you have to choose your time carefully to get good shadows
How exactly should I go about choosing appropriate time, what should I take into account? Are there any samples of "bad" and "good" timed photos?
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If "to get good shadows" he means shadows cast by surface features on the moon, thats entirely a matter of opinion. The moon has dozens of faces, from thin crescents, normal crescents, half moons, gibbous moons, full moons for both waxing and waning, as well as eclipsed moons. I've shot the moon a lot myself, and I can't say there is any "right time". Its the moon, its ever present and always beautiful. Don't limit yourself.
I've never really considered what time I've photographed the moon...it never really seemed to be a factor. I've shot the moon at all times, all phases, day, sunset, night and early morning, in the clouds, above the trees, over cities, and solo. I've shot it in and out of focus, with and without feature shadows. It doesn't really matter what time you photograph the moon. It has a thousand faces, and each one is pretty amazing.
(Note: The only thing that really does matter is focal length. Most of my shots are taken at 400mm, more simply because that is the lens I have than anything else. Longer lenses can be useful in gathering more surface detail, however they can also limit your creativity. With a high resolution camera, you might be surprised how much detail you can get out of the center of the frame at 400mm, and the shorter focal length often lets you capture intriguing foreground detail as well as the moon itself.)
Here are some of my moon shots on 500px:
Here are a few more I have yet to publish anywhere:
Photographing the moon is a lot like shooting a portrait.
When the moon is full the light hitting the moon is coming from your direction, this is flat light, you can get a lot of details but you can't see and texture in the moon because there are no shadows (think about it as the on-camera flash of lunar photography).
When the moon is a thin crescent the light is hitting it from the side, you get shadows and a nice texture but you only see a small part of the moon - and unlike a a portrait you can't use fill flash :-)
Any time between those two extremes is, well, between those two extremes - the smaller the moon is the more shadows and texture you get and the right time is a creative decision and depends mostly on your preference.
I think there are good and bad times to photograph the moon, mostly related to the distance it is from you.
In below link, author mentions about the right time and other details for shooting the full moon, crescent etc.
The moon is a sunlit 11% grey rock that subtends about 1/2 a degree of arc. So even though it is night for you where you are the moon is still in sunlight! The moon also will cross its own diameter from the point of view of your lens in about 2 minutes.
The real problem is that it is small, and you can get closer to it, so you need a really long lens. The normal way to do that is to get a telescope and put a camera adapter on it. The good news is that you can get a 90mm telescope for under $250 and put a camera adapter on it from Orion Telescopes.