(a) The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?

(b) Moon is seen to be of ( �)° diameter from the earth. What must be the relative size compared to the earth?

(c) From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of sun-earth diameters.

(a) Given:

Distance between earth and moon = 60 x earth’s radius

The distance between the earth and moon can be treated as a radius of arc that is subtended by the diameter of the earth from the moon. Let θ be the angle subtended by the arc, R be the earth-moon distance and R_E be the earth’s radius. Then,

2R_E = length of the arc.

And distance between earth and moon = 60R_E

Therefore the angle subtended by the arc

Therefore the diameter of earth as seen from earth will be 2°.

(b) Given:

Diameter of moon as seen from earth =

As calculated before the diameter of earth as seen from moon is approximately 2° and if moon is as seen from earth, then,

Therefore, earth’s diameter is 4 times that of moon’s diameter.

(c) Given:

Distance between sun and earth = 400 x earth-moon distance.

let r_{m �} be the moon’s distance from earth and r_S be the sun’s distance from earth, then we have

Let D_s, D_{m �} and D_e be the diameters of sun, moon and earth respectively. Since we know that the sun and the moon, appear to be the same size from the earth, we have

Also

Therefore, the sun’s diameter is 100 times larger than earth.