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Question
- 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?
- Moon is seen to be of (½)°diameter from the earth. What must be the relative size compared to the earth?
- 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.
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Solution
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 RE
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
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