) and the other thing is our whole galaxy, which consists not only of a central part, but also of stars located in spiral arms, including stars that are relatively close to the Earth that can be seen all over the night-sky as “normal” stars. I HATE this name for our galaxy!

In other directions than the Milky Way, understood as a patch of light on the night-sky, there are also some “invisible” stars, but more importantly there are other space objects, especially galaxies. In fact there are MUCH more objects than you can even imagine! One of the most famous space photos (“Hubble Ultra-Deep Field”) was actually taken in a direction that was practically EMPTY. And this is what was hiding there (click to enlarge!):

Most of the objects on the picture are galaxies! Totally unbelievable! But it's not the point. The point is that the background of the night-sky is NEVER completely black. It's more like a “soup of light” consisting of light rays coming from many different individual sources.

Light pollution makes the background (or rather the foreground) of the night-sky MUCH brighter and it resembles a “soup of light” even more. The (many different) sources of artificial light are much closer to the observer, but you can't see particular street lamps in the sky. What you see as light pollution are light rays that were sent upwards (for example by street lamps), then they were scattered in the atmosphere and then some of them returned back downwards.

VI.4.1. Contrast when increasing magnification.

When you increase magnification all the different individual sources of light that are VERY FAR away (too far to be seen individually) are stretched away from each other, so their light rays become less concentrated and the background gets darker.

The stars that are relatively close to the Earth that previously were equally bright as the background now (after increasing magnification) become visible simply because their light rays are still concentrated in a point (the stars are too far away to see their disks even at higher magnification), so they are not stretched (they don't dim), while the background gets darker (because it's stretched).

Please notice that increasing magnification in light-polluted areas gives more “visible” results because there are more “random” light rays there, so the background (or rather the foreground) gets visibly darker. Under dark skies (without light pollution) the effect is still there (more stars appear) but the difference is not as big because the background is already very dark even at low magnification.

Please remember that under darks skies you can see MUCH MORE stars overall (because the background is much darker even at low magnification) and this is why astronomers LOVE dark locations.

VI.4.2. Calculating contrast vs. calculating brightness.

This post:
https://www.cloudynights.com/topic/677955-background-sky-contrast/?p=9668225

truly opened my eyes. This fragment is one of the best/most important things about astronomy in light-polluted areas that I have ever found:

“- Contrast is the ratio of brightnesses.
- The brightness of an extended object, that is a galaxy, a nebula, a planet, and the sky, depends on the exit pupil, the area of the exit pupil.
(…)
A 60 mm at 50x has a 1.2 mm exit pupil, much dimmer, much darker, than the 250 mm scope. It's about 17 times dimmer. That's about 3 magnitudes.
(…)
A dark sky is not the same as contrast. Stars are points of light at most magnifications so magnifying them does not spread out their light over a greater area. Their brightness just depends on the amount of light gathered, proportional to the area of the mirror or lens.

In your two scopes, the 250 mm will be 17 times brighter than the 60 mm. At the same magnification, the stars are 17 times brighter, the sky is 17 times brighter, the contrast, the ratio of brightnesses is the same.

If you increase the magnification of the 250 mm to 200x so the sky is the same brightness, then the contrast will be 17 times greater because the stars are 17 times brighter.”

I have to add one thing – increasing aperture DOES make more stars visible even if the contrast (the ratio of brightness) stays the same. Why? Because the ABSOLUTE difference becoms bigger. For example the difference between values 2.2 and 2.0 (0.2) is bigger than the difference between values 1.1 and 1.0 (0.1), even though the ratio stays the same (2.2/2.0 = 1.1 = 1.1/1.0).

Anyway, comparing brightness at the same magnification (simply comparing apertures) is like comparing contrast at the same exit pupil. Let's compare a 114/900 Dobson to a 70/700 refractor (at the same magnification):
(114/70)^2 = 2.652

In the point VI.3.3.2. I gave you an example that brightness is (almost exactly) the same in a 70/700 refractor at magnification 28x as in a 114/900 Dobson at magnification 45x. Contrast will be better at higher magnification:
(45/28)^2 = 2.583

There is a small difference because the precise magnification in a Dobson should be 45.6x (then the exit pupil would be exactly 2.5mm, like in the refractor):
(45.6/28)^2 = 2.652

The slight differences come from rounding the values.

From my experience I must say that in big light pollution even the magnification 45x is too low – see the next point.

VI.5. My most often used eyepieces.

