Explain why the gravitational potential energy of a satellite increases as it moves from a low orbit to a higher orbit, yet the total mechanical energy of the satellite also increases.

IB DP Physics Standard Level (2023 syllabus) — D.1 Gravitational fields · Explain · 4 marks · View as Markdown

Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).

A satellite orbits the Earth in a circular orbit. A rocket burn causes the satellite to move to a higher circular orbit.

Model answer (4 marks)

The gravitational potential energy of a satellite is defined as U=−GMm/r, so as the radius r increases the magnitude of U decreases and U becomes less negative (i.e. it increases towards zero). In a circular orbit the kinetic energy is K=½mv² and v²=GM/r, so K=½GMm/r. Therefore as r increases, K decreases. The increase in U (a positive change) is larger in magnitude than the decrease in K (a negative change), so the net change in mechanical energy ΔE=ΔU+ΔK is positive. The rocket burn supplies work that adds energy to the satellite, raising its total mechanical energy.

Examiner tips

  • Use the formula U=−GMm/r to show U becomes less negative; use v²=GM/r to show K decreases; state the net energy change is positive because |ΔU|>|ΔK|; mention the rocket does work.
  • Show the relationship between r, U and K explicitly; keep the explanation concise and use the exact wording from the mark scheme.
  • Include the fact that the rocket’s work is the source of the net energy increase.

Common mistakes

  • Saying U becomes more negative instead of less negative; confusing the sign of U.
  • Forgetting that the kinetic energy decreases with increasing radius; or stating it increases.
  • Not recognising that the rocket’s work is the source of the net energy increase.

Mark scheme (4 marks)

  1. Gravitational potential energy is defined as negative, becoming less negative (increasing towards zero) as the satellite moves further from Earth's centre.
  2. The kinetic energy of the satellite decreases as orbital radius increases, because orbital speed decreases with increasing radius.
  3. The magnitude of the increase in gravitational potential energy is greater than the magnitude of the decrease in kinetic energy.
  4. The rocket burn does work on the satellite, providing the net energy input that raises the total mechanical energy of the satellite.

Key terms in this question

gravitational potential energy · total mechanical energy

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