Show that the altitude of a satellite that remains fixed relative to a point on Earth…

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Show that the altitude

h

of a satellite that remains fixed relative to a point on Earth is given by

h=\left(\frac{G M_{\oplus} T^{2}}{4\pi^{2}}\right)^{1/3}-R_{\oplus},

where

M_{\oplus}

is Earth’s mass,

R_{\oplus}

its radius and

T

the period of Earth’s rotation.