Two circular Earth orbits are considered: • A low-Earth orbit (LEO) at an altitude of

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

Problem

400\,\text{km}

. • A geostationary orbit (GEO) whose period equals one sidereal day

(23.93\,\text{h})

. Take Earth’s radius

R_{E}=6.4\times10^{6}\,\text{m}

and mass

M_{E}=6.0\times10^{24}\,\text{kg}

. (i) Find the orbital radius of the geostationary satellite. (ii) Calculate the ratio of orbital speeds

\dfrac{v_{\text{LEO}}}{v_{\text{GEO}}}

. (iii) For a unit satellite mass, compute the total mechanical energy per unit mass in each orbit and hence find the difference

\left(E_{\text{LEO}}-E_{\text{GEO}}\right)

. (iv) Which orbit requires a greater amount of launch energy per unit mass and why?