Where can I learn Gravitational field of a point mass for Cambridge 9702?

This free lesson on MarkScheme covers syllabus point 13.3 (Gravitational field of a point mass) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/13-3-gravitational-field-of-a-point-mass.

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13.3Physics25 min readPREMIUM

Gravitational field of a point mass

Welcome to the fascinating world of gravitational fields! In this lesson, we'll dive into how massive objects exert an invisible 'pull' on everything around them. We'll explore the fundamental laws governing this interaction, learn to calculate forces, understand field strength, and grasp the concept of gravitational potential energy. Get ready to explore the universe's most fundamental force! This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 13.3.

BY THE END, YOU CAN…

exam checklist — tick these off

1Define a gravitational field and model uniform spherical masses as point masses.
2Apply Newton's Law of Gravitation and understand gravitational field strength, including its derivation.
3Calculate and interpret gravitational potential and potential energy for point masses.
4Understand and apply the relationship between gravitational field strength and potential gradient.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Gravitational field of a point mass

Cambridge 9702 Paper 4 — Gravitational field of a point mass (13.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Force ( $F$ ) is directly proportional to the product of masses ( $m_1m_2$ ).
2
Force ( $F$ ) is inversely proportional to the square of the distance ( $r^2$ ).
3
$G$ is the universal gravitational constant ( $6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ ).
4
The force is always attractive.

What this topic covers

The official Cambridge syllabus points this lesson works through.

13.3.1
Derive, from Newton's law of gravitation and the definition of gravitational field, the equation $g = GM/r^2$ for the gravitational field strength due to a point mass
13.3.2
Recall and use $g = GM/r^2$
13.3.3
Understand why g is approximately constant for small changes in height near the Earth's surface

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Gravity and Orbits

Set one mass to zero — the other still feels a pull. Mass creates the field.

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

A point mass M creates a gravitational…

A point mass M creates a gravitational field in the space around it.

12 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.

12 simulations · 4 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 13.3 · IB D.1
The Value of g
Explore how g varies with location around the globe and with altitude
Why this one: Climb to higher altitude and watch g fall away from 9.81 N/kg as 1/r² from Earth's centre.
Try this
1. Compare g at the equator and the poles.
2. Raise the altitude and watch g.
Look for g falls with altitude and is slightly smaller at the equator than at the poles.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 29702 13.3 · 9702 13.2 · IB D.1
Kepler's Third Law
Change orbital radius and read the period; verify T^2 proportional to r^3
Why this one: Change the orbital radius, read the period and check T² ∝ r³ follows from g = GM/r².
Try this
1. Set an orbital radius and read the period.
2. Quadruple the radius and read the period again.
3. Check T² / r³ for both orbits.
Look for T² is proportional to r³, so quadrupling the radius multiplies the period by eight.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 39702 13.3 · 9702 13.2 · 9702 2.1
Newton's Cannon
Increase a cannonball's launch speed from a mountain until it orbits Earth
Why this one: Raise the launch speed until the ball falls around the Earth instead of onto it — that is an orbit.
Try this
1. Launch at a low speed and watch the cannonball fall to Earth.
2. Increase the launch speed step by step until the ball completes an orbit.
3. Increase the speed further and compare the shape of the orbit.
Look for At the right speed the ball falls toward Earth at the same rate the surface curves away, giving a circular orbit; faster gives an ellipse.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
The Physics ClassroomStart here · 49702 13.3 · IB D.1
The Value of g on Other Planets
Compare the value of g on other planets from each planet's mass and radius
Why this one: Compare g on each planet from its mass and radius using g = GM/R².
Try this
1. Pick a planet and read g.
2. Compare its mass and radius with Earth's.
Look for g equals GM divided by R².
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

