Taking a great moon picture where the moon is the only subject is relatively simple. Taking a great moon picture where the moon is a background subject is a bit trickier. All too often, either the moon or the foreground object appears to be out of focus. However, with a few photography tips, you'll be able to take great pictures with the moon in the background.
You need a camera with shutter speed and aperture controls and a zoom lens that is about 300mm or 10x zoom. A tripod is a helpful... accessory.
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While it is tempting to use a large aperture with a moon-only photo, the resulting shallow depth of field can be a problem when the view includes items in the foreground that you want to be in focus. While no aperture allows a depth of field large enough to put a subject here on Earth and the moon both in perfect focus, a small aperture—a large f-stop—prevents the moon from being nothing more than a blur of light.
Standing far away from your foreground subject helps compress the distance between... the foreground subject and moon for the lens. Zoom lenses usually result in a shallow depth of field, but when you work with such a huge distance, the quirk of zoom lenses that tends to flatten a scene becomes a plus.
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Because light values are usually so different between the moon and the foreground subject you plan to photograph, it is best to bracket the exposures so that you capture the best possible combination. Use at least two series of five shots each.
For the first series, use the largest exposure compensation set from -2 to +2. This means you take one shot at -2, one at -1, one at normal, one at +1, and one at +2. For the second series, set the largest compensation at -1.5 through... +1.5. This way, your second series has images shot at -1.5, -0.5, normal, +0.5, and +1.5 (depending on your camera's design.)
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Choose Time of Shot Carefully
Much like with moon-only photos, photos shot before complete dark are often the easiest to get right when there is a foreground subject. In addition to the change of light color with early morning and late evening, the intensity of the light changes. Just before dark, at civil twilight and later at nautical twilight (Definitions at Naval Observatory Website), light on Earth appears to intensify on objects that the sun still touches, such as mountain tops, because of the contrast between... surrounding shadowed objects. These are good times to take moon photos that have foreground subjects because there is still some natural light, but most objects are in shadow. Lit cityscapes are also easily visible at this time.
The moon appears largest just after it rises, which is usually—but not always—just after sunset. (Several days each month, the moon rises shortly before sunset.) The first 30 minutes after the moon rises, it appears much larger in the sky than later. Your photos can capture more dramatic photos and more detail at this time.