An Earth satellite is to be transferred from an initial circular orbit at an altitude…

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

Problem

An Earth satellite is to be transferred from an initial circular orbit at an altitude of

300\,\text{km}

to a higher circular orbit at an altitude of

3000\,\text{km}

. The mass of the satellite is

800\,\text{kg}

. Use

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

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

and

G=6.67\times10^{-11}\,\text{N m}^2\text{kg}^{-2}

. Neglect all non-gravitational forces. (i) Compute the radii of the two orbits measured from Earth’s centre. (ii) Determine the total mechanical energy per unit mass for each orbit. (iii) Calculate the work that must be done on the satellite to shift it from the lower to the higher orbit.

Related theory

Satellites & Orbital Motion
Gravitation
Orbital velocity and period
Energy of an orbiting satellite

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