What is the gravitational force between two point masses?

The gravitational force between two point masses is the attractive force that acts along the line joining the two masses. According to Newton's law of universal gravitation, this force is directly proportional to the product of the two masses and inversely proportional to the square of the distance between their centers. The formula is F = G * (m1 * m2) / r^2, where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses, and r is the distance between the centers of the two masses.

How does the distance between two point masses affect the gravitational force?

The gravitational force between two point masses decreases with the square of the distance between them. This means that if the distance between the masses is doubled, the gravitational force becomes one-fourth of its original value. This inverse square law is a fundamental principle in the study of gravitational fields and is crucial for understanding how gravity operates over large distances, such as in planetary orbits.

Why is the gravitational force considered a central force?

The gravitational force is considered a central force because it acts along the line joining the centers of two interacting point masses. This means the force is directed towards the center of the mass that is exerting the gravitational pull. Central forces are significant in physics because they lead to predictable motion, such as the elliptical orbits of planets, which is a key concept in the Cambridge International A Levels Physics curriculum.

What role does the gravitational constant (G) play in the gravitational force equation?

The gravitational constant (G) is a fundamental constant that quantifies the strength of the gravitational force in the universe. It appears in the formula for gravitational force, F = G * (m1 * m2) / r^2, and ensures that the units of force are consistent with the units of mass and distance. The value of G is approximately 6.674 × 10^-11 N(m/kg)^2, and it is essential for calculating the gravitational force between any two point masses.

How is the concept of gravitational force between point masses applied in real-world scenarios?

The concept of gravitational force between point masses is applied in various real-world scenarios, such as calculating the gravitational attraction between celestial bodies like planets and moons. It is also used in engineering to design stable structures and in predicting the motion of satellites. Understanding this concept is crucial for students studying Physics at the Cambridge International A Levels, as it provides a foundation for more advanced topics in gravitational fields and astrophysics.

Why is "Confusing $g$ and $G$" a common mistake in Gravitational force between point masses?

Why it happens: Similar symbols. How to avoid it: G is universal constant (6.67 × 10^-11). g is local gravitational field strength (varies, 9.81 on Earth). Source: 9702 Examiner Reports 2022-2024

Gravitational FieldsCambridge International A Levels Physics (9702)

Gravitational force between point masses

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Newton's Law of Gravitation Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

$F = GMm/r^2$ . Inverse square. Universal attraction.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

13.2.1 — Apply Newton's law of gravitation.
13.2.2 — Recognise inverse-square dependence.

Newton's law

$F = GMm/r^2$ .

Law. Two point masses (or spherically symmetric bodies) attract each other with force: $F = \frac{GMm}{r^2}$

$G = 6.67 \times 10^{-11}$ N·m²/kg² — universal constant.

Direction. Always ATTRACTIVE, along line joining centres.

Inverse square. $F \propto 1/r^2$ : doubling distance reduces force to 1/4.

Example. Earth-Moon: $F \approx 1.98 \times 10^{20}$ N.

Cambridge tip. $r$ measured between CENTRES, not surfaces.

$F = GMm/r^2$ .
Always attractive.
Inverse square.

See the full worked example for gravitational force between point masses →

How it’s examined

Newton's law on every A2 paper. Most-tested: $F$ calculation (5 marks), inverse-square reasoning (5 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — Gravitational force between point masses

Step-by-step solutions to past-paper-style questions on gravitational force between point masses, written exactly the way a tutor would explain them at the board.

1Newton's law of gravitation (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• gravitation
Question
Calculate the gravitational force between Earth ( $M = 5.97 \times 10^{24}$ kg) and Moon ( $m = 7.35 \times 10^{22}$ kg), separated by $3.84 \times 10^8$ m. $G = 6.67 \times 10^{-11}$ N·m²/kg². (5 marks)
Step-by-step solution
1. Step 1
  $F = GMm/r^2$ .
  $F = \dfrac{(6.67 \times 10^{-11})(5.97 \times 10^{24})(7.35 \times 10^{22})}{(3.84 \times 10^8)^2}$
2. Step 2
  Evaluate.
  $F \approx 1.98 \times 10^{20} \text{ N}$
Answer
$F \approx 1.98 \times 10^{20}$ N.
2Inverse square law (5 marks)
Extended• inverse square
Question
If distance between two masses doubles, by what factor does the force change? (5 marks)
Step-by-step solution
1. Step 1
  $F \propto 1/r^2$ . Double $r$ → $F$ reduced by factor of 4.
Answer
Force reduces to 1/4.

Key Formulae — Gravitational force between point masses

The formulae you need to memorise for gravitational force between point masses on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Newton's law of gravitation
$F = -\dfrac{GMm}{r^2}$
$G$
gravitational constant $6.67 \times 10^{-11}$ N·m²/kg²
$M, m$
masses
$r$
distance between centres
When to use
Force between two point masses (or spherically symmetric masses). Always attractive (the negative sign).

Key Definitions and Keywords — Gravitational force between point masses

Definitions to memorise and the exact keywords mark schemes credit for gravitational force between point masses answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Newton's law of gravitation
Examiner keyword
The gravitational force between two point masses is proportional to the product of their masses and inversely proportional to the square of their separation.
Gravitational constant $G$
Examiner keyword
$G = 6.67 \times 10^{-11}$ N·m²/kg². Universal constant.

Common Mistakes and Misconceptions — Gravitational force between point masses

The traps other students keep falling into on gravitational force between point masses questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Confusing $g$ and $G$
9702 Examiner Reports 2022-2024
Why it happens
Similar symbols.
How to avoid it
$G$ is universal constant ( $6.67 \times 10^{-11}$ ). $g$ is local gravitational field strength (varies, $\approx 9.81$ on Earth).

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