HOW DID YOU FIND THE ANGLE SUBTENDED AT THE MOON BY THE EDGES OBSERVED FROM TWO DIFFERENT POINTS ON THE EARTH??
Asked by jaswinder
| 25th May, 2012,
11:16: AM
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
)
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
)
Answered by
| 25th May, 2012,
12:14: PM
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