Gravitational field concepts

CIE A-Level Physics· Unit 17: Gravitational fields· 15 min read

1. What is a Gravitational Field?★★☆☆☆⏱ 5 min

📘 Definition

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.

2. Gravitational Field Strength★★☆☆☆⏱ 5 min

📘 Definition

Gravitational field strength

g

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

Example:

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

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 $N kg^{- 1}$ , which is equivalent to $m s^{- 2}$ .

📐 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 $7.8 N kg^{- 1}$ , which is lower than the surface value of $9.8 N kg^{- 1}$ as expected.

3. Gravitational Field Line Patterns★★★☆☆⏱ 6 min

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 $2 r$ . 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 $(2 r)^{2} = 4 r^{2}$ , 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.

4. Common Pitfalls

Wrong move:

Defining a gravitational field as 'the force on a mass' instead of a region of space

Why:

CIE examiners require the definition of a field as a region, not the force itself, to award full marks

Correct move:

Always define a gravitational field as a region of space where a mass experiences an attractive gravitational force

Wrong move:

Drawing gravitational field lines pointing outwards from a planet

Why:

Gravitational force is always attractive, so test masses are pulled towards the massive body

Correct move:

Always draw gravitational field lines pointing inwards towards the centre of the massive body

Wrong move:

Claiming gravitational field strength depends on the mass of the test object in the field

Why:

Field strength is defined as force per unit mass, so the test mass term cancels out

Correct move:

Gravitational field strength is a property of the field at a point, so it is independent of the mass of the test object

Wrong move:

Stating field strength is proportional to 1/r for radial fields around point masses

Why:

Field lines spread over an area proportional to $r^{2}$ , not $r$ , for spherical geometry

Correct move:

Field strength for radial fields is proportional to $\frac{1}{r ^{2}}$ , following the inverse square law

5. Quick Reference 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: $N kg^{- 1}$ , 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 $g = 0$

6. Frequently Asked

What is the difference between gravitational field strength and acceleration due to gravity?

Near the surface of a planet, gravitational field strength is numerically equal to acceleration due to gravity for free fall. Field strength is defined as force per unit mass, which has the same units ( $N kg^{- 1}$ ) as acceleration ( $m s^{- 2}$ ), so the values are equivalent in this context.

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2023 · 1
Field strength definition multiple choice
2022 · 2
Draw field patterns for two masses
2021 · 1
Field line density proportionality question

Going deeper

syllabusCIE 9702 Official SyllabusCheck latest topic requirements

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.