(a) The earth- moon distance is about 60 earth radius. What wil be the diameter of the earth (approximately in degress) as seen from the moon ? (b) Moon is seen to be of `(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.

Explanation

(a) As is clear from fig. 1(EP). 1,
`theta = (l)/(r ) = (2R_e)/(60R_e) = (1)/(30)radian = (1)/(30)xx(180^@)/(pi) = (6^@)/(pi) = (42@)/(22) = 1.9^(@)`.
(b) As is clear from fig. `1 (EP).2`,
`theta = (I)/r ) = (2R_m)/(60R_e) = (1^@)/(2) = (1)/(2)xx(pi)/(180) rad`
`:. (R_m)/(R_e) = (30pi)/(2xx180) = (pi)/(12) = (11)/(42) = (1)/(4)`.


(c ) We are given `("distance of sun from earth")/("distance of moon from earth") = (r_(sun))/(r_(moon)) = 400`
We have to calculate ` = ("diameter of sun")/("diameter of earth") = (D_(sun))/(D_(earth)) = ?`
As seen from the earth, both sun and moon appear to be same angular diameter. `:. theta = (D_(sun)/(r_(sun)) = (D_(moon))/(r_(moon))`
`(D_(sun))/(D_(moon)) = (r_(sun))/(r_(moon)) = 400 ... (i) `
From (b) above, ` (D_(earth))/(D_(moon)) = 4 ...... (ii) `
:. Dividing (i) by (ii), we get = `(D_(sun))/(D_(earth)) = (400)/(4) = 100`