# Substended angle, rotational kinematics

1. Aug 28, 2011

### bulbasaur88

The moon has a diameter of 3.48 x 10^6 m and is a distance of 3.85 x 10^8m from the earth. The sun has a diameter of 1.39 x 10^9 m and is 1.50 x 10^11 m from the earth.

(a.) What are the angles (in radians) subtended by the moon and the sun, as measured by a person standing on the earth.

Because the large planetary masses are so very far away, we can assume that s = diameter

Θ = s/r

For the moon:
S = 3.48E6 m
r = 3.85E8 m
Θ = s/r = 3.48E6/3.85E8

For the sun:
S = 1.39E9 m
r = 1.50E11 m
Θ = s/r = 1.39E9/1.50E11

(b.) Based on the answers to part (a.), is a total eclipse of the sun really "total"?

No, because the angles are not perfectly equal.

(c.) What is the ratio (as a percentage) of the apparent circular area of the moon to the apparent circular area of the sun?

For part C, do I just use Pi(radius)2 and compare the two areas? I just don't understand stand what they mean by "apparent" circular area. Is this problem just to emphasize how much larger the sun is than the moon?

Last edited: Aug 28, 2011
2. Aug 28, 2011

### kuruman

By "apparent" circular area they mean the circular area as it appears to you. Imagine that the moon and the sun as you see them in the sky are two circles on a table in front of you. What will you say the ratio of the areas is?