A geostationary satellite remains fixed over a point on the Earth’s equator

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

Problem

A geostationary satellite remains fixed over a point on the Earth’s equator. The Earth completes one rotation about its axis in

24\,\text{h}

. Take

GM_{\text{E}} = 3.986\times10^{14}\,\text{m}^{3}\,\text{s}^{-2}

and

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

. (i) Derive an expression for the height

h

of a geostationary satellite above the Earth’s surface in terms of

R_{\text{E}}

G

M_{\text{E}}

and the Earth’s rotational period. (ii) Calculate the numerical value of

h

. (iii) Determine the linear speed and the centripetal acceleration of the satellite at this height. (iv) Compare the centripetal acceleration obtained in part (iii) with the value of

g

at the Earth’s surface.

Related theory

Circular & Orbital Motion Dynamics
Satellites & Orbital Motion
Gravitation
Geostationary and polar satellites
Orbital motion
Earth satellites

Browse the problem library