UPDATE (the whole point VI.5., together with all the sub-points):

Recently my preferences have changed significantly! Right now I strongly prefer to scan the night-sky with a 40mm eyepiece and when I want to use a “medium” magnification I switch to a 15mm wide-view eyepiece.

In my 114/900 Dobson a 15mm eyepiece gives the magnification 60x, so the background gets really dark while the exit pupil is still almost 2mm. Not only more stars are visible, but I can see some colors in stars that were colorless at smaller magnifications. The apparent field of view of my 15mm eyepiece is 70 degrees, so the field of view (at magnification 60x) is 1.17 degree.

As far as the longest eyepieces are concerned, my own experience came up totally different from what I had imagined after reading some opinions on the Internet. When I FINALLY bought a 40mm eyepiece with the apparent field of view of just 43 degrees (after hesitating for several months) and I compared it to my 32mm eyepiece with the apparent field of view of 52 degrees (the “final” field of views in both eyepieces were almost exactly the same) side-by-side (or rather one after another) I realized that in my 114/900 Dobson I actually prefer the 40mm eyepiece. It seems to me that for some reason with the 40mm eyepiece it's easier to maintain a proper eye placement. In case of my 70/700 refractor the 32mm eyepiece is a little better because the background is visibly darker (I'm not quite sure why this effect is much smaller in my Dobson – the background is already “dark enough” in the 40mm eyepiece).

VI.5.2. A good “medium” eyepiece.

It is said that a good “medium” eyepiece is an eyepiece that gives the exit pupil of around 2.0mm AND at the same time that has a comfortable eye relief (of at least 14mm). For my 114/900 Dobson it's perfectly true – it's the 15mm eyepiece described in the previous point.

However, in smaller telescopes, for example in my 70/700 refractor it's not as simple because the exit pupil of 2.0mm is obtained at very low magnification 35x. Such magnification is too small to see the Trapezium (its 4 main stars) clearly, at least for me. Magnification of around 45x is definitely good enough, so a good “medium” eyepiece for a 70/700 refractor is also the 15mm eyepiece described in the previous point (precisely it gives the magnification 46.6x and the exit pupil 1.5mm).

VI.5.3. A good “high power” eyepiece.

As far as short eyepieces are concerned there two big problems. The most obvious one is very small exit pupil – only the Moon and the brightest planets look enjoyable then. To me even stars (point-like objects) look worse – the brightest ones look kind of weird (it probably has something to do with my own eye defects) and the weakest ones require some time to be noticed (not fun at all, especially in big light pollution).

The second problem is actually more important – very short eye relief. I myself literally HATE standard 10mm eyepieces – the eye relief is so small that I am afraid that I will touch the prism with my eyelashes. This is why I hold my eye farther than the eye relief, so the “real field of view” is actually smaller than theoretically possible. And this is why I stopped using 10mm eyepieces completely!

Instead of using “high power” (short) eyepiece I use a “medium” or “medium-long” wide-view eyepiece together with a Barlow lens. This way I obtain high, very high or extremely high magnification (for a small telescope) with a relatively big field of view AND I still retain good (long enough) eye relief! Perfect!


VII. Aperture vs. magnification (in telescopes used for visual).

What is more important in a telescope – aperture or magnification? There is a never-ending discussion on this topic, so I have to give you a crucial example – a comparison to the naked-eye view. Please, notice that this example is for telescopes used for visual.

Imagine that you have a telescope with a HUGE aperture, but without ANY magnification (magnification 1x). The exit pupil in such a telescope would be equal to aperture (aperture/1), so it would be HUGE. Such a HUGE exit pupil would be much bigger than the size of human eye pupil at night (around 7mm), so most of the gathered light would be wasted. Using such a telescope would be like looking at the night-sky with the naked eye through a big barrel. It means that a HUGE aperture is totally MEANINGLESS without any magnification!

Now imagine a telescope with a tiny aperture of around 7mm (the size of human eye pupil at night) with magnification 3x. The exit pupil in such a telescope would be 2.3mm (7mm/3 = 2.3mm). Such an exit pupil would be still big enough to see night-sky objects comfortably, but the increased magnification would make more stars visible. Moreover it would make bright non-point-like objects look three times bigger, so you would see more details, especially on the Moon. So, increased magnification is BETTER than naked-eye view.

The end of the never-ending discussion!

Please notice that increasing magnification much further without increasing aperture (of 7mm) would make the exit pupil too small (would make the view too dark). This is why you HAVE to increase aperture in order to PREVENT the exit pupil from getting too small (to prevent the view from getting too dark). Magnification and aperture work in an almost perfect harmony, but in SLOW telescopes used for visual magnification is ALWAYS a little more important because the exit pupils are ALWAYS smaller than 7mm (smaller than the size of human eye pupil at night).

