Physics

Problem

A research satellite orbits a planet very close to its surface (altitude

h \ll R

). The planet is a sphere of uniform density

\rho

and radius

R

. Show that the time period

T

of the satellite depends only on

\rho

and

G

, and calculate the value of

T

\rho = 3000\,\text{kg/m}^{3}

and

G = 6.67 \times 10^{-11}\,\text{Nm}^{2}/\text{kg}^{2}