HOW DID YOU FIND THE ANGLE SUBTENDED AT THE MOON BY THE EDGES OBSERVED FROM TWO DIFFERENT POINTS ON THE EARTH??
The angular diameter of a flat circular object (disc) can be calculated using the formula:
in which is the angular diameter, and and are the visual diameter of and the distance to the object, expressed in the same units. When is much larger than , may be approximated by the formula , in which case the result is in radians.
For a round spherical object whose actual diameter equals , the angular diameter can be found with the formula:
The difference is due to when you look at a sphere, the edges are the tangent points, which are somewhat on your side of the facing hemisphere cross section. measures opposite/adjacent, whereas measures opposite/hypotenuse. For practical use, the distinction between the visual diameter and the actual diameter only makes a difference for spherical objects that are relatively close.
For very distant or stellar objects, the Small-angle approximation can also be used:
Which simplifies the above equations to:
- (for small )