Assume that the average distance of the sun from the earth is 400 times the average distance of the moon from the earth. Now consider a total eclipse of the sun and state conclusions that can be drawn about (a) the relation between the sun's diameter and the moon's diameter; (b) the relative volumes of sun and moon. (c) Find the angle intercepted at the eye by a dime that just eclipses the full moon and is placed at a distance of 2 m from your eye. From this result and the given distance between moon and earth, estimate the diameter of the moon. Use 20 mm for diameter of dime

a) Since the sun is 400 times a moon's distance from earth, that must mean it looks 400 times smaller than it would if it were a moon's distance away. If the moon eclipses the sun perfectly, then that means that the sun is 400 times larger than the moon. Therefore the diameter of the sun is also 400 times larger than the diameter of the moon.

b) If the sun is 400 times bigger than the moon, then the radius of the sun is also 400 times bigger than the radius of the moon. The volume of a sphere is given by 4 3 π r 3 43πr3. If the moon's radius is r, then the sun's radius is 400r. The volume of the sun will then be 6.4*107 times larger than the volume of the moon.

c) the angular size is 2 arctan 0.09 ≈ 10.286 2arctan⁡0.09≈10.286. Using similar triangles, where the height of the new triangle is the given distance to the moon from Earth, then I would calculate the diameter of the moon as 2 ⋅ (3.8 * 10 5) tan 5.14 2⋅ (3.8*105) tan⁡5.14 kilometers ≈ 6.84 * 10 4 ≈6.84*104 kilometers.