# Explain why the gravitational potential at any point in a gravitational field is always negative.

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

> Gravitational potential V at a distance r from the centre of a body of mass M is defined by the work done per unit mass in bringing a small test mass from infinity to that point.

## Mark scheme (4 marks)

1. Gravitational potential at infinity is defined as zero (the reference point).
2. Gravity is always attractive, so the gravitational force on the test mass is directed towards the source mass (i.e. towards decreasing r).
3. As the test mass moves from infinity towards the source mass, the gravitational force does positive work on the test mass (force and displacement are in the same direction).
4. Therefore the work done per unit mass by an external agent in moving the test mass from infinity to that point is negative, making the gravitational potential negative at all finite distances.

## Key terms

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

## 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-potential-at-f71d9e9f) · Published by Druglandscape Ltd.