(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) Angle subtanded at distance r due to an of length l is

`"Given ",l=R_(E),r=60R_(E)`
`theta=R_(E)/(60R_(E))=1/60rad=1/60xx(180)/pi"degree"`
`=3/piapprox1^(@)`
Hence,angle subtended by diameter of the earth=`2 theta=2^(@)`.
(b) Given that moon is seen as `(1/2)^(@)`diameter and earth is seen as `2^(@)` diameter.
`"Hence"," ""Diameter of earth"/"Diameter of moon"=((2//pi)rad)/((1/2pi)rad)=4`
(c) From parallax measurment given that sun is at a distance of about
400 times the earth-moon distance, hence,`(r_(sun))/(r_("moon"))=400`
(Suppose, here r stands for distance and D for diameter)
sun and moon both appear to be of the same sagular diameter as seen from the earth.
`therefore D_(sun)/r_(sun)=D_("moon")/r_("moon")`
`therefore D_(sun)/D_("moon")=400`
`"But"" "D_("earth")/D_("moon")=4`
`thereforeD_(sun)/D_("earth")=100`