Wednesday, 27 November 2013

What is the angular diameter of Earth as seen from the Moon?

The average angular diameter of the Moon, as seen from the Earth, is about 31 arcminutes.



The angular diameter depends on the distance between the two objects and the diameter of the object being viewed. Specifically, for small angles, it is the diameter divided by the distance. When the distance is the same, the angular size is proportional to the diameter.



The distance remains the same when viewing the Earth from the Moon, but the Earth is larger. According to NASA, the diameter of the Moon is 3,476 km, and the diameter of the Earth is 12,756 km.



So, because it's proportional, the angular diameter can be calculated as follows:



$a_{Earth} = a_{Moon} times {d_{Earth}over d_{Moon}}$



$ = 31 arcminutes times {12,756 km over 3,476 km}$



$ approx 114 arcminutes$, or just under 2 degrees.



This is approximate, because not only is this valid only for small degrees, where the tangent of an angle can be approximated by the angle itself (in radians), the Earth-Moon distance varies because the Moon's orbit around the Earth is an ellipse.

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