A geostationary satellite always remains above the same point on the Earth’s equator.

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

Problem

A geostationary satellite always remains above the same point on the Earth’s equator. (i) Derive an expression for the radius

r_g

of its circular orbit in terms of

G

M_E

, and the Earth’s rotational period

T_E

. (ii) Using

T_E = 24\,\text{h}

GM_E = 3.986\times10^{14}\,\text{N\,m}^2\!\text{/kg}

, and

R_E = 6.4\times10^{6}\,\text{m}

, calculate

r_g

. (iii) Determine the altitude of the geostationary orbit above the Earth’s surface and the orbital speed of the satellite.