|MadSci Network: Astronomy|
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 104 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 105 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
Practice Finding Angular Size
Diameter of Earth
Our Place in the Universe
Try the links in the MadSci Library for more information on Astronomy.