Question

(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 (½)°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.

Answer 1

Diameter of the earth as seen from the moon is about 2°.

(b) At earth-moon distance, moon is seen as (1/2)° diameter and earth is seen as 2° diameter. Hence, diameter of earth is 4 times the diameter of moon.

D_earth/D_moon = 4

(c) R_sun/r_moon = 400

(Here r stands for distance, and D for diameter.)

Sun and moon both appear to be of the same angular diameter as seen from the earth.

(D_sun/r_sun)/(D_moon/r_moon)

(D_sun/D_moon) = 400

But D_earth/D_moon = 4 

D_sun/D_earth = 100.