Low-orbit communication satellites are to be deployed around both Earth and Mars at…

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

Problem

Low-orbit communication satellites are to be deployed around both Earth and Mars at an altitude of

400\,\text{km}

above the respective planetary surfaces. The planetary data are:

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

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

;

M_{\text{M}}=6.4\times10^{23}\,\text{kg}

R_{\text{M}}=3.4\times10^{6}\,\text{m}

. (i) Derive an expression for the ratio of the orbital speeds

v_{\text{E}}/v_{\text{M}}

of satellites around Earth and Mars at the stated altitude. (ii) Calculate the numerical value of this ratio. (iii) Determine the actual orbital speed required around each planet. (iv) Based on your results, comment on which planet demands greater launch energy for placing satellites into low circular orbits.

Related theory

Satellites & Orbital Motion
Gravitation
Orbital velocity and period
Earth satellites

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