In simple terms
A friendly intro before the formal notes — no formulas yet.
Gravitational field
Cambridge 9702 Paper 4 — Gravitational field (13.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
is the universal gravitational constant, .
- 2
The force decreases rapidly with distance (inverse square law).
- 3
This law applies to point masses or uniform spheres where is the distance between centres.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 13.1.1
Understand that a gravitational field is an example of a field of force and define gravitational field as force per unit mass
- 13.1.2
Represent a gravitational field by means of field lines
Explore the concept
Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.
Step-synced diagram — highlights what to look for in the simulation above.
Step 1
is the universal gravitational constant, .
6 more simulations for this topic — run them in the Simulations section below
Simulations
Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.
6 simulations · 4 to start with
Start herein this order — each one shows a different piece of the topic
- 3JCN PhysicsStart here · 19702 13.2 · 9702 13.1 · IB D.1
Newton's Gravity
Move two masses closer or farther and see how the gravitational force vector scales
Why this one: Watch the force vector on each mass shrink as you move them apart; both arrows stay equal.
Try this
- Move the two masses closer and watch the force vector grow.
- Double the separation and compare the vector length.
Look for The attraction on each mass is equal and opposite and falls with the inverse square of separation.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- 3JCN PhysicsStart here · 29702 13.3 · 9702 13.1 · 9702 2.1
Newton's Gravity: Jumping on Planets
Jump on different planets; compare jump height and hang time against surface gravity
Why this one: Jump on different planets and see how surface field strength g sets your hang time.
Try this
- Jump on Earth and note the jump height and hang time.
- Jump on the Moon and compare both against its surface gravity.
- Jump on Jupiter and compare again.
Look for For the same take-off speed, jump height and hang time both scale inversely with surface gravity g.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
- PhETStart here · 3IB D.1 · 9702 13.1–13.2 · 12.2
My Solar System
Set the masses, positions and velocities of up to four bodies and watch their gravitational orbits unfold.
Why this one: Set a planet moving in the Sun's field and see the field bend its path into an orbit.
Try this
- Load the Sun–planet preset — turn on the path and the velocity vector.
- Lower the planet’s starting speed — the orbit becomes an ellipse that dips closer to the Sun.
- Raise the speed step by step until the planet escapes.
Look for A circular orbit needs one exact speed; less gives an ellipse, enough gives escape.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- The Physics ClassroomStart here · 49702 13.2 · 9702 13.1 · IB D.1
Orbital Motion
Investigate elliptical orbits and Kepler's laws by changing the satellite's starting speed and position
Why this one: Change a satellite's launch speed and watch the same field give circles, ellipses or escape.
Try this
- Launch a circular orbit.
- Increase the starting speed and watch the ellipse form.
- Compare the speed at the near and far points.
Look for A satellite moves fastest at the point of its orbit closest to the planet.
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
More simulations2 more on this topic — core ones first
- SimuPhysicsCore9702 13.2 · 9702 13.1 · IB D.1
N-Body Gravity Simulator
Place any number of masses, give them initial velocities and watch the gravitational interactions, slingshots, captures and ejections
Try this
- Place two masses and set a stable orbit.
- Add a third mass and watch.
- Give a small mass a slingshot past a large one.
Look for Two bodies orbit predictably while three or more generally do not.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
- 3JCN PhysicsCore9702 13.2 · 9702 13.1 · IB D.1
Gravity Force
Change two masses and their separation; read the gravitational attraction between them
Try this
- Double one mass and read the attraction.
- Double the separation and read the attraction.
- Halve the separation and read the attraction again.
Look for F = Gm1m2 / r²: doubling either mass doubles the force and doubling the separation quarters it.
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
Key formulas
Tap any symbol to reveal exactly what it means and its units.
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Tap a symbol — great for exam definitions
Full topic notes
Formal explanation with the rigour you need for the exam.
What is a Gravitational Field?
A gravitational field is a region of space where any object possessing mass will experience an attractive gravitational force due to another mass. These fields are inherently created by masses, and they're always attractive, never repulsive. To visualise this invisible influence, we use gravitational field lines. These lines have specific properties: they point in the direction of the force on a test mass, their density (how close they are) represents the field's strength, and they never cross. For a single point mass, the field lines are radial, pointing inwards.