More simulations8 more on this topic — core ones first

oPhysicsCore9702 13.2 · 9702 13.3 · IB D.1
Elliptical Orbits & Kepler's 2nd Law
Planet orbiting a sun: set initial speed, distance and masses; see elliptical orbit and equal-area sweeps
Try this
1. Set an initial speed that gives a nearly circular orbit.
2. Lower the initial speed and watch the orbit become elliptical.
3. Increase the sun’s mass with the same starting distance.
Look for The planet moves fastest nearest the sun, and the areas swept in equal times stay equal.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
3JCN PhysicsCore9702 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
Try this
1. Jump on Earth and note the jump height and hang time.
2. Jump on the Moon and compare both against its surface gravity.
3. 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.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 13.3 · 9702 13.2 · IB D.1
Sun and Earth
Vary Earth's orbital speed around the Sun and see circular, elliptical or escape trajectories
Try this
1. Set the orbital speed for a circular orbit and watch one revolution.
2. Reduce the speed and compare the shape of the orbit.
3. Increase the speed until the Earth escapes.
Look for One speed gives a circle; lower or higher speeds give ellipses and beyond escape speed the path is open.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhET9702 13.3 · IB D.1
Kepler’s Laws
Drag a planet’s orbit and watch equal areas sweep in equal times; compare T² with a³.
Try this
1. On “Second Law”, press play — the two swept areas are equal although the arcs differ.
2. On “Third Law”, change the semi-major axis — read T and check T²/a³ stays fixed.
Look for Planets move faster near the star; T² ∝ a³ for every orbit round the same mass.
Open on PhET
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 Classroom9702 13.3 · IB D.1
Your Weight on Other Planets
Hop on the scales on other planets and see how your weight changes with location
Try this
1. Enter your mass.
2. Read your weight on each planet.
Look for Weight equals mass multiplied by the local value of g.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN Physics9702 13.3 · IB D.1
Gravitational Assist - Sling Shot
Fly a probe past a moving planet to gain speed via gravitational assist
Try this
1. Fly the probe past the moving planet and compare its speed before and after.
2. Approach from the other side of the planet and compare.
Look for Passing behind a moving planet adds some of the planet's orbital speed to the probe.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$F = G \frac{m_1 m_2}{r^2}$

Tap a symbol — great for exam definitions

KEY RELATION

$g = \frac{F}{m} = \frac{GM}{r^2}$

Tap a symbol — great for exam definitions

KEY RELATION

$\phi = -\frac{GM}{r}$

Tap a symbol — great for exam definitions

KEY RELATION

$g = -\frac{\Delta\phi}{\Delta r}$

Tap a symbol — great for exam definitions

KEY RELATION

$E_p = -\frac{GMm}{r}$

Tap a symbol — great for exam definitions

Full topic notes

Formal explanation with the rigour you need for the exam.

Gravitational Fields: An Invisible Influence

A gravitational field is essentially a region of space surrounding a mass where another mass would experience an attractive force. For most external calculations, especially with large, uniform objects like planets or stars, we simplify things by treating them as if all their mass is concentrated at a single point – known as a point mass at their centre. This makes calculations much more manageable.

Not clear?

Newton's Universal Law of Gravitation

Sir Isaac Newton's groundbreaking law describes the fundamental attraction between any two masses. It states that the attractive force between them is directly proportional to the product of their masses and inversely proportional to the square of the distance separating their centres. This inverse square law is crucial for understanding how gravity weakens with distance.

$F = G \frac{m_1 m_2}{r^2}$

Force ( $F$ ) is directly proportional to the product of masses ( $m_1m_2$ ).
Force ( $F$ ) is inversely proportional to the square of the distance ( $r^2$ ).
$G$ is the universal gravitational constant ( $6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ ).
The force is always attractive.

Not clear?

Gravitational Field Strength ($g$)

Gravitational field strength ( $g$ ) quantifies how strong the gravitational pull is at a particular point. It's defined as the gravitational force per unit mass acting on a small test mass placed at that point. Importantly, $g$ also represents the acceleration experienced by a free-falling object in that field. Field lines are radial, point inwards, and their density indicates the field's strength.

We can derive the formula for gravitational field strength by combining Newton's Law of Gravitation with the definition of a field.

Derivation:

Start with the definition of gravitational field strength: the force per unit test mass, $m$ . $g = \frac{F}{m}$
Recall Newton's Law of Gravitation for the force $F$ between the source mass $M$ and the test mass $m$ . $F = \frac{GMm}{r^2}$
Substitute the expression for $F$ into the equation for $g$ . $g = \frac{\left( \frac{GMm}{r^2} \right)}{m}$
The test mass $m$ cancels out, leaving the formula for the field strength created by the source mass $M$ . $g = \frac{GM}{r^2}$ This shows that the field strength at a point depends only on the source mass and the distance from it, not on the test mass placed there.

$g = \frac{F}{m} = \frac{GM}{r^2}$

Gravitational field strength is force per unit mass ( $g = F/m$ ).
It also represents the acceleration of free fall.
Follows an inverse square law ( $g \propto 1/r^2$ ).
Field lines are radial, pointing inwards, and closer lines mean a stronger field.

