This is an inverse square law

Gravitational Fields - OCR A-Level Physics

F = \frac{GMm}{r^2}

This is an inverse square lawA relationship in which a physical quantity is inversely proportional to the square of the distance from its source.: doubling r reduces F by a factor of 4.
The force is always attractiveGravity always pulls masses together — there is no gravitational repulsion. and acts along the line joining the centres of the two masses.
By Newton's third lawWhen two objects interact, the forces they exert on each other are equal in magnitude, opposite in direction, and act on different objects., both masses experience equal and opposite forces.
r is measured from the centres of the masses, not their surfaces. For a point above Earth's surface at height h: $r = R_E + h$.
The law applies to point massesObjects treated as if all their mass is concentrated at a single point; valid when the separation ≫ their size. or spherically symmetric masses (which behave as if all mass is at the centre).

Common Mistake MEDIUM

Wrong: Using the radius of the Earth when the question asks for the force at a height h above the surface.
Right: r is the distance between CENTRES. For height h above Earth: r = R_E + h, not just R_E or just h.

Examiner Tips and Tricks

When comparing gravitational fieldA region of space in which a mass experiences a gravitational force. strengths at different distances, use ratios.
If $g = GM/r^2$, then g_1/$g_{2} = r_{2}^2/r_{1}^2$.
This avoids needing to know G or M.