Explain why a satellite in a circular orbit at a greater distance from Earth's centre moves with a smaller orbital speed than a satellite in a circular orbit at a smaller distance.

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).

Model answer (4 marks)

A satellite in orbit is attracted by the Earth's gravitational force, which supplies the required centripetal force for circular motion.

The gravitational force (and hence the field strength) falls off as 1/r², so at a larger distance from the Earth's centre the force is weaker.

For a circular orbit the required centripetal acceleration is v²/r. A weaker force at a larger r means a smaller v²/r can be supplied, so the orbital speed v must be smaller.

Thus a satellite farther from the Earth moves more slowly than one closer to the Earth to maintain a stable circular orbit.

Examiner tips

  • State that gravity provides the centripetal force; mention the 1/r² decrease; link weaker force to smaller v²/r; conclude with the speed comparison.
  • Use correct terms: gravitational field, centripetal force, orbital speed, circular orbit.

Common mistakes

  • Confusing orbital speed with escape velocity; writing v∝1/r instead of v∝1/√r; neglecting the 1/r² dependence of gravity.

Mark scheme (4 marks)

  1. Gravitational force provides the centripetal force for circular orbital motion
  2. Gravitational field strength / gravitational force decreases with increasing distance from Earth's centre (inverse-square relationship)
  3. For a circular orbit, the centripetal acceleration (or force) required is proportional to v²/r, so a smaller force at larger r requires a smaller value of v²/r
  4. Therefore, the satellite at greater orbital radius requires a smaller speed to maintain a stable circular orbit

Key terms in this question

orbital speed · circular orbit

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