# Gravitational fields

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u17-overview/
> Weight: n/a

This unit introduces gravitational fields, one of the four fundamental interactions, covering core concepts, key laws, field properties, and applications to orbital motion of planets and satellites.

**Prerequisites:** Understanding of circular motion, centripetal force and energy concepts

## Learning objectives

- Understand gravitational fields as a fundamental force field that interacts with mass
- Apply Newton's law of universal gravitation to calculate gravitational forces between masses
- Distinguish between gravitational field strength and gravitational potential, and solve for both at any point in a field
- Apply core gravitational concepts to solve problems involving orbital motion of planets and satellites

## Unit at a Glance

Gravitation is the fundamental force that governs large-scale motion in the universe, holding solar systems together and keeping satellites in stable orbits. This unit builds from foundational definitions to applied problem-solving, connecting abstract field concepts to real-world orbital motion.

The learning arc progresses step-by-step: you will start with basic field definitions, then learn Newton's universal gravitational law, quantify field strength and potential, and end by applying all prior concepts to solve orbital motion problems.

This unit is split into 5 connected sub-topics:
- [Gravitational field concepts](https://www.owlsprep.com/study/cie-9702-u17-gravitational-field-concepts/) — Introduces gravitational fields as force fields and defines core terms for describing field interactions with mass.
- [Newton's law of gravitation](https://www.owlsprep.com/study/cie-9702-u17-newton-s-law-of-gravitation/) — Covers Newton's universal law of gravitation and how to calculate force between point and spherical masses.
- [Gravitational field strength](https://www.owlsprep.com/study/cie-9702-u17-gravitational-field-strength/) — Explains how to calculate gravitational field strength for point masses, uniform spheres, and uniform near-Earth fields.
- [Gravitational potential](https://www.owlsprep.com/study/cie-9702-u17-gravitational-potential/) — Defines gravitational potential and potential energy, and links these concepts to field strength and gravitational force.
- [Orbital motion](https://www.owlsprep.com/study/cie-9702-u17-orbital-motion/) — Applies gravitational concepts to analyze circular and geostationary orbits of planets, moons, and artificial satellites.

## Common pitfalls

- **Wrong:** Confusing gravitational field strength with gravitational potential.
  - Why it fails: Both are properties of a point in a gravitational field, but have different physical meanings and units.
  - Correct: Remember $g = -dV/dr$: $g$ is force per unit mass, $V$ is energy per unit mass.
- **Wrong:** Using positive values for gravitational potential with the standard infinity zero reference.
  - Why it fails: Zero potential is defined at infinity, and work must be done to move a mass from any point in the field to infinity.
  - Correct: Always use negative values for gravitational potential unless explicitly told to use a different reference.
- **Wrong:** Adding extra force terms to centripetal force calculations for stable orbital motion.
  - Why it fails: Confusion between orbital motion and circular motion near a planet's surface where multiple forces act.
  - Correct: For stable orbits, gravitational force provides all the centripetal force required, so equate them directly.

## Cheatsheet

| Concept | Key Formula |
| --- | --- |
| Newton's law of gravitation | $F = G \frac{m_1 m_2}{r^2}$ |
| Gravitational field strength (point mass) | $g = G \frac{M}{r^2}$ |
| Gravitational potential (point mass) | $V = - \frac{GM}{r}$ |
| Gravitational potential energy | $U = - \frac{GMm}{r}$ |
| Orbital speed | $v = \sqrt{\frac{GM}{r}}$ |
| Kepler's third law | $T^2 = \frac{4 \pi^2 r^3}{GM}$ |
| Escape speed | $v_{esc} = \sqrt{\frac{2GM}{r}}$ |

## What's next

Begin your learning with the first sub-topic on core gravitational field concepts to build a solid foundation for the rest of the unit. After completing all sub-topics in this unit, you will move on to study electric fields, which share many analogous mathematical and conceptual structures with gravitational fields.

- [Gravitational field concepts](https://www.owlsprep.com/study/cie-9702-u17-gravitational-field-concepts/)
- [Newton's law of gravitation](https://www.owlsprep.com/study/cie-9702-u17-newton-s-law-of-gravitation/)
- [Gravitational field strength](https://www.owlsprep.com/study/cie-9702-u17-gravitational-field-strength/)

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