---
title: "Newton's Law of Gravitation and Gravitational Field Strength"
description: "Any two masses attract with a force that falls off as the square of their separation. Dividing that force by the test mass leaves a field strength that belongs to the source alone."
canonical: https://lightmysky.com/learn/science/newtons-law-of-gravitation-and-gravitational-field-strength-mt_uUYXl3L0oW
source: https://lightmysky.com/learn/science/newtons-law-of-gravitation-and-gravitational-field-strength-mt_uUYXl3L0oW.md
retrieved: 2026-11-12
---

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# Newton's Law of Gravitation and Gravitational Field Strength

Any two masses attract with a force that falls off as the square of their separation. Dividing that force by the test mass leaves a field strength that belongs to the source alone.

Subject: Science · Area: Forces & Motion · Ages 16 to 17
Page: https://lightmysky.com/learn/science/newtons-law-of-gravitation-and-gravitational-field-strength-mt_uUYXl3L0oW

## Ready when they can

- Uses F = GMm over r squared with r measured centre to centre
- Shows that surface g follows from GM over R squared, and predicts g at a stated height
- Sketches the radial field of a single mass and says what the spacing of the lines shows

## Lesson: Gravity between every pair of masses

Every mass attracts every other mass along the line joining their centres. The force grows with each mass and shrinks with the square of the distance r between centres. In symbols, F equals G M m over r squared, where G is the gravitational constant.

**Example.** The same pull holds an apple on its tree and the Moon in its orbit. Each body pulls the other equally hard in opposite directions, even when one mass is far larger.

Field strength g is the force per unit mass, in newtons per kilogram. Divide F by the test mass m and g equals G M over r squared, which depends on the source mass alone. At the surface r is the planet's radius R. A radial field sketch uses inward lines, spaced wider where the field is weaker.

**Example.** Measure r from centre to centre. Since g equals G M over r squared, g at distance r is the surface value times (R over r) squared. At 3 Earth radii from the centre, g = 9.8 / 3 squared = 9.8 / 9, about 1.09 N/kg. The same rule means doubling any separation quarters the force.

**Recap.** Masses pull along their joining line with a force that falls as one over r squared.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Universal Gravitation](https://lightmysky.com/learn/science/universal-gravitation-mt_oLjz18CxDg)

## Opens up

- [Gravitational Potential and Escape Speed](https://lightmysky.com/learn/science/gravitational-potential-and-escape-speed-mt_drqTwCD9W8)
- [Coulomb's Law and the Electric Field of a Point Charge](https://lightmysky.com/learn/science/coulombs-law-and-the-electric-field-of-a-point-charge-mt_p7FuzIsQch)
- [Orbits: Period, Speed and Kepler's Third Law](https://lightmysky.com/learn/science/orbits-period-speed-and-keplers-third-law-mt_PLKLykGF8Z)