It seems to me that some people confuse the contest "aperture vs. magnification" with the contest "big telescope vs. small telescope". It's not the same! Obviously a bigger telescope is better than a smaller telescope, but the example above proves that magnification is actually a little more important overall. Not much, but still.


VIII. Small telescope vs. expectations.

Some people have some unrealistic expectations about small telescopes because some Internet sites, including some online astronomy shops, state that you can see many Messier objects (object from the Messier Catalogue) even in small telescopes. It's true, HOWEVER please remember that the word “see” in this context should be understood as “I see that I can see something”, which is better than “I can’t see the object at all”.

What’s worse some Internet sites give you “examples” of what you can see by showing pictures taken with really BIG telescopes, which is is extremely misleading for total amateurs! On the picture below there is a comparison how the M13 (Hercules Globular Cluster) looks in binoculars (the very first example) and several different telescopes.


By the way: most of the photos of night-sky objects you can find on the net are not really “true photos” but they are hundreds or even thousands of different photos taken with a long exposure time and then averaged/stacked together. There is NO WAY to see anything like this with your own eyes even in a big telescope.

A small telescope is great for looking at very bright large objects like the Moon, Jupiter or Saturn and all point-like objects like stars (especially in open star clusters) or the brightest moons of Jupiter and Saturn. Non-point-like objects like globular clusters, nebulas and galaxies can be seen only as “faint fuzzies” – they look like a cloud of light – something clearly different from the stars that are simply dots. Unfortunately many of such non-point objects can't be seen in a small telescope from a city with significant light pollution at all. I described in detail what can be seen from a city with big light pollution in the point I.

Please notice that the most famous catalog of astronomical objects – the Messier Catalogue was created only because these objects were blurry and could be mistaken for a comet! Moreover there was hardly any light pollution in those times (18th century), so they were blurry under very dark skies!


IX. Filters.

UPDATE (the whole point IX.):

The most important goal of using a filter is too make the view dimmer without changing magnification (gray filters) OR to block some light wavelengths (color filters). On the net I found a picture of the Moon taken with a truly orange filter I instantly fell in love with the view. To me the Moon looked a little like Mars and the view was much more interesting than the typical gray view of the Moon.

Out of curiosity I bought several inexpensive filters and after lots of experimenting I can say that to me:
1. In general filters are good only for looking at very bright objects like the Moon and the planet Jupiter, but the planet Saturn looks best without any filter, at least to me (in my small telescope). I haven't tried any filters on the Mars yet, but this planet is clearly smaller than Jupiter, so I doubt if there would be any features visible anyway.
2. The best overall filter for visual use is the green/light green #56 filter (light transmission 53%). I enjoy this filter very much while looking at Jupiter (best details, at least to me) and also at the Moon (very relaxing color). Unfortunately it's a little weaker for astrophotography with a smartphone.
3. The best single filter for the Moon is the dark yellow #15 filter (light transmission 66%) – in my 114/900 Dobson the color is actually light-orange. It's great both for visual use as well as astrophotography with a smartphone.
4. Slightly better results for the Moon can be actually achieved with a combination of the dark yellow #15 filter and the yellow #12 filter (light transmission 74%). Please notice that the final light transmission is around 60% because mostly the same light wavelengths are blocked – I think it's something like this:

I don't like how long an eyepiece is when it's combined with two filters at the same time, so I stopped using this combination – I use just the dark yellow #15 filter.
5. The blue #80A filter (29% light transmission) is too "cold" for visual use, especially while looking at the Moon. The color is actually piercing light-blue and it's much brighter than the light transmission 29% suggests. Even while looking at Jupiter it's worse than the green/light green #56 filter. It's not great for astrophotography with a smartphone either because there is lots of dark noise. Only the Moon looks good on smartphone pictures with this filter, but as I prefer visual observations I stopped using the blue #80A filter completely.
6. The gray (neutral density 0.6 – light transmission 25%) filter is boring and kind of useless. Instead of using this filter you can simply use a shorter eyepiece without any filter – for example increasing magnification from 50x to 100x gives EXACTLY the same effect as far as brightness is concerned, but everything looks bigger (so better – with more details) at magnification 100x. The magnification 50x is good for taking pictures of the whole Moon, but even during the full Moon the brightness is never problematic because you can change the settings for ISO and/or for shutter speed (exposure time). For visual use it's much better to use magnifications over 100x anyway.
7. My "orange" #21 filter (light transmission 46%) looks rather red-orange (instead of pure orange), even while looking at the Moon, but I realized this fact only after buying the dark yellow #15 filter. In fact my "orange" #21 filter looks more red than orange during daylight, but I have to point out that on the net I found some pictures of other orange filters that look actually truly orange during daylight, so they should be better also during night. My "orange" #21 filter is simply terrible for astrophotography with a smartphone because the pictures are even more red than orange. I stopped using the "orange" #21 filter completely.