Not clear?

Gravitational Potential ($\phi$)

Gravitational potential ( $\phi$ ) is a scalar quantity representing the work done per unit mass to move a test mass from infinity to a specific point within the field. By convention, the gravitational potential at infinity is defined as zero. Since gravity is always attractive and work is done by the field as a mass approaches the source, gravitational potential is always a negative value.

$\phi = -\frac{GM}{r}$

Gravitational potential is work done per unit mass from infinity.
Potential at infinity is conventionally zero.
It is always negative, as energy is released moving towards the mass.

Not clear?

The Link Between Field Strength and Potential

There is a direct mathematical relationship between gravitational field strength ( $g$ ) and gravitational potential ( $\phi$ ). The field strength at a point is equal to the negative of the potential gradient at that point. The potential gradient is the rate of change of potential with distance. This means that a region with a rapidly changing potential (a steep slope on a potential-distance graph) will have a strong gravitational field.

$g = -\frac{\Delta\phi}{\Delta r}$

The negative sign is important: it signifies that the gravitational field vector ( $g$ ) always points in the direction of decreasing potential. Think of it like a ball rolling downhill – it moves from a higher potential to a lower potential, and the direction of its acceleration is down the steepest slope. For a point mass, potential becomes less negative (increases) as you move away from the mass, and the field $g$ points inwards, towards the mass, in the direction of decreasing potential.

This relationship is visualized in graphs. A graph of potential ( $\phi$ ) against distance ( $r$ ) for a point mass is a curve in the negative quadrant, approaching zero as $r$ approaches infinity. The gradient of this graph at any point $r$ is equal to $-g$ . A graph of field strength ( $g$ ) against distance ( $r$ ) shows an inverse square relationship, always positive, and also approaching zero as $r$ increases.

Not clear?

Gravitational Potential Energy ($E_p$)

Gravitational potential energy ( $E_p$ ) is the energy an object possesses due to its position within a gravitational field. For a system of two masses, it represents the work done to assemble them from infinite separation to their current distance. Like gravitational potential, $E_p$ is also a negative value. To completely remove an object from a field, you'd need to supply energy equal to the negative of its current potential energy.

$E_p = -\frac{GMm}{r}$

Gravitational potential energy is the energy of a mass in a gravitational field.
It is always negative for attractive fields, defined relative to zero at infinity.
Energy required to escape the field is the absolute value of $E_p$ .

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

Calculate the gravitational field strength on the surface of Mars, given its mass is $6.42 \times 10^{23} \text{ kg}$ and its radius is $3.39 \times 10^6 \text{ m}$ . Use the universal gravitational constant $G = 6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ .

1
Identify known values:

EXAMPLE 2

A satellite of mass 1200 kg is in a stable circular orbit at an altitude of 500 km above the Earth's surface. Calculate the work done required to move it to a higher stable orbit at an altitude of 2000 km. (Mass of Earth, M = $5.97 \times 10^{24}$ kg; Radius of Earth, $R_E = 6.37 \times 10^6$ m; $G = 6.67 \times 10^{-11}$ N m $^2$ kg $^{-2}$ )

1
Identify the principle: The work done is the change in the satellite's gravitational potential energy (GPE).

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAGravitational field of a point mass

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.

point mass: For most external calculations, especially with large, uniform objects like planets or stars, we simplify things by treating them as if all their mass is concentrated at a single point – known as a point mass at their centre. This makes calculations much more manageable.
inverse square law: This inverse square law is crucial for understanding how gravity weakens with distance.
Derivation: Derivation:
Gravitational field: A region surrounding a mass where other objects with mass experience an attractive force.
Gravitational field strength ( $g$ ): The gravitational force per unit mass experienced by a small test mass, also equal to the acceleration of free fall.
Gravitational potential ( $\phi$ ): The work done per unit mass to move a test mass from infinity to a specific point within the field.
gravitational potential: φ is inversely proportional to the distance: φ ∝ -1/r.

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 14 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

Force ( $F$ ) is directly proportional to the product of masses ( $m_1m_2$ ).
Force ( $F$ ) is inversely proportional to the square of the distance ( $r^2$ ).
$G$ is the universal gravitational constant ( $6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ ).
The force is always attractive.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q2(b)(i)

PhysicsOctober/November 2024

(b) (i)

For the position of the probe where x = 1.47 × 10¹¹m: (i) calculate g

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/O/N/24

Question 2 of 29702/42 · Q2(c)(i)

PhysicsOctober/November 2024

Show that, for any particular value of x, the numerical values of g and F are related by g = (4πGM / L) F where M is the mass of the Sun, L is the luminosity of the Sun and G is the gravitational constant.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/O/N/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

What is the main difference between gravitational field strength and gravitational potential?

