For satellites moving in circular orbits around Earth

PHYSICS · Multi-part · CBSE · Physics · Gravitation · Gravitation

Problem

For satellites moving in circular orbits around Earth, the relation

T^{2}=k\,r^{3}

holds, where

T

is the orbital period and

r

the orbital radius. (i) A satellite with period

24\,\text{h}

orbits at a radius of

4.24\times10^{7}\,\text{m}

. Taking

T

in hours and

r

in metres, calculate the numerical value of the constant

k

. (ii) Using the value of

k

obtained in part (i), find the orbital radius (in kilometres) required for a satellite to have a period of

90\,\text{min}