2007M2. In March 1999 the Mars Global Surveyor (GS) entered its final orbit about…

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

Problem

2007M2. In March 1999 the Mars Global Surveyor (GS) entered its final orbit about Mars, sending data back to Earth. Assume a circular orbit with a period of

1.18 \times 10^{2}

minutes

=7.08 \times 10^{3} \mathrm{~s}

and orbital speed of

3.40 \times 10^{3} \mathrm{m} / \mathrm{s}

. The mass of the GS is 930 kg and the radius of Mars is

3.43 \times 10^{6} \mathrm{~m}

. (a) Calculate the radius of the GS orbit. (b) Calculate the mass of Mars. (c) Calculate the total mechanical energy of the GS in this orbit. (d) If the GS was to be placed in a lower circular orbit (closer to the surface of Mars), would the new orbital period of the GS be greater than or less than the given period?____ Greater than ____ Less than Justify your answer. (e) In fact, the orbit the GS entered was slightly elliptical with its closest approach to Mars at

3.71 \times 10^{5} \mathrm{~m}

above the surface and its furthest distance at

4.36 \times 10^{5} \mathrm{~m}

above the surface. If the speed of the GS at closest approach is

3.40 \times 10^{3} \mathrm{~m} / \mathrm{s}

, calculate the speed at the furthest point of the orbit.

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