# Explain why the gravitational field strength at the surface of a planet is not the same as the gravitational field strength at a point high above its surface, and outline how the concept of gravitational potential energy accounts for the work done in moving a mass between these two points.

> IB DP Physics Higher Level (2023 syllabus) — D.1 Gravitational fields · Explain · 4 marks

> A spacecraft of mass m is launched from the surface of a planet of mass M and radius R to an orbital altitude h above the surface.

## Mark scheme (4 marks)

1. Gravitational field strength g is inversely proportional to the square of the distance from the centre of the planet (g ∝ 1/r²), so g decreases as distance from the centre increases.
2. At the surface the distance from the centre is R, whilst at altitude h it is (R + h), which is greater, so the field strength at altitude h is smaller than at the surface.
3. Gravitational potential energy (E_p) is defined as the work done per unit mass / the work done against the gravitational field in moving a mass from infinity to that point; it is negative and becomes less negative (increases) as distance from the planet increases.
4. The work done in moving the spacecraft from the surface to altitude h equals the change in gravitational potential energy: W = ΔE_p = −GMm/(R+h) − (−GMm/R), which is positive, meaning energy must be supplied to the spacecraft.

## Key terms

- [gravitational field strength](https://www.gradenine.co.uk/glossary/gravitational-field-strength)
- [gravitational potential energy](https://www.gradenine.co.uk/glossary/gravitational-potential-energy)
- [work done](https://www.gradenine.co.uk/glossary/work-done)

## Related

- [Revision notes for IB DP Physics Higher Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
- [Practice this with AI marking (free)](https://www.gradenine.co.uk/start)

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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-the-gravitational-field-strength-a68de898) · Published by Druglandscape Ltd.