Question

The orbital period of sa satellite near the surface of the planet of radius R is given by (`rho` is the density of the planet):
A. `(3pi)/(rho G)^(1//2)`
B. `(4pi)/(3rho G)^(1//2)`
C. `(4pi)/(rho G)^(1//2)`
D. `(3pi)/(4rhoG)^(1//2)`

Answer 1

Correct Answer - 1
`(Mv^(2))/(r )=(GMm)/(r^(2))`
`&v=(2pir)/(T)`
`therefore T=(2pir^(3//2))/(GM)^(1//2)`
`For r =R & M = (4)/(3) pi R^(3) rho`
`T=((3pi)/(rhoG))`