Calculate the ratio of the mean densities of the earth and the sun from the following approximate data.
θ = angular diameter of the sun seen from the earth = 
.
λ = length of 1º of latitude on the earth's surface = 100 km.
T = one year = 3 × 10 7 s.
g = 10 ms –2 .
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Sol. Let r be the distance between the sun and the earth, M e and M s be the masses and R e and R s be the radii of the earth and the sun respectively, and G be the gravitational constant. We then have
= M e r ω 2 ,
= 
= 
rad,
i.e. r = 
.
The above gives 
= ω 2 ,
or 
= 
.
For a mass m on the earth's surface,
= mg,
Giving 
= 
= 
= 
.
Hence 
= 
= 3.31.
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