In simple terms
A friendly intro before the formal notes — no formulas yet.
Gravitational potential
Cambridge 9702 Paper 4 — Gravitational potential (13.4). Senpai Corner diagram-backed pilot with premium structure and live visuals.
- 1
G is the Universal Gravitational Constant (6.67 x 10^-11 N m^2 kg^-2).
- 2
M is the mass of the body creating the gravitational field (e.g., a planet).
- 3
r is the distance from the centre of the mass M to the point in question.
- 4
The negative sign is crucial: it signifies that the potential is defined as zero at infinity, and energy is released as a mass is brought closer.
What this topic covers
The official Cambridge syllabus points this lesson works through.
- 13.4.1
Define gravitational potential at a point as the work done per unit mass in bringing a small test mass from infinity to the point
- 13.4.2
Use for the gravitational potential in the field due to a point mass
- 13.4.3
Understand how the concept of gravitational potential leads to the gravitational potential energy of two point masses and use
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
G is the Universal Gravitational Constant (6.67 x 10^-11 N m^2 kg^-2).
2 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.
2 simulations · 2 to start with
Start herein this order — each one shows a different piece of the topic
- PhETStart here · 19702 13.3–13.4
Gravity and Orbits
Orbits around a point mass — change masses and distance, watch period and shape respond.
Why this one: Follow an elliptical orbit and watch speed rise as the satellite falls closer, where the potential is more negative.
Try this
- Choose Sun–Earth and show the “Path”; double the Earth’s starting distance — time one orbit.
- Drag the Earth’s velocity arrow shorter — the orbit becomes an ellipse that dips inward.
- Set the Sun’s mass higher — the same orbit now needs more speed.
Look for Field strength falls as 1/r²; an orbit needs v² = GM/r.
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
- SimuPhysicsStart here · 29702 18.5 · 9702 13.4 · IB D.2
Potential Energy and Electric Potential
A ball lifted through height contours beside a charge moved through equipotential rings; drag either and change its size
Why this one: Lift the ball through height contours beside a charge crossing equipotential rings: potential is energy per unit mass.
Try this
- Drag the ball up and read the energy and gh.
- Drag the charge out and read the energy and V.
- Place 1 C, 2 C and 3 C at the same point.
Look for Stored energy scales with mass or charge, while gh and V do not.
Open on SimuPhysicsRuns on their siteSimuPhysics by Mohamed Abdelsalam · Licensed to MarkScheme (site publishes no licence; served with frame-ancestors self)
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
Full topic notes
Formal explanation with the rigour you need for the exam.
What is Gravitational Potential (\phi)?
Gravitational potential, symbolised by , tells us the work an external force must perform to bring a unit mass (a 1 kg mass) from an infinitely far point (where gravity's influence is zero) to a specific location within a gravitational field. It’s a scalar quantity, meaning it only has magnitude, not direction, and is measured in Joules per kilogram (J kg^-1).
The Formula for Gravitational Potential
G is the Universal Gravitational Constant (6.67 x 10^-11 N m^2 kg^-2).
M is the mass of the body creating the gravitational field (e.g., a planet).
r is the distance from the centre of the mass M to the point in question.
The negative sign is crucial: it signifies that the potential is defined as zero at infinity, and energy is released as a mass is brought closer.
For a uniform spherical body, M can be treated as a point mass at its centre for any point outside the sphere.
Why is Potential Negative?
Gravitational forces are always attractive. As a mass moves from infinity towards a gravitating body, the field itself does work, releasing energy. Since gravitational potential is defined as the work done by an external agent to bring a unit mass from infinity, and energy is released, this work is negative. Hence, potential is always negative at any finite distance from a source mass.
Equipotential Surfaces
An equipotential surface is a surface on which the gravitational potential () is constant at every point. For an isolated point mass or a spherical body, these surfaces are concentric spheres. A key property is that no work is done in moving a mass along an equipotential surface, because the change in potential energy () is zero.
Equipotential surfaces are always perpendicular to gravitational field lines.
The spacing between equipotential surfaces indicates the strength of the field. Closer surfaces mean a stronger field and a steeper potential gradient.
Relationship with Gravitational Field Strength (g)
Gravitational field strength (g) and gravitational potential () are intimately related. The field strength is the negative of the potential gradient. This means the field strength at a point is equal to how steeply the potential changes with distance at that point.
This relationship is analogous to a topographical map: the gravitational field strength 'g' is like the steepness of a hill, while the gravitational potential 'φ' is like the altitude. A steep hill (large 'g') corresponds to rapidly changing altitude (large potential gradient).
Gravitational Potential Energy (E\_p)
While gravitational potential () is for a unit mass, gravitational potential energy (E_p) is the total energy an object of mass 'm' possesses due to its position in a gravitational field. It's the total work an external agent must do to bring that specific mass 'm' from infinity to its current location.
'm' is the mass whose potential energy is being calculated.
Alternatively, E_p can be calculated as E_p = m.
Units for E_p are Joules (J).
E_p is also negative, reflecting the 'bound' state of the mass.
The energy required to 'escape' a field to infinity is -E_p.
Worked examples
See the formulas applied — reveal one step at a time, like the exam.
Calculate the gravitational potential and gravitational potential energy of a 2.5 kg satellite orbiting Earth at an altitude of 600 km. ()
- 1
First, calculate the radial distance 'r' from Earth's centre:
A satellite of mass 1200 kg is in a circular orbit at an altitude of 500 km above the Earth's surface. It is then moved to a higher geostationary orbit at an altitude of 35,786 km. Calculate the work done to move the satellite to the higher orbit. (Earth's mass M = 5.97 x 10^24 kg, Earth's radius R = 6.37 x 10^6 m, G = 6.67 x 10^-11 N m^2 kg^-2)
- 1
Calculate the initial radial distance (r_1):
How it all connects
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Glossary
Key terms for this topic — skim now; the Check step will test them.
- Gravitational potential
The work done per unit mass by an external agent to move a unit mass from infinity to a specific point within a gravitational field.
- energy required to move
It is equal to the negative of its initial gravitational potential energy (or the absolute value of its initial gravitational potential energy).
- Equipotential surface
A surface in space where the gravitational potential is the same at all points. No work is done when moving a mass along an equipotential surface.
- distinction between GPE
GPE = mgh is an approximation for the change in potential energy in a uniform gravitational field near a planet's surface. E_p = -GMm/r is the general formula for potential energy in a radial field, valid at any distance 'r' from the centre of mass M.
Quick check
Write your answer first, then compare it with the model one — the gap is what you would have lost.
Teach it back
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Teach it back
Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.
Revision flashcards
Guess first, then flip — retrieval beats re-reading.
Key takeaways
Review these before you close the topic — retrieval beats re-reading.
G is the Universal Gravitational Constant (6.67 x 10^-11 N m^2 kg^-2).
M is the mass of the body creating the gravitational field (e.g., a planet).
r is the distance from the centre of the mass M to the point in question.
The negative sign is crucial: it signifies that the potential is defined as zero at infinity, and energy is released as a mass is brought closer.
For a uniform spherical body, M can be treated as a point mass at its centre for any point outside the sphere.
Practice — then mark it
The whole point: a real Cambridge question, marked mark-by-mark.
Explain why the gravitational potential at X is negative.
Define gravitational potential at a point.
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 9702/41 · Q1(b)(i) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.
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