Apply Newton's law of universal gravitation and the concept of gravitational field strength to interactions between masses.

What this dot point is asking

You need to apply Newton's law of universal gravitation to calculate the attractive force between two masses, understand its inverse-square dependence, and relate it to gravitational field strength.

The law

Key features:

• The force is always attractive and acts along the line joining the two centres.
• It is mutual: by Newton's third law each mass pulls the other with the same magnitude, regardless of how different the masses are.
• It follows an inverse-square law: doubling the separation reduces the force to a quarter; tripling it reduces it to a ninth.
• It is directly proportional to each mass: doubling one mass doubles the force.

For spherical bodies such as planets, $r$ is measured from centre to centre, so for an object on Earth's surface $r$ is the radius of the Earth.

Gravitational field strength

A mass creates a gravitational field around it. The field strength $g$ at a point is the force per unit mass placed there.

This is why $g \approx 9.8 \text{ N kg}^{-1}$ at Earth's surface, and falls off as you move to higher altitude or orbit.

Why it matters

This single law explains the fall of an apple and the orbit of the Moon - the same gravitational interaction governs both. Combined with the centripetal force requirement, it underpins satellite and planetary orbits (covered in the next dot point).