3.7.1.1FieldsCore

Gravitational Fields and Newton’s Law

Every single object with mass pulls on every other object with mass — a genuinely universal force, acting across the entire universe with no minimum range. This is $gravity$ , and Newton’s law of gravitation captures its behaviour in a single, remarkably simple equation that governs everything from a falling apple to two orbiting galaxies.

40 min Video by ZPhysics 3.7.1 Gravitational fields

A Level Physics Revision: All of Gravitational FieldsWatch the full walkthrough before the notes below.

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What you'll be able to do

State and use Newton’s law of gravitation
Define gravitational field strength and relate it to force
Calculate gravitational field strength for a point (or spherical) mass
Describe uniform and radial gravitational fields
Sketch and interpret gravitational field lines

Newton’s law of gravitation

$Newton’s law of gravitation$ states that any two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. The force is always $attractive$ and acts along the line joining the two masses.

This is an $inverse-square law$ : doubling the separation reduces the force to a quarter, tripling it reduces the force to a ninth, and so on. For extended spherical bodies (like planets), the law still applies exactly, treating all the mass as concentrated at the centre.

F = \frac{G m _{1} m _{2}}{r ^{2}}

G = gravitational constant (6.67 × 10⁻¹¹ N m² kg⁻²).

1Use

F = \frac{G m _{1} m _{2}}{r ^{2}}

F = \frac{6.67 \times 1 0 ^{- 11} \times 1000 \times 1000}{2. 0 ^{2}}

F = \frac{6.67 \times 1 0 ^{- 5}}{4.0}

Answer

F \approx 1.67 \times 1 0^{- 5}

N — tiny, which is why gravity between everyday objects is never noticeable.

Tip — Gravity is by far the weakest of the four fundamental forces — it only dominates on large scales because mass is never negative, so its effect always accumulates rather than cancelling out (unlike charge).

Gravitational field strength

A $gravitational field$ is a region of space where a mass experiences a force. $Gravitational field strength$ , $g$ , at a point is defined as the force per unit mass a small test mass would experience there — a vector, pointing in the direction of the force (toward the mass creating the field).

Near the Earth’s surface, over the small height range of everyday objects, the field is essentially $uniform$ : parallel, equally-spaced field lines, and $g \approx 9.81$ N kg⁻¹ everywhere. Around a point or spherical mass, however, the field is $radial$ : field lines point straight toward the centre, becoming less densely packed (weaker field) further out, following an inverse-square law exactly like the force itself.

g = \frac{F}{m} = \frac{GM}{r ^{2}}

Gravitational field strength: force per unit mass, or directly from the source mass M and distance r.

1Use

g = \frac{GM}{r ^{2}}

g = \frac{6.67 \times 1 0 ^{- 11} \times 5.97 \times 1 0 ^{24}}{( 6.37 \times 1 0 ^{6} ) ^{2}}

g = \frac{3.98 \times 1 0 ^{14}}{4.06 \times 1 0 ^{13}}

Answer

g \approx 9.81

N kg⁻¹ — matching the familiar value used throughout mechanics.

Tip — Always measure r from the CENTRE of a spherical mass, not from its surface — a very common source of errors when a question gives an "altitude" or "height above the surface".

Equation recap

F = \frac{G m _{1} m _{2}}{r ^{2}}

Newton’s law of gravitation.

g = \frac{F}{m} = \frac{GM}{r ^{2}}

Gravitational field strength.

Common mistakes to avoid

Measuring r from the surface of a planet rather than its centre.

Both Newton’s law and the field strength equation use r as the distance from the CENTRE of the mass — always add the planet’s radius to any given altitude.

Thinking gravitational force can ever be repulsive.

Gravity is always attractive between any two masses — unlike electric force, there is no equivalent of "like charges repel".

Assuming field strength is constant everywhere around a planet, like near the Earth’s surface.

Field strength only looks constant very close to a large mass; further away (or for smaller-scale problems) it follows a genuine inverse-square (radial) variation.

Key takeaways

Newton’s law of gravitation: F = Gm₁m₂/r², always attractive, inverse-square with separation.
Gravitational field strength g = F/m = GM/r², a vector pointing toward the source mass.
Near a planet’s surface the field is approximately uniform; further out (or on smaller scales) it is radial, following an inverse-square law.
Always measure r from the centre of a spherical mass, not its surface.

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Gravitational Fields and Newton’s Law

Every single object with mass pulls on every other object with mass — a genuinely universal force, acting across the entire universe with no minimum range. This is

gravity

, and Newton’s law of gravitation captures its behaviour in a single, remarkably simple equation that governs everything from a falling apple to two orbiting galaxies.

40 min Video by ZPhysics 3.7.1 Gravitational fields