A satellite of mass is required to move in a circular orbit of altitude above the…

PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

A satellite of mass

700\,\text{kg}

is required to move in a circular orbit of altitude

300\,\text{km}

above the Earth’s surface. The mass of the Earth is

5.97\times10^{24}\,\text{kg}

and its radius is

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

. The universal gravitational constant is

6.67\times10^{-11}\,\text{N m}^{2}\text{kg}^{-2}

. (i) Name the real force that provides the necessary centripetal force for the satellite. (ii) Derive an expression for the orbital speed

v

of a satellite moving in a circular orbit of radius

r

around the Earth, expressing your answer in terms of

G

M_{E}

(mass of Earth) and

r

. (iii) Using the expression obtained, calculate the orbital speed and the time period of revolution of the satellite at the given altitude.