5.4FieldsCore

Gravitational Fields and Newton’s Law

Every mass in the universe pulls on every other mass — a genuinely universal force with no minimum range, governing everything from a dropped apple to two colliding galaxies, all through one deceptively simple equation.

40 min Video by ZPhysics Module 5.4 Gravitational fields

A Level Physics: The Law of GravitationWatch 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
Calculate gravitational field strength for a point or spherical mass
Describe uniform and radial gravitational fields

Newton’s law of gravitation

Any two point masses attract each other with a force proportional to the product of their masses and inversely proportional to the square of their separation — always attractive, and following an inverse-square law.

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

G = 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 500 \times 500}{1. 5 ^{2}}

Answer

F \approx 7.41 \times 1 0^{- 6}

N — negligible for everyday masses.

Gravitational field strength

Gravitational field strength, $g$ , is the force per unit mass at a point. Near a planet’s surface the field is approximately uniform; further out, or around a point mass, it is radial, following an inverse-square law.

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

Gravitational field strength.

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}}

Answer

g \approx 9.81

N kg⁻¹

Tip — Always measure r from the CENTRE of a spherical mass, not its 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 rather than the centre of a planet.

Both equations use r as the distance from the CENTRE — always add the planet’s radius to a given altitude.

Thinking gravitational force can be repulsive.

Gravity is always attractive between any two masses.

Assuming field strength is constant everywhere around a planet.

Field strength is only approximately constant very close to the surface; further out it follows a genuine inverse-square variation.

Key takeaways

Newton’s law of gravitation: F = Gm₁m₂/r², always attractive, inverse-square.
Gravitational field strength g = F/m = GM/r².
Near a planet’s surface the field is approximately uniform; further out it is radial.

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