An artificial satellite revolves around a planet in circular orbit close to its surface. Obtain the formula for period of the satellite in terms of density U and radius R of planet.

Explanation

Period of satellite is given by,
` T = 2pi sqrt((R + h)^3)/(GM))`
Here, the satellite revolves close to the surface of planet, hence h is negligible, hence `R + h R`
`rho = M/V`
` therefore M = rho V ` …(2)
As planet is spherical in shape, volume of planet is given as
`V = 4/3 pi R^3`
` therefore M = 4/3 pi R^3 rho ` .....(3)
Substituting the values form eq. (2) and (3) in Eq. (1), we get
`T = 2pi sqrt((R^3)/(G xx 4/3 pi R^3 rho))`
` therefore T = sqrt((3pi)/(G rho))`