Question

A satellite is revolving very close to a planet of density D. What is the time period of that satellite?

(a) [3/(D*G)]^1/2

(b) [3/(D*G)]^3/2

(c) [3/(2*D*G)]^1/2

(d) [(3*G)/D]^1/2

The question was posed to me in homework.

My enquiry is from Gravitation topic in chapter Gravitation of Physics – Class 11

Answer 1

Right choice is (c) [3/(2*D*G)]^1/2

For explanation I would say: The time period of a satellite flying very close to the surface of the earth is;

T = 2 x pi x [R^3 / (G X M)]^1/2;  [Height is negligible compared to the radius of the earth].

Mass (M) = Density (D) x Volume

M = D x (4/3 x pi x R^3)

Substituting the relation of mass into the time period, we get;

T = [3/(2 x D x G)]^1/2