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A:
This is basically a geometry
problem. If you look at the diagram above, you'll see that
the angle subtended by the Sun from Earth (call that angle
x) can be solved for by breaking the diagram into triangles.
You'll see that tangent of angle
(x/2) = r/D
(since the tangent of an angle is equal to the opposite side
of the triangle divided by the adjacent side of the
triangle. Also, note that r is the radius of the Sun and D
is the distance from the Earth to the Sun). For small
angles, the tangent of the angle is just about equal to the
angle itself (in radians), so the problem can be simplified
to:
(x/2)=r/D
Now, solve
for x, and you get:
x=2r/D
Now, back to your question, to double
the apparent angle, x, you have to decrease D (the distance
from the Sun) by half (since r, the radius of the Sun is
constant). Remember that this is only for relatively small
vales of x. This calculation works not only for the Sun, but
for planets, too. |