Why do we treat a spherical mass as a point mass?

Does the gravitational force ever become zero?

What does the negative sign in the potential energy formula signify?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q2(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS13.2 Gravitational force between point masses NEXT →13.4 Gravitational potential

Discuss Gravitational field of a point mass

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Revise Gravitational field of a point mass for Cambridge 9702 (13.3)

Looking for free Physics 9702 notes on Gravitational field of a point mass? This A-Level lesson covers official syllabus point 13.3 on Paper 4: A Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Gravitational field of a point mass 9702 revision", "9702 13.3 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

13.3Physics25 min readPREMIUM

Gravitational field of a point mass

BY THE END, YOU CAN…

exam checklist — tick these off

1Define a gravitational field and model uniform spherical masses as point masses.
2Apply Newton's Law of Gravitation and understand gravitational field strength, including its derivation.
3Calculate and interpret gravitational potential and potential energy for point masses.
4Understand and apply the relationship between gravitational field strength and potential gradient.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Gravitational field of a point mass

Cambridge 9702 Paper 4 — Gravitational field of a point mass (13.3). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Force ( $F$ ) is directly proportional to the product of masses ( $m_1m_2$ ).
2
Force ( $F$ ) is inversely proportional to the square of the distance ( $r^2$ ).
3
$G$ is the universal gravitational constant ( $6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ ).
4
The force is always attractive.

What this topic covers

The official Cambridge syllabus points this lesson works through.

13.3.1
Derive, from Newton's law of gravitation and the definition of gravitational field, the equation $g = GM/r^2$ for the gravitational field strength due to a point mass
13.3.2
Recall and use $g = GM/r^2$
13.3.3
Understand why g is approximately constant for small changes in height near the Earth's surface

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure PhET simulation1 / 4

Loading simulation…

Fetching from PhET…

Gravity and Orbits

Set one mass to zero — the other still feels a pull. Mass creates the field.

If the embed does not load, use Open on PhET.

Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)

Step-synced diagram — highlights what to look for in the simulation above.

A point mass M creates a gravitational…

A point mass M creates a gravitational field in the space around it.

12 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.

12 simulations · 4 to start with

Start herein this order — each one shows a different piece of the topic

The Physics ClassroomStart here · 19702 13.3 · IB D.1
The Value of g
Explore how g varies with location around the globe and with altitude
Why this one: Climb to higher altitude and watch g fall away from 9.81 N/kg as 1/r² from Earth's centre.
Try this
1. Compare g at the equator and the poles.
2. Raise the altitude and watch g.
Look for g falls with altitude and is slightly smaller at the equator than at the poles.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN PhysicsStart here · 29702 13.3 · 9702 13.2 · IB D.1
Kepler's Third Law
Change orbital radius and read the period; verify T^2 proportional to r^3
Why this one: Change the orbital radius, read the period and check T² ∝ r³ follows from g = GM/r².
Try this
1. Set an orbital radius and read the period.
2. Quadruple the radius and read the period again.
3. Check T² / r³ for both orbits.
Look for T² is proportional to r³, so quadrupling the radius multiplies the period by eight.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsStart here · 39702 13.3 · 9702 13.2 · 9702 2.1
Newton's Cannon
Increase a cannonball's launch speed from a mountain until it orbits Earth
Why this one: Raise the launch speed until the ball falls around the Earth instead of onto it — that is an orbit.
Try this
1. Launch at a low speed and watch the cannonball fall to Earth.
2. Increase the launch speed step by step until the ball completes an orbit.
3. Increase the speed further and compare the shape of the orbit.
Look for At the right speed the ball falls toward Earth at the same rate the surface curves away, giving a circular orbit; faster gives an ellipse.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
The Physics ClassroomStart here · 49702 13.3 · IB D.1
The Value of g on Other Planets
Compare the value of g on other planets from each planet's mass and radius
Why this one: Compare g on each planet from its mass and radius using g = GM/R².
Try this
1. Pick a planet and read g.
2. Compare its mass and radius with Earth's.
Look for g equals GM divided by R².
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)

