Two communication satellites A and B revolve around the Earth in separate circular orbits

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

Problem

Two communication satellites A and B revolve around the Earth in separate circular orbits. Satellite A takes

6\,\text{h}

to complete one revolution, while satellite B takes

12\,\text{h}

. (i) Derive the general relation between their orbital radii

r_{A}

and

r_{B}

in terms of their respective periods

T_{A}

and

T_{B}

. (ii) Using the relation obtained, find the numerical ratio

\dfrac{r_{B}}{r_{A}}

. (iii) Taking the Earth’s radius as

6.37\times10^{6}\,\text{m}

, calculate the difference in heights of the two satellites above the Earth’s surface.