Explain why the gravitational potential at any point in a gravitational field is always negative.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
Gravitational potential V at a distance r from the centre of a body of mass M is defined by the work done per unit mass in bringing a small test mass from infinity to that point.
Model answer (4 marks)
Gravitational potential is defined as the work per unit mass required to bring a test mass from infinity to a point in the field. The reference point at infinity is taken to have V=0. Gravity is an attractive force, so the force on the test mass points towards the source mass, i.e. towards decreasing r. As the test mass moves from infinity towards the source mass, the gravitational force acts in the same direction as the displacement, so the force does positive work on the test mass. The external agent that moves the test mass must therefore do negative work to overcome this positive work of gravity. Dividing this negative work by the mass gives a negative value for the potential. Hence, at every finite distance from the source mass the gravitational potential is negative.
Examiner tips
- State the reference point (V=0 at infinity).
- Explain that gravity is attractive and force points towards the source.
- Show that gravity does positive work on the test mass.
- Conclude that the external work, and thus V, is negative.
Common mistakes
- Confusing the sign of the work done by gravity with the external work.
- Failing to mention the reference point at infinity.
Mark scheme (4 marks)
- Gravitational potential at infinity is defined as zero (the reference point).
- Gravity is always attractive, so the gravitational force on the test mass is directed towards the source mass (i.e. towards decreasing r).
- As the test mass moves from infinity towards the source mass, the gravitational force does positive work on the test mass (force and displacement are in the same direction).
- Therefore the work done per unit mass by an external agent in moving the test mass from infinity to that point is negative, making the gravitational potential negative at all finite distances.
Key terms in this question
Related
- All IB DP Physics Standard Level (2023 syllabus) revision notes →
- How to answer a "Explain" question →
- Decode the mark scheme abbreviations →
More Gravitational fields questions
- Explain why the gravitational field strength at the surface of the Moon is less …
- Explain why a satellite in a circular orbit at a greater distance from Earth's c…
- Explain why the gravitational field strength inside a uniform spherical planet d…
- Explain why the gravitational potential energy of a satellite increases as it mo…