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Gravitational fields (A-level only)

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Question 13

A satellite of mass m=450 kgm = 450\text{ kg}m=450 kg orbits Mars in a circular path at a height hhh above the surface of Mars. Mars has mass MMM and radius RRR.

Useful data:

  • Gravitational constant, G=6.67×10−11 N m2 kg−2G = 6.67 \times 10^{-11}\text{ N m}^2\text{ kg}^{-2}G=6.67×10−11 N m2 kg−2
  • Mass of Mars, M=6.42×1023 kgM = 6.42 \times 10^{23}\text{ kg}M=6.42×1023 kg
  • Radius of Mars, R=3.39×106 mR = 3.39 \times 10^{6}\text{ m}R=3.39×106 m
1.

Show that the angular speed ω\omegaω of the satellite is given by:

ω=GM(R+h)3 \omega = \sqrt{\frac{GM}{(R+h)^3}} ω=(R+h)3GM​​
[3]
2.

Calculate the orbital period TTT of the satellite when h=6.00×106 mh = 6.00 \times 10^6\text{ m}h=6.00×106 m.

[3]
3.

Calculate the gravitational potential energy of the satellite when in this orbit.

[3]

Gravitational fields (A-level only) Questions

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