(a) Given:
θ = \(\frac{l}{r}\), l = RE
r = 60 RE
θ = \(\frac{R_E}{60R_E}=\frac{1}{60}rad \simeq 1°\)
Hence, angle subtended by diameter of earth = 2θ = 2°
∴ Diameter of the earth as seen from the moo is about 2.
(b) At earth-moon distance, moon is seen as \((\frac{1}{2})°\)diameter and earth is seen as 2° diameter. Hence, diameter of earth is 4 times the diameter of moon.
\(\frac{D_{earth}}{D_{earth}}=\frac{({2}{\pi})rad} {(\frac{1}{2\pi})rad}=4\) .....(i)
(c) From parallax measurement, sun is at distance of about 400 times the earth-moon distance,
\(\frac{r_{sun}}{r_{moon}}=400=\frac{D_{earth}}{D_{earth}}\) .....(ii)
(Here r stands for distance and D for diameter.)
Dividing eqn (ii) by (i)
We get,
\(\frac{D_{sun}/D_{moon}}{D_{earth}/D_{moon}}=\frac{400}{4}\)
∴\(\frac{D_{sun}}{D_{earth}}=100\)