# Gravitational field concepts

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u17-gravitational-field-concepts/

This sub-topic introduces core concepts of gravitational fields, including field strength, field line representation, and how fields act on masses. You will learn to describe field patterns for common arrangements of spherical masses.

**Prerequisites:** [Newton's law of universal gravitation](https://www.owlsprep.com/study/cie-9702-u17-newtons-law-of-gravitation/); [Forces and Newton's laws of motion](https://www.owlsprep.com/study/cie-9702-u04-forces-newtons-laws/)

## Learning objectives

- Define gravitational field and gravitational field strength correctly for exam answers
- Distinguish between gravitational force and gravitational field strength
- Draw and interpret gravitational field patterns for common mass arrangements
- Relate field line density to the magnitude of field strength

## What is a Gravitational Field?

**Gravitational field** — A region of space where a mass experiences an attractive non-contact gravitational force due to the presence of another massive body.

*Example:* Any object near Earth is in Earth's gravitational field, and experiences a force pulling it towards Earth's centre.

A key property of fields is that they exist as a property of space, even if no test mass is present to experience the force. Unlike electric fields, gravitational fields are always attractive — there is no negative mass to cause repulsion.

**Worked example:** A region of deep space has no mass present within it. Does a gravitational field exist in this region, due to a distant star? Explain your answer.

1. Recall the definition of a gravitational field
2. A field is defined as a region of space where a force would act on a test mass if one was placed there, it does not require a mass to be present to exist.
3. The gravitational influence of the distant star extends throughout this region, so:
4. Yes, a gravitational field exists in the region. The field is a property of the space caused by the distant star, regardless of whether a mass is present.

> **Exam tip:** CIE examiners almost always ask for the definition of a gravitational field — you must mention it is a *region of space* to get full marks.

## Gravitational Field Strength

**Gravitational field strength** — The force per unit mass experienced by a small stationary test point mass at a given point in the field.

*Notation:* g

*Example:* At Earth's surface, $g \approx 9.8 \text{ N kg}^{-1}$.

From the definition, the formula for gravitational field strength is:

$$g = \frac{F}{m}$$

Where $F$ is the gravitational force acting on the test mass $m$. Field strength has units of $\text{N kg}^{-1}$, which is equivalent to $\text{m s}^{-2}$.

> **tip**
>
> Gravitational field strength is an intensive property: it does not depend on the mass of the test object placed in the field. Dividing force by mass cancels out the test mass term, leaving a value that is a property of the field itself.

**Worked example:** A 3.0 kg test mass experiences a gravitational force of 23.5 N when placed at a point 1000 km above Earth's surface. Calculate the gravitational field strength at this point.

1. Start with the definition formula for field strength:
2. $$g = \frac{F}{m}$$
3. Substitute the given values for force and mass:
4. $$g = \frac{23.5}{3.0} = 7.8 \text{ N kg}^{-1}$$
5. The gravitational field strength 1000 km above Earth's surface is $7.8 \text{ N kg}^{-1}$, which is lower than the surface value of $9.8 \text{ N kg}^{-1}$ as expected.

## Gravitational Field Line Patterns

Field lines are a visual tool to represent gravitational fields, and follow two core rules:

- Field lines point in the direction of the gravitational force that a small test mass would experience at that point
- The density of field lines (number per unit area perpendicular to the lines) is proportional to the magnitude of the gravitational field strength

- **Uniform field (near a planet surface):** Parallel, equally spaced lines pointing vertically towards the planet's centre (constant $g$)
- **Radial field (around a point/spherical mass):** Radial lines pointing inwards to the centre of the mass
- **Field between two equal spherical masses:** Lines curve towards each mass, with a neutral point at the midpoint where field strength is zero

**Worked example:** For a radial field around a point mass, point X is at distance $r$ from the centre, point Y is at distance $2r$. Use field line density to find the ratio of field strength at X to field strength at Y.

1. For a radial field, field lines spread out over the surface of a sphere of radius $r$. The area of this sphere is:
2. $$A = 4\pi r^2$$
3. Field line density (lines per unit area) is inversely proportional to area, so inversely proportional to $r^2$.
4. For point Y, $r$ doubles, so area becomes $(2r)^2 = 4r^2$, so density is 1/4 of the density at X.
5. Since field strength is proportional to density, the ratio $g_X : g_Y = 4:1$

> **Exam tip:** Always draw gravitational field lines pointing inwards to the massive body. Outward lines will lose you marks, as gravity is always attractive.

## Common pitfalls

- **Wrong:** Defining a gravitational field as 'the force on a mass' instead of a region of space
  - Why it fails: CIE examiners require the definition of a field as a region, not the force itself, to award full marks
  - Correct: Always define a gravitational field as a region of space where a mass experiences an attractive gravitational force
- **Wrong:** Drawing gravitational field lines pointing outwards from a planet
  - Why it fails: Gravitational force is always attractive, so test masses are pulled towards the massive body
  - Correct: Always draw gravitational field lines pointing inwards towards the centre of the massive body
- **Wrong:** Claiming gravitational field strength depends on the mass of the test object in the field
  - Why it fails: Field strength is defined as force per unit mass, so the test mass term cancels out
  - Correct: Gravitational field strength is a property of the field at a point, so it is independent of the mass of the test object
- **Wrong:** Stating field strength is proportional to 1/r for radial fields around point masses
  - Why it fails: Field lines spread over an area proportional to $r^2$, not $r$, for spherical geometry
  - Correct: Field strength for radial fields is proportional to $\frac{1}{r^2}$, following the inverse square law

## Cheatsheet

| Concept | Definition/Formula | Key Exam Notes |
| --- | --- | --- |
| Gravitational field | Region of space where mass experiences force | Always attractive, exists without test mass |
| Gravitational field strength | $g = F/m$, force per unit test mass | Units: $\text{N kg}^{-1}$, independent of test mass |
| Uniform field | Parallel, equally spaced lines | $g$ is constant everywhere |
| Radial field (point mass) | Radial lines pointing inwards | $g \propto 1/r^2$, inverse square law |
| Two equal masses | Curved lines to each mass | Neutral midpoint where $g=0$ |

## What's next

This sub-topic lays the foundational conceptual framework for all further work on gravitational fields in CIE A-Level Physics. Understanding the definition of field strength and how to interpret field patterns is critical when you move on to calculate gravitational potential, orbital motion, and escape velocity, all of which are heavily assessed in both Paper 1 and Paper 2 exams. Gravitational field concepts are also directly analogous to electric field concepts later in the syllabus, so mastering these core ideas early will make learning electric fields much more intuitive and faster to master.

- [Gravitational potential](https://www.owlsprep.com/study/cie-9702-u17-gravitational-potential/)
- [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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