A research team is comparing satellite speeds in two Earth orbits

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

Problem

A research team is comparing satellite speeds in two Earth orbits. Data to be used (take numerical values only if required):

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

M_{\rm E}=5.97\times10^{24}\,\text{kg}

R_{\rm E}=6.37\times10^{6}\,\text{m}

. (i) Derive an expression for the speed

v

of a satellite moving in a circular orbit of radius

r

around a planet of mass

M

. (ii) Using the data above, calculate the orbital speed of (a) a low-Earth satellite at an altitude of

300\,\text{km}

and (b) a communication satellite in a circular orbit of radius

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

(close to geostationary). (iii) Find the percentage by which the speed in part (a) exceeds the speed in part (b).