AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Total energy of an orbiting satellite.
Full specification wording
Orbits of planets and satellites (A-level only): Total energy of an orbiting satellite.
For a satellite in a circular orbit, gravitational attraction provides the centripetal force.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 1 of 4
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
For a satellite in a circular orbit, gravitational attraction provides the centripetal force. This gives kinetic energy Eₖ = GMm/(2r), gravitational potential energy Eₚ = −GMm/r, and therefore total energy E = Eₖ + Eₚ = −GMm/(2r). The total energy is negative, showing the satellite is bound, and becomes less negative as r increases. You should derive or use these expressions, explain why a satellite in a lower orbit has greater kinetic energy but more negative total energy, and calculate energy changes when a satellite moves between orbits.
What earns the marks
- States that gravitational force provides the centripetal force, leading to mv²/r = GMm/r² and hence v² = GM/r.
- Derives kinetic energy Eₖ = ½mv² = GMm/(2r) for a circular orbit.
- Uses gravitational potential energy Eₚ = −GMm/r, measured with zero at infinity.
- Adds kinetic and potential energy to obtain total energy E = −GMm/(2r).
- Explains that total energy is negative for a bound orbit and increases towards zero as orbital radius increases.
- Calculates the energy required to move a satellite between circular orbits using the difference in total energy.
Common mistakes and how to put them right
Using Eₚ = +GMm/r.
Put it right: Gravitational potential energy is negative when the zero is at infinity.
Forgetting the factor of ½ and writing total energy as −GMm/r.
Put it right: E = Eₖ + Eₚ = GMm/(2r) − GMm/r = −GMm/(2r).
Assuming a more distant orbit has more kinetic energy.
Put it right: Eₖ decreases as r increases, even though total energy becomes less negative.
Exam tips
- Start from the force equation mv²/r = GMm/r² whenever you need to link speed, radius and mass.
- Keep the negative sign throughout the potential and total energy calculations, and interpret it as a bound state.
- When calculating an energy change, subtract the initial total energy from the final total energy and state whether energy is absorbed or released.
Try the lesson
The start of the Orbits of planets and satellites (A-level only): Total energy of an orbiting satellite. lesson, made from checked teaching notes for this specification point.
Have a go first
A satellite moves in a circular orbit around a planet. Which statement about the total energy of the satellite is correct?
Listen
For a satellite in a circular orbit, gravitational attraction provides the centripetal force. This gives kinetic energy Eₖ = GMm/(2r), gravitational potential energy Eₚ = −GMm/r, and therefore total energy E = Eₖ + Eₚ = −GMm/(2r). The total energy is negative, showing the satellite is bound, and becomes less negative as r increases. You should derive or use these expressions, explain why a satellite in a lower orbit has greater kinetic energy but more negative total energy, and calculate energy changes when a satellite moves between orbits. A strong answer earns marks for these points. States that gravitational force provides the centripetal force, leading to mv²/r = GMm/r² and hence v² = GM/r. Derives kinetic energy Eₖ = ½mv² = GMm/(2r) for a circular orbit. Uses gravitational potential energy Eₚ = −GMm/r, measured with zero at infinity. Adds kinetic and potential energy to obtain total energy E = −GMm/(2r). A common slip: Using Eₚ = +GMm/r. Instead, gravitational potential energy is negative when the zero is at infinity. Exam tip: Start from the force equation mv²/r = GMm/r² whenever you need to link speed, radius and mass.
Key words
Say what each word means before you turn the card.
Gravitational force as centripetal force
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Kinetic, potential and total energy in circular orbits
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Negative total energy and bound orbits
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Energy changes between orbits
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See every definition
- Gravitational force as centripetal force
- For a satellite in a circular orbit, gravitational attraction provides the centripetal force, leading to mv²/r = GMm/r² and hence v² = GM/r.
- Kinetic, potential and total energy in circular orbits
- Kinetic energy is Eₖ = GMm/(2r), gravitational potential energy is Eₚ = −GMm/r, and total energy is E = Eₖ + Eₚ = −GMm/(2r).
- Negative total energy and bound orbits
- The total energy is negative, showing the satellite is bound, and becomes less negative as r increases.
- Energy changes between orbits
- The energy required to move a satellite between circular orbits is calculated using the difference in total energy.
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