Gravitational Field Strength (g)
Gravitational field strength, denoted by 'g', is defined as the gravitational force experienced per unit mass at a particular point within the field. Its SI units are Newtons per kilogram (N kg⁻¹), which is equivalent to metres per second squared (m s⁻²). This equivalence highlights that 'g' also represents the acceleration a body would undergo if it were to fall freely within that field. Near Earth's surface, 'g' is approximately uniform, but further away from large masses, fields become radial, with strength varying significantly with distance.
Newton's Law of Gravitation
Sir Isaac Newton formulated the universal law describing the attractive force between any two point masses. This law states that the gravitational force (F) between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance separating their centres. This groundbreaking law allows us to calculate the force between any two objects in the universe.
is the universal gravitational constant, .
The force decreases rapidly with distance (inverse square law).
This law applies to point masses or uniform spheres where is the distance between centres.
Radial Gravitational Field Strength
For a radial field, like the one created by a planet, we can combine the definitions of 'g' and Newton's Law of Gravitation. If 'M' is the mass creating the field and 'm' is a small test mass, then . Since , we can derive a specific formula for the gravitational field strength in a radial field. This clearly shows that 'g' also follows an inverse square law, meaning its strength diminishes significantly with increasing distance from the central mass.
Gravitational Potential ($\phi$)
Gravitational potential () at a point is defined as the work done per unit mass required to bring a unit mass from infinity to that specific point within the field. Conventionally, the gravitational potential at an infinite distance from a mass is set to zero. As energy is released (work is done by the field) when a mass moves from infinity into the field, gravitational potential is always a negative value. Think of it as 'energy debt' – the deeper into the field, the more negative the potential.
Work done per unit mass from infinity to a point.
Potential at infinity is conventionally zero.
Always negative, as energy is released when entering the field.
Measured in Joules per kilogram (J kg\textsuperscript{-1}).
Gravitational Potential Energy ($E_p$)
Gravitational potential energy () is the total energy an object possesses due to its position within a gravitational field. It's the work done to move a mass from infinity to that point. This means it's simply the gravitational potential () multiplied by the mass of the object ('m'). Like potential, it's also a negative value, representing the binding energy of the system. For orbiting objects, the gravitational force acts as the centripetal force.
Graphical Representation of g and $\phi$
Understanding how gravitational field strength (g) and gravitational potential () vary with distance (r) from a central mass M is crucial. Their graphical representations reveal key aspects of the inverse square law. For a spherical mass, we consider the distance r from its centre.
Graph of g vs. r: The field strength is proportional to . This graph starts at a maximum value on the surface of the mass (if it's a planet) and curves downwards, approaching the r-axis asymptotically. It is always positive as strength is a magnitude.
Graph of vs. r: The potential is proportional to -1/r. This graph lies entirely in the fourth quadrant (negative y-axis). It starts at its most negative value on the surface and curves upwards, approaching the r-axis (where = 0) asymptotically as r approaches infinity.
Relationship: The gravitational field strength is the negative of the gradient of the gravitational potential graph (g = -d/dr). This means the steepness of the potential graph at any point tells you the strength of the field at that point.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
Calculate the gravitational force between a 70 kg student and a 1200 kg car, if their centres are 3.0 m apart. ()
- 1
Identify known values: , , , .
Mars has a mass of and a mean radius of . Calculate the gravitational field strength on the surface of Mars. (Use )
- 1
State the formula for gravitational field strength for a radial field: .
How it all connects
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Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.
Glossary
Key terms for this topic — skim now; the Check step will test them.
- For calculations
As if it's concentrated entirely at its centre, acting as a point mass.
- Universal gravitational constant G
A fundamental constant () that quantifies the strength of the gravitational force.
- Gravitational potential ()
The work done per unit mass to bring a unit mass from infinity to a specific point in the field.
- gravitational field
It follows an inverse square law (g \propto 1/r^2).
Quick check
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Teach it back
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Teach it back
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Revision flashcards
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Key takeaways
Review these before you close the topic — retrieval beats re-reading.
is the universal gravitational constant, .
The force decreases rapidly with distance (inverse square law).
This law applies to point masses or uniform spheres where is the distance between centres.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
State what is represented by a gravitational field line.
On Fig. 2.1, draw field lines to represent the Earth's gravitational field outside the Earth.
Extra simulations & links
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Frequently asked
Checkpoint
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Reading it isn’t knowing it — prove it.
Before you move on: do 9702/42 · Q2(a)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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