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How to Observe the Moon
We can look directly at the Moon with no eye protection required (unlike with the Sun even though they both have the same angular diameter). And, as the brightest object (most of the time) on the night sky, it's a really good starting point for any beginner amateur astronomer and astrophotographer. Here we'll focus mainly on the observing part.
How to observe our satellite? To answer to this question, let me first ask you What do you want to see? or more precisely What kind of details you are hoping to detect? Thus, let's split the answer to your question in a few sections, depending upon your equipment or lack of such.
Observe the Moon with naked eyes
This is the easiest way of looking at the Moon. No equipment required. However, you won't be able to see much details - probably just the Moon seas. So that may not be the best way to go. Nevertheless, you could see the Moon phases without difficulty.
Observe the Moon with a binocular
Using a binocular could help a lot in finding large craters and some other big features on the Moon surface. Also, binoculars don't require much space and you could easily carry them around when you are on an observing trip somewhere.
Average astronomical binoculars usually have magnification in the range 8x - 15x, but there are exceptions. Magnifications of 5x or less would not be very practical, unless, of course you are admiring opera concerts :). With larger magnifications one would usually need a tripod to make the object of interest not wander in your filed of view. Build-in image stabilization would help a lot to observe the Moon, or anything else for that matter, but that would bump up the price of the binocular.
Observe the Moon with a telescope
Telescopes are more powerful than binoculars and also could provide the largest variety of magnifications - from 30-50 up to... as much as you can make it. Keep in mind that extremely high magnifications (> 300-400, although your system will be a major factor determining that number) may not be so desirable. The image will be blurry and even the smallest vibration will make your view to jerk in all directions. No matter what kind of magnification you would use, you would need a sturdy mount, and if it has a guiding motor so much the better.
So, with a decent set of eyepieces (40, 25, 10 and 6 mm) you could have a nice span in magnifications to observe the Moon. Your telescope is also very (if not most) important part of your observing experience. 4.5-6'' aperture would do just fine. You could get a decent image even with less than 4.5'' telescope, but you won't be able to use larger magnifications. The best case would be something like 8-10'' telescope. Well, the best case is to use as a large telescope as you could find, but let me remind you that this site is oriented toward beginners who might no be able to, or want to, find/buy something huge.
Observe the Moon with naked eyes
This is the easiest way of looking at the Moon. No equipment required. However, you won't be able to see much details - probably just the Moon seas. So that may not be the best way to go. Nevertheless, you could see the Moon phases without difficulty.
Observe the Moon with a binocular
Using a binocular could help a lot in finding large craters and some other big features on the Moon surface. Also, binoculars don't require much space and you could easily carry them around when you are on an observing trip somewhere.
Average astronomical binoculars usually have magnification in the range 8x - 15x, but there are exceptions. Magnifications of 5x or less would not be very practical, unless, of course you are admiring opera concerts :). With larger magnifications one would usually need a tripod to make the object of interest not wander in your filed of view. Build-in image stabilization would help a lot to observe the Moon, or anything else for that matter, but that would bump up the price of the binocular.
Observe the Moon with a telescope
Telescopes are more powerful than binoculars and also could provide the largest variety of magnifications - from 30-50 up to... as much as you can make it. Keep in mind that extremely high magnifications (> 300-400, although your system will be a major factor determining that number) may not be so desirable. The image will be blurry and even the smallest vibration will make your view to jerk in all directions. No matter what kind of magnification you would use, you would need a sturdy mount, and if it has a guiding motor so much the better.
So, with a decent set of eyepieces (40, 25, 10 and 6 mm) you could have a nice span in magnifications to observe the Moon. Your telescope is also very (if not most) important part of your observing experience. 4.5-6'' aperture would do just fine. You could get a decent image even with less than 4.5'' telescope, but you won't be able to use larger magnifications. The best case would be something like 8-10'' telescope. Well, the best case is to use as a large telescope as you could find, but let me remind you that this site is oriented toward beginners who might no be able to, or want to, find/buy something huge.