Gravitational potential Edexcel International A Level Physics revision
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In plain words
Lifting something away from a planet takes work, and the higher you go the more you have done. Gravitational potential labels each point in space with the energy per kilogram a mass has there. It is taken to be zero infinitely far away, which makes it negative everywhere else: you are always down a well, and it takes energy to climb out.
4 things to know
- The gravitational potential φ at a point is the work done per unit mass in bringing a small test mass from infinity to that point. Units: J/kg.
- For a point mass M, or outside a sphere of mass M: φ = −GM ÷ r. It is negative because gravity attracts, and zero at infinity.
- The gravitational potential energy of two point masses is E = −GMm ÷ r, which is m × φ.
- The work done in moving a mass m between two points is m × (the change in potential).
Worked example
Find the gravitational potential at the Earth's surface, and the least energy needed to move a 1000 kg spacecraft from the surface to a very great distance. (GM = 3.98 × 10¹⁴ N m² kg⁻¹; radius = 6.37 × 10⁶ m.)
- φ = −GM ÷ r = −3.98 × 10¹⁴ ÷ 6.37 × 10⁶ = −6.25 × 10⁷ J/kg.
- At a very great distance the potential is zero, so it rises by 6.25 × 10⁷ J/kg.
- Energy needed = 1000 × 6.25 × 10⁷ = 6.25 × 10¹⁰ J.
Tips and tricks
- Potential is a scalar. To find the potential due to several masses, just add the numbers (they are all negative).
- mgΔh only works near the surface, where g is constant. For big changes in height use the change in −GMm ÷ r.
It lands in your notebook with its questions as flashcards.
Gravitational potential: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
Where is gravitational potential zero?
That is how it is defined.
What are the units of gravitational potential?
Energy per unit mass.
The distance from the centre of a planet doubles. What happens to the size of the gravitational potential?
Potential is proportional to 1 ÷ r, not 1 ÷ r².
Is gravitational potential a scalar or a vector?
It has no direction, so potentials simply add.
The potential at a point is −40 MJ/kg. How much work is needed to move a 2 kg mass from there to infinity?
The potential must rise by 40 MJ for every kilogram.
Quiz
5 questions
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Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Gravitational potential
Edexcel International A Level Physics WPH · 7 marks · papermunch.org
Name ______________________________ Date ______________
Explain why gravitational potential is always negative.[2]
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It is defined as zero at infinity. Gravity attracts, so work must be done on a mass to move it out to infinity: everywhere nearer has less potential than zero.
The potential at the Earth's surface is −6.25 × 10⁷ J/kg. Find the work done in lifting a 200 kg satellite to a point twice as far from the Earth's centre.[3]
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6.3 × 10⁹ J. The potential there is −3.13 × 10⁷ J/kg, a rise of 3.13 × 10⁷ J/kg.
Find the gravitational potential energy of a 500 kg satellite 7.0 × 10⁶ m from the centre of the Earth. (GM = 3.98 × 10¹⁴ N m² kg⁻¹.)[2]
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−2.8 × 10¹⁰ J.
Answers: Gravitational potential
- 1. It is defined as zero at infinity. Gravity attracts, so work must be done on a mass to move it out to infinity: everywhere nearer has less potential than zero.
- 2. 6.3 × 10⁹ J. The potential there is −3.13 × 10⁷ J/kg, a rise of 3.13 × 10⁷ J/kg.
- 3. −2.8 × 10¹⁰ J.