What is gravitational potential in the context of gravitational fields?

Gravitational potential at a point in a gravitational field is defined as the work done per unit mass in bringing a small test mass from infinity to that point. It is a scalar quantity and is measured in joules per kilogram (J/kg). In the Cambridge International A Levels Physics curriculum, understanding gravitational potential helps in analyzing the energy changes in gravitational fields.

How is gravitational potential different from gravitational potential energy?

Gravitational potential is the work done per unit mass to bring a mass from infinity to a point in a gravitational field, whereas gravitational potential energy is the total work done to bring a specific mass to that point. Gravitational potential is a property of the field itself, while gravitational potential energy depends on the mass being moved. This distinction is crucial in A Level Physics when solving problems related to energy in gravitational fields.

Why is gravitational potential considered negative?

Gravitational potential is considered negative because work is done against the gravitational force to bring a mass from infinity to a point in the field. Since gravitational force is attractive, the potential decreases as you move closer to the mass creating the field. This convention helps in maintaining consistency with the concept that work done against a force is negative, which is a key concept in the study of gravitational fields in A Level Physics.

How do you calculate gravitational potential due to a point mass?

The gravitational potential V due to a point mass M at a distance r is given by the formula V = -GM/r, where G is the gravitational constant. This formula is essential for solving problems related to gravitational fields in the Cambridge International A Levels Physics syllabus, as it allows students to calculate the potential at any point around a mass.

What is the significance of gravitational potential in orbital mechanics?

Gravitational potential plays a crucial role in orbital mechanics as it helps determine the energy required for a satellite to maintain its orbit. By understanding gravitational potential, students can calculate the energy changes involved in moving satellites between different orbits, which is an important application of gravitational fields in A Level Physics. This knowledge is vital for understanding how gravitational forces influence the motion of celestial bodies.

Why is "Treating gravitational PE as positive" a common mistake in Gravitational potential?

Why it happens: mgh form is positive near surface. How to avoid it: Universal form is U = -GMm/r. Negative because zero is at infinity. mgh measures CHANGE in PE from a chosen reference. Source: 9702 Examiner Reports 2022-2024

Gravitational FieldsCambridge International A Levels Physics (9702)

Gravitational potential

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Gravitational Potential Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Potential $\phi = -GM/r$ . Energy considerations. Escape velocity.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

13.4.1 — Define gravitational potential.
13.4.2 — Compute GPE.
13.4.3 — Find escape velocity.

Gravitational potential

Negative; zero at infinity.

Definition. Work done per unit mass to bring test mass from infinity to point.

Formula. $\phi = -GM/r$ for point mass.

Always negative. Test mass attracted toward source: external work needed to MOVE AWAY (positive); going TOWARD source releases energy (negative).

Reference. $\phi \to 0$ as $r \to \infty$ .

GPE. $U = m\phi = -GMm/r$ .

Cambridge tip. State 'zero at infinity' for top marks.

$\phi = -GM/r$ .
Negative everywhere.
Zero at infinity.

See the full worked example for gravitational potential →

Escape velocity

$\sqrt{2GM/R}$ .

Setup. Object at surface with speed $v$ . Reach infinity (minimum: arrive with $v = 0$ ).

Energy conservation. $\tfrac{1}{2}mv_{\text{esc}}^2 + \left(-\frac{GMm}{R}\right) = 0$ $v_{\text{esc}} = \sqrt{\frac{2GM}{R}}$

Earth. $v_{\text{esc}} \approx 11.2$ km/s. Moon. ~2.4 km/s. Sun (from surface). ~618 km/s.

Black hole. Escape velocity = $c$ at event horizon (Schwarzschild radius).

Cambridge tip. Independent of escape ANGLE — only speed matters (ignoring air resistance).

$v_{\text{esc}} = \sqrt{2GM/R}$ .
From energy conservation.
Earth ~11.2 km/s.

See the full worked example for gravitational potential →

How it’s examined

Gravitational potential central to A2. Most-tested: GPE (5-7 marks), escape velocity (8 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

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Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Gravitational potential, ready to print or save as PDF.

Step-by-step worked examples — Gravitational potential

Step-by-step solutions to past-paper-style questions on gravitational potential, written exactly the way a tutor would explain them at the board.

