A planet of small mass `m` moves around the sun of mass `M` along an elliptrical orbit such that its minimum and maximum distance from sun are `r` and `R` respectively. Its period of revolution will be:

Options

A. `2pisqrt(((r+R)^(3))/(6GM))`
B. `2pisqrt(((r+R)^(3))/(3GM))`
C. `pisqrt(((r+R)^(3))/(2GM))`
D. `2pisqrt(((r+R)^(3))/(GM))`

Answer

C

Explanation

`T=2pi((a^(3))/(Gm))^(1//2)` (Kepler's law)
and `a=(r+R)/2`, Hence `T=pisqrt(((r+R)^(3))/(2GM))`.