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.
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.
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)
- Gravitational force provides the centripetal force for circular orbital motion
- Gravitational field strength / gravitational force decreases with increasing distance from Earth's centre (inverse-square relationship)
- 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
- 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
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
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