For a novice amateur astronomer, binoculars may be very useful as a first instrument for several reasons: they are relatively inexpensive, have a large field of view and show images "right side up" (which makes finding things in the sky easier), are easily portable and require little to no setup. For more experienced amateurs, they may still be useful for most of the reasons mentioned above, even for those who have (or have access to) more powerful instruments. So, how do you pick good binoculars for amateur astronomy?
Binoculars are basically two small telescopes mounted side-by-side, with a set of internal mirrors and prisms that cause the images to be seen right-side-up and non-mirrored. There are two "models" of internal prisms: "roof" prisms are those used in "straight" binoculars, in which the objectives are exactly aligned with the eyepieces and the optical tube is straight, while "Porro" prisms cause the objectives to be more separated than the eyepieces and the optical tube not to be straight (that is the format that most people think of when thinking of binoculars). Functionally there is almost no difference between the two models, although Porro models tend to give you a wider field of view, while roof models can be more compact than Porro models (and tend to be more expensive).
Binoculars are primarily identified by two numbers; for example, 7x50 or 10x40. The first number denotes the magnification achieved by the binoculars, while the second is the size, in millimetres, of the objective (front) lenses. Both numbers are important, and are a good starting point to pick the best possible instrument.
First, magnification, or power. That indicates how much larger an image will appear than if you were just using your eyes. It may seem that the larger this number is, the better, but that is not necessarily so. For astronomy use, unless you intend to use a tripod, magnifications between 7 and 10 are the most indicated. Anything over 12 will cause the image to shake way too much, unless the instrument is stabilized (by a tripod, for example).
Now, lens size, or aperture. The reason this number is important is that it tells you how much light the instrument gathers. Binoculars not only magnify the objects you're seeing, they also act as larger light receptors than your eyes. Your pupils, when you're in a dark location and fully adapted to the light conditions, will have a diameter of between 5 and 7 millimetres (the younger you are - as an adult -, the closer to 7mm it is; as you get older, it gets smaller). Since the light gathering ability is defined by the area of the objective, a 50mm binocular will gather over 50 times more light than your naked eyes. This will increase your limiting magnitude by around 4, under dark conditions (from 6 to 10, for example).
As a general rule, any aperture smaller than 40 millimetres in useless for astronomy; you simply will not get enough light into your eyes. 50 is a good size; anything much larger will be, well, too large and too heavy for comfortable use. It will be significantly more expensive, as well.
Power and aperture together define another interesting measure: the exit pupil. That is the size of the image that is formed on the eyepiece and that, ultimately, is delivered to your eyes; you can get this size by dividing the aperture by the magnification power (for a 7x50 binocular, the exit pupil will be 50/7 = 7.14mm). Ideally, this should be exactly the same size as your dark-adapted pupil or very slightly smaller, so that your whole pupil is used in collecting light and no light is wasted. Since pupils are not all the same size, this is clearly impossible; you should shoot for an exit pupil in the range of 5 to 7mm.
In the next article, I'll talk about lens coatings and quality, focusing, field of view and considerations for people who wear eyeglasses (such as myself), closing with some tips on what to do once you are at the store.
While i agree with everything, my primary asto-binoculars are 8x21. There are 3 P's to picking an astronomical instrument. Price, Portability, and Performance. These 8x21 roof-prism binoculars cost $50US, weight 3.5 oz (100 grams) and perform nearly as well as much larger binoculars under my heavily light polluted skies. They're small enough to fit in a pocket, and so there's hardly any excuse not to have them.
These days, however, i do more astronomy with a 10 inch (254 mm) reflector. The 8x21's are handy for finding daytime planets and larger asterisms.
Saturn is my favorite object for comparison of optics. Naked eye, it's a dot. In 8x21 binoculars, it's a line. In a 8x42 binoculars, it has some sort of odd ear like things on it. In a 22x60 spotting scope, the rings are clear. In the 240x254 reflector, the Cassini division is evident. The Huygens probe saw ice rocks 5 cm across on Titan.