Below there are my own photos of the Moon (most of them cropped and/or resized) taken with a smartphone at very low magnifications (this is why they lack details).

The filters green/light green #56, blue #80a, combination of dark yellow #15 and yellow #12 (light orange) and “no filter” – click to enlarge:

The dark yellow #15 filter (shorter exposure time is helpful to achieve the orange color) – click to enlarge:

My #21 “orange” filter with different settings for ISO and/or exposure time (it's impossible to take a single good picture with a smartphone with this filter) – click to enlarge:

X. Tips for amateur observations.

X.1. Keep magnification reasonable.

UPDATE (the whole point X.1.):

Recently my preferences have changed significantly as far as a Barlow lens is considered! Right now I use it regularly on the Moon and brightest planets, but with a different eyepiece. In fact right now I own three Barlow lenses: 2x, 2.5x and 3x. The only thing that keeps me from using magnifications of more than 140x is the fact that in my telescopes there is no micro-focusing, so it's very difficult to find focus then. In my 70/700 refractor the additional limit is the small exit pupil (0.5mm at the magnification 140x), but my 114/900 Dobson could theoretically much handle bigger magnifications.

I have to explain why I changed my views in this regard. The very first time I looked at the Moon at the magnification 140x I was using my 70/700 refractor with a standard 10mm eyepiece and a Barlow lens 2x. I didn't enjoy the view and I thought it was the fault of the Barlow lens and also of the small exit pupil (0.5mm). HOWEVER after I bought a 114/900 Dobson (with much bigger aperture) I realized that even at the magnification 90x I didn't enjoy the standard 10mm eyepiece, even without a Barlow lens AND that I did enjoy a combination of a wide-view 20mm eyepiece and a Barlow lens 3x VERY much!

The problem turned out to be the standard 10mm eyepiece itself! The main problem is the very short eye relief of this eyepiece – it's so small that I am afraid that I will touch the prism with my eyelashes. This is why I hold my eye farther than the eye relief, so the “real field of view” is actually smaller than theoretically possible. And this is why I stopped using 10mm eyepieces completely!

Instead of using “high power” (short) eyepiece I use a “medium” or “medium-long” wide-view eyepiece together with a Barlow lens. This way I obtain high, very high or extremely high magnification (for a small telescope) with a relatively big field of view AND I still retain good (long enough) eye relief! Perfect!

Please, notice that the bigger field of view of a wide-view eyepiece is almost as important as the longer eye relief. The very first time I used very high magnification (140x) while looking at the rings of Saturn (with my 70/700 refractor) I had to move my telescope a little to the side relatively often to keep the planet in the field of view (the Earth is rotating, so “the sky is moving” and the Saturn “slides” outside the field of view after some time) and it was annoying! A wide-view medium eyepiece combined with a stronger Barlow lens gives me similar magnification, but with a significantly bigger field of view (together with a longer eye relief).


X.2. Forget about a toy finder scope!

Seriously, you should forget about a toy finder scope that comes with a small telescope. I attached it to each of my telescopes once and I will never do it again. It is simply too weak when looking from my balcony, with all those street lights blinding me. All that matters to me is the telescope itself.

As my finder scope I use my 8x42 binoculars, but the truth is that ANY binoculars should be good enough. If you don't have any binoculars then you should rely only on the stars that are visible with the naked eye. You have to rely on them even while using binoculars because you have to use some kind of reference point anyway.

The problem is that it's very hard to point a telescope in exactly the same direction as binoculars just a moment ago. The angles are totally different unless you sit down with your butt on the ground and aim binoculars along the tube of the telescope. It's relatively easy to do with a refractor and much more difficult with a Dobson. Either way, a total amateur needs a long eyepiece that gives the maximum (or almost maximum) field of view. I think that a 32mm eyepiece OR a 40mm eyepiece is a must buy.

In the last point I showed you how to search for some objects with the naked eye even in big light pollution.

X.3. Use a comfortable chair!

