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 in seen to be of  \((\frac{1}{2})^°\)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

(a) Given:

θ = \(\frac{l}{r}\), l = R_E

r = 60 R_E

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,

\(\frac{D_{sun}/D_{moon}}{D_{earth}/D_{moon}}=\frac{400}{4}\)

∴\(\frac{D_{sun}}{D_{earth}}=100\)