If a satellites is revolving close to a planet of density `rho` with period `T`, show that the quantity `rho T_(2)` is a universal constant.

Answer

A

Explanation

Close to earth, `T = 2 pisqrt((R)/(g)) = 2 pi sqrt((R)/(GM//R^(2)))`
or `T^(2) = (4 pi^(2) R^(3))/(GM)`
`= (4 pi^(2) R^(3))/(G((4)/(3) pi R^(3) rho))`
or `rhoT^(2) = (3 pi)/(G) = a` aniversal constant