Gravitational field of a point mass
Cambridge A-Level Physics (9702) · Unit 13: Gravitational fields · 7 flashcards
Gravitational field of a point mass is topic 13.3 in the Cambridge A-Level Physics (9702) syllabus , positioned in Unit 13 — Gravitational fields , alongside Gravitational field, Gravitational force between point masses and Gravitational potential. In one line: The gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically: F = Gm₁m₂ / r².
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 — 2 definitions, 4 key concepts and 1 calculation — covering the precise wording mark schemes reward. Use the 2 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.
Newton's Law of Gravitation
The gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically: F = Gm₁m₂ / r².
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.
- derive, from Newton’s law of gravitation and the definition of gravitational field, the equation g = GM / r 2 for the gravitational field strength due to a point mass
- recall and use g = GM / r 2
- understand why g is approximately constant for small changes in height near the Earth’s surface
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 field of a point mass
- › 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).
State Newton's Law of Gravitation.
The gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically: F = Gm₁m₂ / r².
Derive the formula for gravitational field strength (g) due to a point mass.
Starting with Newton's Law of Gravitation (F = GMm/r²) and the definition of gravitational field strength (g = F/m), substitute F to get g = (GMm/r²)/m. Simplifying, g = GM/r².
What is the equation for gravitational field strength (g) due to a point mass?
g = GM/r², where G is the gravitational constant, M is the mass of the point mass, and r is the distance from the center of the point mass.
Calculate the gravitational field strength on the surface of a planet with mass M = 6 x 10^24 kg and radius r = 6.4 x 10^6 m. (G = 6.67 x 10^-11 Nm²/kg²)
Using g = GM/r², g = (6.67 x 10^-11 Nm²/kg² * 6 x 10^24 kg) / (6.4 x 10^6 m)² = 9.77 N/kg (or m/s²).
Explain why 'g' is approximately constant for small changes in height near the Earth's surface.
Near the Earth's surface, small changes in height (Δr) result in negligible changes to the overall distance 'r' from the Earth's center. Since g is inversely proportional to r², g remains approximately constant (g ≈ GM/r²).
Describe the relationship between gravitational field strength and distance from a point mass.
Gravitational field strength (g) is inversely proportional to the square of the distance (r) from the point mass (g ∝ 1/r²). As distance increases, field strength decreases rapidly.
If the distance from a planet's center doubles, how does the gravitational field strength change?
If the distance doubles, the gravitational field strength is reduced to one-quarter of its original value. Since g ∝ 1/r², if r becomes 2r, then g becomes g/4.
Review the material
Read full revision notes on Gravitational field of a point mass — definitions, equations, common mistakes, and exam tips.
Read NotesMore topics in Unit 13 — Gravitational fields
Gravitational field of a point mass 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 field of a point mass deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
How to study this Gravitational field of a point mass deck
Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.
Study Mode
Rate each card Hard, Okay, or Easy after flipping.