1GPE at distance $r$ (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• GPE
Question
Find the gravitational potential energy of a 500 kg satellite at $r = 7.0 \times 10^6$ m from Earth's centre. $M_E = 5.97 \times 10^{24}$ kg, $G = 6.67 \times 10^{-11}$ . (5 marks)
Step-by-step solution
1. Step 1
  $U = -GMm/r$ .
  $U = -\dfrac{(6.67 \times 10^{-11})(5.97 \times 10^{24})(500)}{7.0 \times 10^6} \approx -2.84 \times 10^{10} \text{ J}$
Answer
$U \approx -2.84 \times 10^{10}$ J.
2Escape velocity (8 marks)
Extended• escape velocity
Question
Find escape velocity from Earth's surface. $M_E = 5.97 \times 10^{24}$ kg, $R_E = 6.37 \times 10^6$ m. (8 marks)
Step-by-step solution
1. Step 1
  Escape velocity: KE at surface = $|\text{PE at surface}|$ .
  $\tfrac{1}{2}mv_{\text{esc}}^2 = \dfrac{GMm}{R}$
2. Step 2
  Solve.
  $v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}} = \sqrt{\dfrac{2 \times 6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{6.37 \times 10^6}} \approx 1.12 \times 10^4 \text{ m/s}$
Answer
$v_{\text{esc}} \approx 11.2$ km/s.

Key Formulae — Gravitational potential

The formulae you need to memorise for gravitational potential on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Gravitational potential
$\phi = -\dfrac{GM}{r}$
$\phi$
potential energy per unit mass
When to use
Energy needed per unit mass to move from $r$ to infinity. Always negative — zero at infinity.
Gravitational PE
$U = -\dfrac{GMm}{r}$
When to use
Energy stored at distance $r$ . Reference: $U = 0$ at $r = \infty$ .
Escape velocity
$v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}}$
When to use
Minimum speed to escape from surface of body to infinity. From energy conservation.

Key Definitions and Keywords — Gravitational potential

Definitions to memorise and the exact keywords mark schemes credit for gravitational potential answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Gravitational potential $\phi$
Examiner keyword
Work done per unit mass to move from infinity to a point. Always negative; zero at infinity.
Escape velocity
Examiner keyword
Minimum speed needed to leave a planet's gravitational field (reach infinity).

Common Mistakes and Misconceptions — Gravitational potential

The traps other students keep falling into on gravitational potential questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Treating gravitational PE as positive
9702 Examiner Reports 2022-2024
Why it happens
$mgh$ form is positive near surface.
How to avoid it
Universal form is $U = -GMm/r$ . Negative because zero is at infinity. $mgh$ measures CHANGE in PE from a chosen reference.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Gravitational potential — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Gravitational FieldsCambridge International A Levels Physics (9702)

Gravitational potential

Work through the notes, try the practice questions, then take the quiz. The report tells you exactly what to revise next.

PreviousNext

Learn this Topic

Start with the slides for the quick version, then go deeper with the full study notes.

Short Study Notes in the form of Slides

Read the notes first. If the method in a worked example clicks, you're ready for the questions.

Page 1 / 0

Detailed Study Notes

Full prose, callouts and a recap — built for A* mastery, not just a quick scan.

Take these study notes with you

Download a branded PDF — full prose, callouts, recap and memorise list for Gravitational potential, ready to print or save offline.

Gravitational Potential Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Potential $\phi = -GM/r$ . Energy considerations. Escape velocity.

What you’ll learn

Mapped to the Cambridge IGCSE 9702 syllabus (2025-2027).

13.4.1 — Define gravitational potential.
13.4.2 — Compute GPE.
13.4.3 — Find escape velocity.

Gravitational potential

Negative; zero at infinity.

Definition. Work done per unit mass to bring test mass from infinity to point.

Formula. $\phi = -GM/r$ for point mass.

Always negative. Test mass attracted toward source: external work needed to MOVE AWAY (positive); going TOWARD source releases energy (negative).

Reference. $\phi \to 0$ as $r \to \infty$ .

GPE. $U = m\phi = -GMm/r$ .

Cambridge tip. State 'zero at infinity' for top marks.

$\phi = -GM/r$ .
Negative everywhere.
Zero at infinity.

See the full worked example for gravitational potential →

Escape velocity

$\sqrt{2GM/R}$ .

Setup. Object at surface with speed $v$ . Reach infinity (minimum: arrive with $v = 0$ ).

Energy conservation. $\tfrac{1}{2}mv_{\text{esc}}^2 + \left(-\frac{GMm}{R}\right) = 0$ $v_{\text{esc}} = \sqrt{\frac{2GM}{R}}$

Earth. $v_{\text{esc}} \approx 11.2$ km/s. Moon. ~2.4 km/s. Sun (from surface). ~618 km/s.