Generally it's a very good idea to place a normal (relatively heavy, but comfortable) chair next to your telescope. To me it was like a God-sent idea because I tried it out when I was looking at the rings of Saturn for the first time ever. The view was simply hypnotizing and I spent LOTS of time in the same position! And right after that I switched to watching Jupiter and its moons from the exact same spot! It was in 2021, so the planets appeared quite close to each other on the night sky. What a night! Unforgettable!

X.4. Watch out for differences in temperatures.

1. Cold air + warm telescope.

The cold air that “touches” the warm telescope gets warmer (making the telescope colder), but this warmer air instantly mixes up with the cold air that is farther away from the telescope, so the air close to the telescope is constantly “moving”, similarly to the air over a very hot object during summer. So, it's important to cool down the telescope as a whole.

2. Warm air + cool telescope.

If you wear glasses then you know that when it's cold outside and you go into a warm building the glasses will instantly fog up. If you don't wear glasses then fill an empty glass with ice water – on the outside side of the glass small drops of water will appear. It's all about water condensation. Please, read the long answer on this site:
https://www.reddit.com/r/Astronomy/comments/9c94nu/why_does_my_telescope_get_so_much_condensation/

Please remember that you should AVOID wiping the dew off your eyepieces! You don't want to scratch the eyepieces by accident – there can be some dust or grit on the eyepiece besides the dew that you won't be able to see in the darkness.

X.5. Observing conditions are not only about the light pollution!

One night I used my telescope and even though there were no clouds the observing conditions were much worse than previously! I couldn't even clearly see the Orion's Belt with the naked eye! To be honest I had never thought that there could be such a big difference independent from the light pollution. On the net I found the info that “Bad transparency is caused by pollutants in the air, either artificial, natural, or (most often) both.” and “Bad seeing is caused by turbulence combined with temperature differences in the atmosphere”. On this site:
https://www.cloudynights.com/topic/487715-why-does-poor-seeing-happen-or-is-it-poor-transparency/
there is an interesting discussion on this topic.

I found a great site with a complex astronomy forecast:
https://clearoutside.com

This site is great for another reason – you can check at what time starts and ends the astronomical darkness AND you can also see a picture for the whole year! Just click the button “Annual Darkness”.

Los Angeles:

Seattle:

My home city:

Please notice that in my home city during the summer months there are “astronomical white nights” when the night sky is never fully dark because the Sun is too little below the horizon and the astronomical twilight never ends.

A site that is even better for checking the exact times for twilight end, nautical twilight end and astronomical twilight end is this:
https://sunrise-sunset.org

X.6. How much are your “astronomy hours” skewed?

Have you ever wondered what does the word midnight mean? The word midnight means literally the middle of a night. Unfortunately in the vast majority of cases the true (astronomical) middle of a night is not at midnight local time. And I am not even talking about daylight saving time!

“Astronomy hours” at some places are simply ridiculous. At some places they are ridiculous only during the DST (daylight saving time – summer time), but in some other places, like the western China, they are ridiculous all year long. On the other hand there are some places where the astronomy hours are perfect all year long.

Here's a very interesting solar noon map that I found on the net (click to enlarge):

The picture is for standard/winter time, but when the DST starts many places go “more red”. In the western Spain during the DST the Sun is highest above the horizon around 2:30PM, so the middle of the astronomical night is around 2:30AM. Interestingly the Great Britain lies at the same longitudes as Spain, but it is in a different time zone, which is much more reasonable.

In China there is no DST, but there is one whole big time zone, so in the western China the Sun is highest above the horizon around 3:00PM, so the middle of the astronomical night is around 3:00AM. Oh, man.

On the site sunrise-sunset.org (link given above) there is info also about solar noon, so you can calculate the true (astronomical) middle of the night right away (+12hours from the solar noon).

X.7. Apparent magnitude and limiting magnitude.

Apparent magnitude is a number that shows how bright a particular object appears from a particular place. The lower the number the brighter the object. Here are examples of apparent magnitude as seen from the Earth at maximum brightness:
– full Moon: -12.9
– planet Venus: -4.92
– planet Jupiter: -2.94
– planet Mars: -2.94
– star system Sirius: -1.47
– star Canopus: -0.72
– planet Saturn: -0.55

All the night-sky objects above are extremely bright and can be easily seen with the naked eye even in the worst light pollution. From my own experience I can say that in a small telescope even stars of magnitude around 0.5 still look literally like diamonds in the sky and stars of magnitude around 2 still look relatively bright. Unfortunately weaker stars (magnitude 3 and above) are more and more negatively influenced by light pollution.

