# Explain why the gravitational field strength inside a uniform spherical planet decreases as one moves from the surface towards the centre.

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

> A geophysicist models the Earth as a uniform sphere of mass M and radius R. She considers how the gravitational field strength varies at points within the planet.

## Mark scheme (4 marks)

1. Gravitational field strength depends on the mass that is enclosed within the sphere of radius r (the mass 'below' the point), not the total mass of the planet.
2. The enclosed mass is proportional to r³ (for a uniform density planet), so it decreases as r decreases.
3. Gravitational field strength g = GM_enc / r², so both the numerator (M_enc ∝ r³) and denominator (r²) change; the numerator decreases faster, giving g ∝ r.
4. At the centre r = 0, the enclosed mass is zero and the gravitational field strength is zero, consistent with the linear relationship.

## 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-4691929d) · Published by Druglandscape Ltd.