Question

1. 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?
2. Moon is seen to be of (½)°diameter from the earth. What must be the relative size compared to the earth?
3. 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. As the distance between moon and earth is greater than the radius of the earth, then radius of the earth can be treated as an arc.

According to the problem,

R, = length of arc

Distance between moon and earth = 60 R_E

So, the angle subtended at distance r due to an arc of length `l` is

`θ_E = l/r = (2R_E)/(60  R_E) = 1/30` rad

= `1/30 xx 180^circ/pi` degree

= `6^circ/3.14` degree

= 1.9° ≈ 2°

Hence, the angle is subtended by the diameter of the earth 2θ = 2°.

b. According to the problem, the moon is seen as `(1/2)^circ` diameter from the earth and the earth is seen as 2° diameter from the moon.

As θ is proportional to diameter,

Hence, `"Diameter of earth"/"Diameter of moon" = 2/((1/2))` = 4

c. From parallax measurement given that the sun is at a distance of about 400 times the earth-moon distance, hence, `r_("sun")/r_("moon")` = 400

Sun and moon both appear to be of the same angular diameter as seen from the earth. (Suppose, here r stands for distance and D for diameter)

∴ `D_(sun)/r_(sun) = D_("moon")/r_("moon")`

⇒ `D_(sun)/D_("moon")` = 400

But `D_(earth)/D_("moon")` = 4

⇒ `D_(sun)/D_(earth)` = 100