The magnitude of the weakest stars that can be seen with the naked eye depends on light pollution and it varies greatly. Without any light pollution the maximum magnitude is 7 or 8 and in the worst light pollution it's less than 4. Interestingly, even in significant light pollution a small telescope will show you stars of magnitude over 9 – more than you could ever see with the naked eye even in darkest locations on Earth! The catch is that the field of view in any telescope is extremely small when compared to the field of view of the naked eye, so the “WOW effect” is greatly diminished. But it's cool anyway!

The maximum magnitude of stars that can bee seen in a telescope is called limiting magnitude and it depends on many different things, not only light pollution. A fantastic telescope limiting magnitude calculator can be found on this site:
https://www.cruxis.com/scope/limitingmagnitude.htm

It's worth to notice that in big light pollution it's better to increase magnification than aperture. Just set the value Naked Eye Limiting Magnitude near the Zenith to 4 (which means big light pollution), then set a particular aperture and a particular magnification and press “Calculate”. Remember the result then double the magnification, press “Calculate” and see the new result (much bigger). Reverse to the original magnification, press “Calculate” to see the original result again, then double the aperture, press “Calculate” and see the newest result (hardly any change in reference to the original result = much LOWER result than the result with doubled magnification).

Please notice that when you increase magnification very much (use a 10mm eyepiece) then the view gets very dark and the “new stars” are barely visible. To me it's not enjoyable at all. When I want to see more stars I change from my longest (40mm or 32mm) eyepiece to my 15mm eyepiece that gives magnification 60x in my 114/900 Dobson or 47x in my 70/700 refractor.

I have to point out that at first I thought that the yellow (#12) filter (light transmission 74%) with my 32mm eyepiece doesn't really change the limiting magnitude of stars (when compared to the unfiltered view through the same eyepiece), BUT I noticed a difference when scanning the night-sky by moving a telescope while looking into the eyepiece. It's much easier to find some “moving” stars without any filter.

There is one additional thing to remember – the apparent magnitude of a galaxy, a nebula or a star cluster is NOT the same as the magnitude of a single star (a point-like object). On the net I found these quotes (a question and an answer):

“Is it possible, that I can see apparent magnitude stars of 10 or 11 in my ten inch dob, and not be able to see AM 8 and 9 DSOs.”

“A 1'x1' galaxy at magnitude 10 has a surface brightness of 10 and would be easily seen in a small scope. A 20'x20' face-on galaxy of magnitude 10 has a surface brightness of magnitude 16.2. That 2nd one would be tough in a big scope.
Both have the same Total Integrated magnitude, but radically different surface brightnesses. Since the background sky behaves like a large object and also has a surface brightness, it is the contrast between the object and the sky we see. In the first example, we'd see a white dot against a charcoal background. Easy. In the 2nd example, we'd see a large charcoal patch against a charcoal background. Tough.”

X.8. Free maps of the night sky.

Thankfully we live in modern times a we can use sites like this:
https://stellarium-web.org

This awesome site allows you to search for a particular night-sky object without learning anything about star constellations! You can also change date and time to see where a particular object was (in the past) or where it will be (in the future). AWESOME!

A good method is to change the time minute by minute until a particular object is exactly in the direction you want it to be. It's quite useful on a balcony where you have some parts of the sky obstructed by nearby apartment buildings.

Please notice that you can simulate the night sky seen with the naked eye in big light pollution by setting the time to an early hour, but it's not quite realistic. Most examples in the next point are made this way.

I have also installed the free program Stellarium from this site:
https://stellarium.org/
The program is not perfect but it's still very good:
1) the program has much more options and is much more configurable,
2) the program is much less burdening for the computer.

Please notice that I still regularly use the website, especially when I want quick results, better visuals or deeper star field.

I described the program Stellarium in detail here:
Stellarium program vs. Stellarium website

There is also a free astronomy Android app – Stellarium Mobile (153MB in total) that I installed on my smartphone. It shows only stars of magnitude below 8, but at least it seems consistent, unlike another free Android app that I installed (I will not name it).

X1. More astronomy fun.

You can find plenty of interesting things about astronomy on the net, but here I HAVE to point at two fantastic things – a great Youtube video and a beautiful free Android app.

XI.1. Great timelapse of a night sky.

I enjoy timelapses of the night sky and this Youtube video is by far the best I have ever seen! It's best to watch it at full-screen!


