Gravitational potential
Cambridge A-Level Physics (9702) · Unit 13: Gravitational fields · 7 flashcards
Gravitational potential is topic 13.4 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 13 — Gravitational fields , alongside Gravitational field, Gravitational force between point masses and Gravitational field of a point mass. In one line: Gravitational potential (ϕ) at a point is the work done per unit mass in bringing a small test mass from infinity to that point. It's a scalar quantity and is always negative.
Marked as A2 Level: examined at A Level in Paper 4 (A Level Structured Questions) and Paper 5 (Planning, Analysis and Evaluation). It is not tested on the AS-only papers (Papers 1, 2 and 3).
The deck below contains 7 flashcards — 3 definitions, 3 key concepts and 1 calculation — covering the precise wording mark schemes reward. Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and calculation cards to handle explain, describe, calculate and compare questions.
Gravitational potential (ϕ) at a point in a gravitational field
Gravitational potential (ϕ) at a point is the work done per unit mass in bringing a small test mass from infinity to that point. It's a scalar quantity and is always negative.
What the Cambridge 9702 syllabus says
Official 2025-2027 spec · A2 LevelThese are the exact learning outcomes Cambridge sets for this topic. The candidate is expected to be able to do each of these on the relevant paper.
- define gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to the point
- use ϕ = –GM / r for the gravitational potential in the field due to a point mass
- understand how the concept of gravitational potential leads to the gravitational potential energy of two point masses and use EP = –GMm / r
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 9702 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Tips to avoid common mistakes in Gravitational potential
- › Define gravitational potential as the work done *per unit mass* when moving a mass from infinity.
- › Definitions of potential always require the 'per unit mass' or 'per unit charge' component to be dimensionally correct.
- › Be precise with language; Newton’s law involves the product of masses and the inverse square of the separation between their centers.
- › State that force is proportional to the product of the masses and inversely proportional to the square of the separation between their centers.
- › Read the question carefully to distinguish between requests for field lines (radial with arrows) and equipotential lines (concentric circles).
Define gravitational potential (ϕ) at a point in a gravitational field.
Gravitational potential (ϕ) at a point is the work done per unit mass in bringing a small test mass from infinity to that point. It's a scalar quantity and is always negative.
State the formula for gravitational potential (ϕ) due to a point mass M at a distance r.
The gravitational potential (ϕ) is given by: ϕ = –GM / r, where G is the gravitational constant and r is the distance from the center of mass M. Note the negative sign; it indicates that work needs to be done *against* the gravitational field to increase potential.
Explain why gravitational potential is always a negative value.
Gravitational potential is negative because the gravitational force is attractive. Work is done *by* the field as a mass moves from infinity towards another mass. Since potential is defined as work done *against* the field, it is negative at all finite distances.
How does gravitational potential change as you move further away from a point mass?
As the distance (r) from a point mass increases, the gravitational potential (ϕ) becomes less negative (i.e., increases). At infinity, the gravitational potential is defined to be zero.
State the formula for gravitational potential energy (EP) of two point masses, M and m, separated by a distance r.
The gravitational potential energy (EP) is given by: EP = –GMm / r, where G is the gravitational constant. This represents the work done to separate the masses to infinity.
Describe the relationship between gravitational potential energy and gravitational potential.
Gravitational potential energy (EP) is the product of the gravitational potential (ϕ) at a point and the mass (m) placed at that point: EP = mϕ. Therefore, if you know the potential at a location, you can easily determine the potential energy of any mass placed there.
A 10kg mass is placed 5m away from a 1000kg mass. What is the gravitational potential energy of the 10kg mass?
E_p = -GMm/r = -(6.67 x 10^-11)(1000)(10)/5 = -1.33 x 10^-7 J. Remember to use appropriate units.
Review the material
Read full revision notes on Gravitational potential — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 13 — Gravitational fields
Gravitational potential sits alongside these A-Level Physics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Key terms covered in this Gravitational potential deck
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