Black hole. Escape velocity = $c$ at event horizon (Schwarzschild radius).

Cambridge tip. Independent of escape ANGLE — only speed matters (ignoring air resistance).

$v_{\text{esc}} = \sqrt{2GM/R}$ .
From energy conservation.
Earth ~11.2 km/s.

See the full worked example for gravitational potential →

How it’s examined

Gravitational potential central to A2. Most-tested: GPE (5-7 marks), escape velocity (8 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

Master this Topic

Worked examples, formulae, definitions and the mistakes examiners flag — everything you need to push from a pass to an A*.

Take this whole topic with you

Download a branded revision sheet — worked examples, formulae, definitions and common mistakes for Gravitational potential, ready to print or save as PDF.

Step-by-step worked examples — Gravitational potential

Step-by-step solutions to past-paper-style questions on gravitational potential, written exactly the way a tutor would explain them at the board.

1GPE at distance $r$ (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• GPE
Question
Find the gravitational potential energy of a 500 kg satellite at $r = 7.0 \times 10^6$ m from Earth's centre. $M_E = 5.97 \times 10^{24}$ kg, $G = 6.67 \times 10^{-11}$ . (5 marks)
Step-by-step solution
1. Step 1
  $U = -GMm/r$ .
  $U = -\dfrac{(6.67 \times 10^{-11})(5.97 \times 10^{24})(500)}{7.0 \times 10^6} \approx -2.84 \times 10^{10} \text{ J}$
Answer
$U \approx -2.84 \times 10^{10}$ J.
2Escape velocity (8 marks)
Extended• escape velocity
Question
Find escape velocity from Earth's surface. $M_E = 5.97 \times 10^{24}$ kg, $R_E = 6.37 \times 10^6$ m. (8 marks)
Step-by-step solution
1. Step 1
  Escape velocity: KE at surface = $|\text{PE at surface}|$ .
  $\tfrac{1}{2}mv_{\text{esc}}^2 = \dfrac{GMm}{R}$
2. Step 2
  Solve.
  $v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}} = \sqrt{\dfrac{2 \times 6.67 \times 10^{-11} \times 5.97 \times 10^{24}}{6.37 \times 10^6}} \approx 1.12 \times 10^4 \text{ m/s}$
Answer
$v_{\text{esc}} \approx 11.2$ km/s.

Key Formulae — Gravitational potential

The formulae you need to memorise for gravitational potential on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Gravitational potential
$\phi = -\dfrac{GM}{r}$
$\phi$
potential energy per unit mass
When to use
Energy needed per unit mass to move from $r$ to infinity. Always negative — zero at infinity.
Gravitational PE
$U = -\dfrac{GMm}{r}$
When to use
Energy stored at distance $r$ . Reference: $U = 0$ at $r = \infty$ .
Escape velocity
$v_{\text{esc}} = \sqrt{\dfrac{2GM}{R}}$
When to use
Minimum speed to escape from surface of body to infinity. From energy conservation.

Key Definitions and Keywords — Gravitational potential

Gravitational potential $\phi$
Examiner keyword
Work done per unit mass to move from infinity to a point. Always negative; zero at infinity.
Escape velocity
Examiner keyword
Minimum speed needed to leave a planet's gravitational field (reach infinity).

Common Mistakes and Misconceptions — Gravitational potential

The traps other students keep falling into on gravitational potential questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Treating gravitational PE as positive
9702 Examiner Reports 2022-2024
Why it happens
$mgh$ form is positive near surface.
How to avoid it
Universal form is $U = -GMm/r$ . Negative because zero is at infinity. $mgh$ measures CHANGE in PE from a chosen reference.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

Get a report showing which sub-topics you've nailed and which ones still need work.

Video lesson

Short walkthrough of the concepts students most often get stuck on.

Gravitational potential — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Gravitational potential

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1GPE at distance rrr (5 marks)

2Escape velocity (8 marks)

Gravitational potential

Gravitational PE

Escape velocity

Gravitational potential ϕ\phiϕ

Escape velocity

✕Treating gravitational PE as positive

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Gravitational potential — frequently asked questions

Gravitational potential

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1GPE at distance rrr (5 marks)

2Escape velocity (8 marks)

Gravitational potential

Gravitational PE

Escape velocity

Gravitational potential ϕ\phiϕ

Escape velocity

✕Treating gravitational PE as positive

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Gravitational potential — frequently asked questions

1GPE at distance $r$ (5 marks)

Gravitational potential $\phi$

1GPE at distance $r$ (5 marks)

Gravitational potential $\phi$