What’s especially good:
1. There are numerous timelapses (combined into one movie) from the same place and almost from the same time (all were recorded in a span of 10 days), but aiming at different parts of the (same) night sky.
2. It’s the southern sky, which is mostly alien for a person from the central Europe like me.
3. All the timelapses are at least very good and some of them are simply fantastic.
4. Some night-sky objects are named and there are also some other comments.
5. The timelapses are not too fast, but not too slow – simply perfect.
6. The music is beautiful on its own and fits the timelapses perfectly.
7. You can see that night-sky objects move in a very curious way, especially when you look in a relatively narrow field of view – “from right to left” when looking in one direction and “from left to right” when looking in another direction. The catch is that the night-sky objects always set (hide behind the horizon) going in the same direction – “from right to left” on the southern hemisphere and “from left to right” on the northern hemisphere.

XI.2. Beautiful free Android app with cool travel through space, even to other stars.

Solar System Scope is a free Android app with cool travel through space, even to other stars! It's not perfect – for example the positions of some Messier objects seem to be incorrect, but I don't care about it because there is no “visit” option to travel to them anyway.

It's very hard to describe this beautiful app with words, so I made a video focusing on the travel aspect:


It's 14 minutes long, so it's easy to miss some things if you randomly jump through the movie, so I made some screenshots (you still have to watch the video to see the actual travel):










XII. Examples of how to find night-sky objects.

In most of the pictures below I used the site stellarium.org to simulated the night sky seen with the naked eye in big light pollution by setting the time to an early hour, so most of the stars are NOT visible.

XII.1. Orion's Sword with the Orion Nebula (M42) in the middle.

It's a little below the Orion's Belt. To be honest I didn't notice the Orion Nebula in a small telescope the first time I looked at it, probably because my expectations were too big after I had seen some pictures of the nebula on the net. The nebula can be seen even in binoculars, but only as a little glow (that actually looks cool).

XII.1b. Trapezium.

The Trapezium is a tight open star cluster in the heart of the Orion Nebula. In a small telescope you can see it's main 4 stars even at the magnification 45x, but this asterism (a pattern of stars on the night sky) is very small then. At the magnification 60x (or more) it's much easier to see.

XII.2. Pleiades (M45).

The easiest way to locate them is to find the bright star Aldebaran to the right and a little above of the line of the Orion's Belt and then look 50% farther to the right, roughly in the same direction, but a little lower. The Pleiades are quite spectacular even in binoculars.

XII.3. Hyades (Aldebaran region).

Hyades are right next to the star Aldebaran. Not as spectacular as the Pleiades, but in bigger magnification you can see many more stars.

XII.4. Lambda-Lambda asterism.

The name of this asterism comes from the fact that its shape resembles the letter lambda, and its central star is Lambda Orionis (Meissa) – the “head” of the Orion constellation.
By the way, this asterism is a great way to verify what is the current range of your observing tool. When you buy a telescope you are given its theoretical range, but in the middle of a city with big light pollution you will never see such weak stars. Thanks to this asterism (or rather its main part) you can judge the current range yourself. It works also for binoculars that are NOT given theoretical range at all.

When I was playing around on the site stellarium-web.org I noticed that when very few stars are visible this asterism looks like a mirrored letter L. What's more important the brightest stars appear almost one by one, which is very important to my idea. Here's the crucial part of the asterism seen with a very deep range.
I noted the magnitudes of most the stars in the crucial part of the asterism AND I numbered the 11 brightest ones.
In my 70/700 refractor with the magnification 28x I could see clearly more than 11 stars, so the then range of my telescope was definitely over 9.


XII.5. Andromeda Galaxy (M31) – my first “faint fuzzy”.

In this post:
Binoculars and spotting scopes brightness comparison
I described how to find the Andromeda Galaxy in detail, but you need a big part of the night sky to do it that way. Please notice that I made that post in a totally different time of year, so now this part of the night sky looks almost upside-down, like this:
Instead, you can visit the site stellarium-web.org and search for the constellation Cassiopeia and find the crucial triangle of stars right away. Then you have to extend the “bottom” line of this triangle to the “right” by a little more than 100% and a little “below” this line there is the Andromeda Galaxy. Please remember that the concepts “bottom”, “right” and “below” change CONSTANTLY, so you have to be careful. In this case the “bottom” can be defined as the side of the triangle with 4 stars.

XII.6. Alpha Persei Cluster (Mirphak region).

The star Mirphak is bright enough to be visible to the naked eye. The first time I have ever looked in that direction in my small telescope the observing conditions were very weak, but the view was interesting anyway.

