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Gravitational fields (A-level only)

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Question 39

A space probe of mass m=680 kgm = 680\text{ kg}m=680 kg is sent to study Saturn's moon Titan. The probe is placed in a stable circular orbit at an altitude hhh above Titan's surface. Titan has a mass MMM and a 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 Titan, M=1.35×1023 kgM = 1.35 \times 10^{23}\text{ kg}M=1.35×1023 kg
  • Radius of Titan, R=2.58×106 mR = 2.58 \times 10^{6}\text{ m}R=2.58×106 m
a.

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

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

Calculate the orbital period TTT of the probe when its altitude h=1.42×106 mh = 1.42 \times 10^6\text{ m}h=1.42×106 m.

[3]
c.

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

[2]
Markscheme

Gravitational fields (A-level only) Questions

  1. A Level
  2. /Physics
  3. /Gravitational fields (A-level only)

52 exam-style questions on AQA A Level Physics Gravitational fields (A-level only), covering Newton's law (A-level only), Gravitational field strength (A-level only), Gravitational potential (A-level only), and Orbits of planets and satellites (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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