Define gravitational fields and read field lines
Define gravitational field strength and use field lines to describe the direction and relative strength of a gravitational field.
Section 13 · Gravitational fields
A Level; Cambridge International Physics 9702, 2025–2027 syllabus, Topic 13. These original explanations and calculations are study aids; full timed assessment and human subject-teacher review remain outstanding.
Before you begin
- Use Newton's laws, circular motion, vectors, scientific notation and SI units.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
How is gravitational field strength defined?
What you will learn
- Define a gravitational field as a field of force
- Define gravitational field strength as force per unit mass
- Represent gravitational fields using field lines
A gravitational field acts on mass at a distance
A gravitational field is a field of force: a mass placed in it experiences a gravitational force. Field strength g at a point is the gravitational force per unit mass, g = F/m. It is a vector with the direction of the force on a small positive test mass.
Near a planet, the field points toward the planet's centre. Field strength can be measured in N kg⁻¹; because a newton is kg m s⁻², this is equivalent to m s⁻². Do not confuse field strength g with the gravitational constant G.
Field lines show direction and relative strength
Draw an arrow on a field line to show the direction a small test mass would be forced to move. Around an isolated spherical mass, field lines are radial and point inward.
Closer field lines represent a stronger field; lines that spread out represent a weaker field. Field lines do not cross, because the field at one point cannot have two different directions. A uniform field is represented by parallel, equally spaced lines.
Pause and explain
At a point, a 0.50 kg mass experiences 4.0 N of gravitational force. What is g?
Worked example
A 2.0 kg test mass experiences a gravitational force of 19.6 N. Find the field strength and state its direction near Earth's surface.
Show the worked solution
- Use g = F/m.
- Divide 19.6 N by 2.0 kg.
- Give N kg⁻¹ and the direction of the force.
Answer g = 9.8 N kg⁻¹, vertically downward toward Earth's centre.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A 3.0 kg object experiences a gravitational force of 24 N. Calculate the field strength.
Give me a hint
Divide the force by the mass and retain the field-strength unit.
Compare my reasoning
- Use g = F/m.
- Substitute 24 N / 3.0 kg.
- State N kg⁻¹.
g = 8.0 N kg⁻¹.
Look for these in your work
- Definition selected
- Substitution correct
- Unit stated
Describe the field lines around an isolated spherical planet, including their direction and spacing farther from it.
Give me a hint
Imagine the force direction on a small test mass and compare the field strength at different distances.
Compare my reasoning
- Lines are radial around the planet.
- Arrows point inward toward the centre.
- Lines become farther apart with increasing distance, indicating a weaker field.
The lines are radial and point toward the centre; they become less dense farther away as the field weakens.
Look for these in your work
- Radial shape stated
- Direction stated
- Spacing interpreted
A diagram has two gravitational field lines crossing. Explain why the crossing cannot represent a physical field.
Give me a hint
Compare the directions a test mass would be forced to move at the intersection.
Compare my reasoning
- Each line's arrow gives the field direction.
- At the crossing the two lines would assign two directions to one point.
- A field has one resultant direction at each point, so gravitational field lines cannot cross.
The crossing would imply two field directions at one point, which is impossible for a single resultant gravitational field.
Look for these in your work
- Field direction interpreted
- Contradiction identified
- No-crossing rule explained
Common mistakes
- Treating g and G as the same quantity
- Giving field strength a direction away from the attracting mass
- Drawing field lines that cross
What can you explain now?
How is gravitational field strength defined?
Compare with the explanation
Force per unit mass
It is the gravitational force divided by the test mass.
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Make it stick
How do the direction and spacing of gravitational field lines describe the field?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.