# Explain why the gravitational field strength at the surface of the Moon is less than the gravitational field strength at the surface of the Earth, even though the Moon has a smaller radius.

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

> The Moon has a mass of approximately 7.3 × 10²² kg and a mean radius of 1.7 × 10⁶ m. The Earth has a mass of approximately 6.0 × 10²⁴ kg and a mean radius of 6.4 × 10⁶ m.

## Mark scheme (4 marks)

1. Gravitational field strength at a surface is given by g = GM/R², where M is the mass of the body and R is its radius.
2. The Moon's mass is very much smaller than the Earth's mass (by a factor of about 80), which acts to reduce g significantly.
3. A smaller radius alone would increase g (since g ∝ 1/R²), so the Moon's smaller radius partially counteracts the effect of its smaller mass.
4. The reduction in g due to the Moon's much smaller mass outweighs the increase in g from its smaller radius, so the Moon's surface gravitational field strength is smaller overall.

## Key terms

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

## Related

- [Revision notes for IB DP Physics Standard Level (2023 syllabus)](https://www.gradenine.co.uk/learn)
- [How to answer "Explain" questions](https://www.gradenine.co.uk/tools/command-word-cheatsheet)
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Source: [GradeNine](https://www.gradenine.co.uk/q/explain-why-the-gravitational-field-strength-71b4da8b) · Published by Druglandscape Ltd.