Question

Obtain an expression for time period of a satellite orbiting very close to earth’s surface in terms of mean density.

Show that, \(T = \sqrt{\frac{3\pi}{G\rho}},\) where ρ = mean density of earth

Answer 1

Time period in terms of mean density:

where ρ = mean density of the earth

c. Substituting, the value of M in the equation (i),

d. When satellite is orbiting very close to the earth, h ≈ 0.

\(\therefore\) Equation (ii) becomes,