MadSci Network: Astronomy |

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Hi, Justin,

In order to calculate the angular size of an object (in degrees), you
divide the size of the object by its distance, being careful to use the
*same units*. Then you multiply that value by 360/2 pi (1).

If you were to stand five feet away from a picture of the Earth that is seven inches across, then

(7 in)/(60 in) x (360/2 pi) ~ 7 degrees

For comparison, the full Moon as viewed from Earth subtends about 1/2 degree(3). The Big Dipper subtends about 20 degrees and your fist at arm's length will subtend about 10 degrees(4).

You also asked how far you would have to be from your seven-inch image
for it to be the same angular size as the Earth as viewed from the Moon.
If Earth has a diameter of 1.28 x 10^{4} km(2),
your image of the Earth is
seven inches (1.78 x 10^{-4} km) in diameter, and the Moon is about 3.85
x 10^{5} km from Earth(5), you can solve for the
distance "d"

(1.78 * 10^-4 km)/d = (1.28 * 10^4 km)/(3.85 * 10^5 km) (1.78 * 10^-4 km) = d(1.28 * 10^4 km)/(3.85 * 10^5 km) d = (1.78 * 10^-4 km)/((1.28 * 10^4 km)/(3.85 * 10^5 km)) d = 0.00534 km = about 18 feet

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