Actually, choosing binoculars for astronomy is a lot like choosing a telescope for astronomy; the bigger the aperture the better - within limits of course.
10x50's will do fine in most circumstances, but you will be surprised at how many more stars you will see with 11x70s. They gather considerably more light than the 10x50's, and this is what you really need. Most 11x50's are still light enough that they can be held steadily by bare hands, but any of the larger binos (like 12x80's, or 15x100's will require a tripod.
In 10x50, the ten refers to the magification, and the 50 refers to the aperture Divide the aperture by the magnification, and you get the "exit pupil" - a very important consideration in binos. Most younger people (under 30) have a night time pupil size of between 5 and 7mm. For optimal "seeing" with binos' you want the "exit pupil" of the eyepiece to match the size (or fall within the range ) or your night time pupil. For an older person over say, 50, their night time pupil size might be only 4 mm, and therefore the excess light in a 7mm exist pupil would be wasted - it would fall outside of the pupil and therefore be unseen. they would be better off with binos of slightly higher magnification to aperature size; 15x70's would produce an exist pupil of about 4.5 - much more suited to their night time viewing.
Carl