More simulations8 more on this topic — core ones first

oPhysicsCore9702 13.2 · 9702 13.3 · IB D.1
Elliptical Orbits & Kepler's 2nd Law
Planet orbiting a sun: set initial speed, distance and masses; see elliptical orbit and equal-area sweeps
Try this
1. Set an initial speed that gives a nearly circular orbit.
2. Lower the initial speed and watch the orbit become elliptical.
3. Increase the sun’s mass with the same starting distance.
Look for The planet moves fastest nearest the sun, and the areas swept in equal times stay equal.
Open on oPhysics
Simulation by Tom Walsh, oPhysics.com — made with GeoGebra · Licensed to MarkScheme (site: free for non-profit educational use; applets made with GeoGebra)
3JCN PhysicsCore9702 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
Try this
1. Jump on Earth and note the jump height and hang time.
2. Jump on the Moon and compare both against its surface gravity.
3. 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.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
3JCN PhysicsCore9702 13.3 · 9702 13.2 · IB D.1
Sun and Earth
Vary Earth's orbital speed around the Sun and see circular, elliptical or escape trajectories
Try this
1. Set the orbital speed for a circular orbit and watch one revolution.
2. Reduce the speed and compare the shape of the orbit.
3. Increase the speed until the Earth escapes.
Look for One speed gives a circle; lower or higher speeds give ellipses and beyond escape speed the path is open.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhET9702 13.3 · IB D.1
Kepler’s Laws
Drag a planet’s orbit and watch equal areas sweep in equal times; compare T² with a³.
Try this
1. On “Second Law”, press play — the two swept areas are equal although the arcs differ.
2. On “Third Law”, change the semi-major axis — read T and check T²/a³ stays fixed.
Look for Planets move faster near the star; T² ∝ a³ for every orbit round the same mass.
Open on PhET
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 Classroom9702 13.3 · IB D.1
Your Weight on Other Planets
Hop on the scales on other planets and see how your weight changes with location
Try this
1. Enter your mass.
2. Read your weight on each planet.
Look for Weight equals mass multiplied by the local value of g.
Open on The Physics Classroom
Physics Interactives by The Physics Classroom · Licensed to MarkScheme (site terms otherwise permit linking only)
3JCN Physics9702 13.3 · IB D.1
Gravitational Assist - Sling Shot
Fly a probe past a moving planet to gain speed via gravitational assist
Try this
1. Fly the probe past the moving planet and compare its speed before and after.
2. Approach from the other side of the planet and compare.
Look for Passing behind a moving planet adds some of the planet's orbital speed to the probe.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$F = G \frac{m_1 m_2}{r^2}$

Tap a symbol — great for exam definitions

KEY RELATION

$g = \frac{F}{m} = \frac{GM}{r^2}$

Tap a symbol — great for exam definitions

KEY RELATION

$\phi = -\frac{GM}{r}$

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KEY RELATION

$g = -\frac{\Delta\phi}{\Delta r}$

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KEY RELATION

$E_p = -\frac{GMm}{r}$

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Full topic notes

Formal explanation with the rigour you need for the exam.

Gravitational Fields: An Invisible Influence

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Newton's Universal Law of Gravitation

$F = G \frac{m_1 m_2}{r^2}$

Force ( $F$ ) is directly proportional to the product of masses ( $m_1m_2$ ).
Force ( $F$ ) is inversely proportional to the square of the distance ( $r^2$ ).
$G$ is the universal gravitational constant ( $6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ ).
The force is always attractive.

Not clear?

Gravitational Field Strength ($g$)

We can derive the formula for gravitational field strength by combining Newton's Law of Gravitation with the definition of a field.

Derivation:

Start with the definition of gravitational field strength: the force per unit test mass, $m$ . $g = \frac{F}{m}$
Recall Newton's Law of Gravitation for the force $F$ between the source mass $M$ and the test mass $m$ . $F = \frac{GMm}{r^2}$
Substitute the expression for $F$ into the equation for $g$ . $g = \frac{\left( \frac{GMm}{r^2} \right)}{m}$
The test mass $m$ cancels out, leaving the formula for the field strength created by the source mass $M$ . $g = \frac{GM}{r^2}$ This shows that the field strength at a point depends only on the source mass and the distance from it, not on the test mass placed there.

