If T is the period of revolution of an artificial satellite orbiting very close to the earth's surface and `rho` is the density of the earth, then show that `rho T^2` is a universal constant.

Explanation

The period of revolution of an artificial satellite orbiting very close to the earth.s surface is given by
`T=2pi sqrt(R/g),` R=radius of the earth
g=acceleration due to gravity on the earth.s surface
We know that the average density of the earth is given by
`rho =(3g)/(4pi GR) or, R/g=(3)/(4pi G rho)`
`therefore T=2pi sqrt(3/(4pi Grho))`
or, `T^2 =(4pi^2xx3)/(4pi G rho) or, rho T^2=(3pi)/G` (a universal constant)