XII.7. NGC 869 (h Persei) and NGC884 (chi Persei).

Outside a city, under relatively dark skies and through binoculars the Double Cluster looks very good, but it's very small. From my balcony I can't see it with binoculars at all. I did find it in my 114/900 Dobson and it looked better than I expected.

XII.8. M34.

From my balcony I can't see this open star cluster with binoculars at all. I did find it in my 114/900 Dobson. To me M34 looks like a flying bird with a long neck.



XII.9. M35.

From my balcony I can't see this open star cluster with binoculars at all. M35 is high “above” the constellation of Orion. Seeing M35 in my 114/900 Dobson gave me a true WOW effect. Even in my wildest dreams I would never imagine that an open star cluster can look so good from my balcony. The best descriptions that comes to my mind is “rich in stars”.

XII.10. Praesepe (M44).

There is a very easy way to find Praesepe. First of all you should go to the site stellarium-web.org and search for the constellation Gemini (Twins). In big light pollution you won’t be able to see most of its stars, but when you know in what direction to look then you can find the 2 crucial stars – the heads of the twins.



Imagine a line between these two stars and extend this line by around 300% to the left and a little above this line there is Praesepe.


This open star cluster is quite interesting, but the stars are not as bright as in the Pleiades. I found Praesepe with my 12x60 binoculars (magnification x12 and FOV of 5.3 degree), but the view was shaky.

This open star cluster is even better to verify what is the current range of your observing tool than the Lambda-Lambda asterism, especially in my 114/900 Dobson.

XII.11. Coma Berenices Star Cluster (Melotte 111).

This star cluster is rarely mentioned on the Internet, but in the binoculars it's SPECTACULAR! When I saw it in my 12x60 binoculars for the first time I was stunned! I was not prepared for what I saw – it was totally a WOW effect!

Go to the site stellarium-web.org and search for the constellation Leo. In big light pollution you won’t be able to see most of its stars, but when you know in what direction to look then you should be able to find the 4 crucial stars.



Imagine a line between the two top stars and extend this line by around 130% to the left and a little above this line there is the Coma Berenices Star Cluster.


Please notice that the star Gamma Comae Berenices (“15 Comae Berenices”), which is a part of the star constellation Coma Berenices, is on the edge of the Coma Berenices Star Cluster. The best part of this cluster is a little BELOW this star!


In my 12x60 binoculars I could see the whole area above, but in a telescope the FOV is smaller, so you won't be able to see everything at once.

XII.12. Coathanger asterism (Collinder 399)

This asterism really looks like a coathanger! It's relatively easy to find even from my balcony. Go to the site stellarium-web.org and search for the stars Vega and Altair. These stars are one of the brightest stars in the sky, so they are easily visible even from my balcony. The Coathanger asterism is between them, closer to the star Altair, as shown below. There is also a third relatively bright star (marked with yellow circle) that can be helpful, if you can see it.


The third star (marked with yellow circle) is called Albireo and it's actually a double star with a striking colour contrast between the brighter yellow star and its fainter blue companion. It was visible even in my 114/900 Dobson!

XII.13. Hercules Globular Cluster (M13) – another “faint fuzzy”.

The M13 is the first night sky object that I found after simulating light pollution for a particular hour of observations thanks to the free program Stellarium. Previously, when I was using the website stellarium-web.org, I was simulating light pollution by setting the time to an early hour, but the star constellations were tilted then.

To find the M13 you have to start with the stars Vega and Altair.

The yellow circle marks a crucial star that is “the point of an arrow”. The arrow is very easy to locate in 8x42 binoculars because the field of view is “almost big enough” then. A little below to the left there is the M13.

XII.14. Bright stars.

Even if there is a time of year when you can't see “anything interesting” from you balcony, you can simply look at bright stars. Some of them look literally like diamonds in the sky and some other show some strong colors (blue, yellow, orange or almost red). They all look cool in a small telescope.

XII.15. Scan the night sky in a totally random way.

You can scan the night sky in a totally random way and still have fun! Well, there are so many interesting night sky objects, including relatively bright stars that I hardly ever do it, but sometimes when I try to locate a specific target I find a cool small unnamed asterism by sheer accident and I say to myself: “Wow, it looks cool!”

PS. There are many other interesting night-sky objects that can be seen in a small telescope, but finding some of them is quite a challenge. From my own experience I can say that every observing session teaches you something new and month after month you can feel more and more comfortable at using your telescope.

Clear skies!