$g = \frac{F}{m} = \frac{GM}{r^2}$

Gravitational field strength is force per unit mass ( $g = F/m$ ).
It also represents the acceleration of free fall.
Follows an inverse square law ( $g \propto 1/r^2$ ).
Field lines are radial, pointing inwards, and closer lines mean a stronger field.

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Gravitational Potential ($\phi$)

$\phi = -\frac{GM}{r}$

Gravitational potential is work done per unit mass from infinity.
Potential at infinity is conventionally zero.
It is always negative, as energy is released moving towards the mass.

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The Link Between Field Strength and Potential

$g = -\frac{\Delta\phi}{\Delta r}$

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Gravitational Potential Energy ($E_p$)

$E_p = -\frac{GMm}{r}$

Gravitational potential energy is the energy of a mass in a gravitational field.
It is always negative for attractive fields, defined relative to zero at infinity.
Energy required to escape the field is the absolute value of $E_p$ .

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Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

1
Identify known values:

EXAMPLE 2

1
Identify the principle: The work done is the change in the satellite's gravitational potential energy (GPE).

How it all connects

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MAIN IDEAGravitational field of a point mass

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Glossary

Key terms for this topic — skim now; the Check step will test them.

point mass: For most external calculations, especially with large, uniform objects like planets or stars, we simplify things by treating them as if all their mass is concentrated at a single point – known as a point mass at their centre. This makes calculations much more manageable.
inverse square law: This inverse square law is crucial for understanding how gravity weakens with distance.
Derivation: Derivation:
Gravitational field: A region surrounding a mass where other objects with mass experience an attractive force.
Gravitational field strength ( $g$ ): The gravitational force per unit mass experienced by a small test mass, also equal to the acceleration of free fall.
Gravitational potential ( $\phi$ ): The work done per unit mass to move a test mass from infinity to a specific point within the field.
gravitational potential: φ is inversely proportional to the distance: φ ∝ -1/r.

10Apply

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0 of 6 answered

11Understand

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Your explanation — no notes

12Remember

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Your guess — write it before you look

1 / 14 · ← → space

Key takeaways

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close the tab only after these stick

Force ( $F$ ) is directly proportional to the product of masses ( $m_1m_2$ ).
Force ( $F$ ) is inversely proportional to the square of the distance ( $r^2$ ).
$G$ is the universal gravitational constant ( $6.67 \times 10^{-11} \text{ N m}^2 \text{kg}^{-2}$ ).
The force is always attractive.

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q2(b)(i)

PhysicsOctober/November 2024

(b) (i)

For the position of the probe where x = 1.47 × 10¹¹m: (i) calculate g

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/O/N/24

Question 2 of 29702/42 · Q2(c)(i)

PhysicsOctober/November 2024

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/O/N/24

Extra simulations & links

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Frequently asked

What is the main difference between gravitational field strength and gravitational potential?

Why do we treat a spherical mass as a point mass?

Does the gravitational force ever become zero?

What does the negative sign in the potential energy formula signify?

Checkpoint

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Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q2(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

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Revise Gravitational field of a point mass for Cambridge 9702 (13.3)

In simple terms

What this topic covers

Explore the concept

Simulations

The Value of g

Kepler's Third Law

Newton's Cannon

The Value of g on Other Planets

Elliptical Orbits & Kepler's 2nd Law

Newton's Gravity: Jumping on Planets

Sun and Earth

Kepler’s Laws

Your Weight on Other Planets

Gravitational Assist - Sling Shot

Key formulas

Full topic notes

Gravitational Fields: An Invisible Influence

Newton's Universal Law of Gravitation

Gravitational Field Strength ($g$)

Gravitational Potential ($\phi$)

The Link Between Field Strength and Potential

Gravitational Potential Energy ($E_p$)

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Gravitational field of a point mass

Revise Gravitational field of a point mass for Cambridge 9702 (13.3)

In simple terms

What this topic covers

Explore the concept

Simulations

The Value of g

Kepler's Third Law

Newton's Cannon

The Value of g on Other Planets

Elliptical Orbits & Kepler's 2nd Law

Newton's Gravity: Jumping on Planets

Sun and Earth

Kepler’s Laws

Your Weight on Other Planets

Gravitational Assist - Sling Shot

Key formulas

Full topic notes

Gravitational Fields: An Invisible Influence

Newton's Universal Law of Gravitation

Gravitational Field Strength ($g$)

Gravitational Potential ($\phi$)

The Link Between Field Strength and Potential

Gravitational Potential Energy ($E_p$)

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Gravitational field of a point mass