A Level Gravitational Fields Hub
A Level Physics gravitation hub: Newton's Law, field strength, potential energy, and satellite orbits.
Learning goals
- Apply Newton's law of gravitation to point and spherical masses.
- Derive and apply gravitational field strength, including the near-surface model.
- Derive the gravitational field strength due to a point mass from Newton's law of gravitation and the definition of field strength.
- Relate gravitational potential, potential energy and field gradient.
- Analyse escape speed using conservation of energy.
- Analyse circular gravitational orbits and geostationary satellite conditions.
Gravitational fields connect an inverse-square force model to field strength, potential, escape and satellite motion. The key is to keep centre-to-centre distance, signs and system boundaries consistent.
Understand first: this topic is one workflow with force, potential, and circular motion, not separate formula lists.
Minimum prerequisite route:
Common mark-loss errors: using r from the surface instead of the centre, sign mistakes in potential work, and skipping the “towards centre” direction statement.
After this hub: complete the A Level Gravitation Quiz, then attempt the Gravitation Structured Set before cross-checking orbit setup on circular-motion drills. Move to structured work when: you can solve a mixed orbit + potential-energy question without changing sign convention halfway.
Lessons
Work through these lessons in order.
- Gravitational force and field strength
- Potential, potential energy and field gradient
- Escape speed through energy stores and transfers
- Circular and geostationary orbits
- Newton's Law of Universal Gravitation
Use Newton’s law of gravitation F = GMm/r², including the inverse-square relationship and the centre-to-centre distance r (A Level Physics).
- Gravitational Field Strength & Field Lines
Define gravitational field strength g, derive g = GM/r² for a point mass, and interpret gravitational field lines (A Level Physics).
- Gravitational Potential & Gravitational Potential Energy
Define gravitational potential φ as work done per unit mass from infinity, use φ = −GM/r and U = mφ, and apply g = −dφ/dr (A Level Physics).
- Escape Speed
Derive escape speed using energy: v_esc = √(2GM/r), apply it at different altitudes, and avoid common traps (A Level Physics).
- Circular Orbits & Geostationary Satellites
Analyse circular orbits using gravity as centripetal force, use v = √(GM/r) and T² ∝ r³, and solve geostationary satellite problems (A Level Physics).
Revision
Quick Reference
| Quantity | Formula | Unit |
|---|---|---|
| Force magnitude | F = GMm/r² | N |
| Field strength | g = F/m = GM/r² (magnitude) | N kg⁻¹ |
| Potential | φ = -GM/r | J kg⁻¹ |
| Potential Energy | U = mφ = -GMm/r | Joule (J) |
Satellite Orbit: GMm/r² = mv²/r ⇒ v = square root of (GM/r)
Exam templates (fast marks)
1) Force / field strength
- Use centre-to-centre distance: r = R + h if altitude h is given.
- Use F = GMm/r² or g = GM/r² (magnitudes).
- Add direction in words: “towards the centre of the mass”.
2) Potential / potential energy
- Write φ = -GM/r and U = mφ.
- For slow transfer from A to B, external work is Wₑₓₜ = m(φ_B-φ_A); work done by gravity has the opposite sign.
- Keep track of signs; potential becomes more negative as r decreases.
3) Circular orbit
- Set gravitational force = centripetal resultant: GMm/r² = mv²/r.
- Solve for v = square root of (GM/r) and (if needed) T = (2π r)/v.
What You Must Memorise
- Newton’s Law of Gravitation: Every particle attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
- Gravitational Field Strength (g): The force per unit mass experienced by a small test mass at that point.
- Gravitational Potential (φ): The work done per unit mass by an external force in bringing a small test mass from infinity to that point. For an isolated mass with zero at infinity, φ < 0 at finite r.
- Geostationary orbit: A circular equatorial orbit in Earth’s rotational direction, with period equal to Earth’s rotation, so the satellite appears fixed above one point.
Top Exam Traps
- Negative Signs: Force and Energy in gravitation are attractive/bound, so they are often negative. Potential is zero at infinity and becomes more negative as you approach the mass.
- Distance r: r is the distance from the CENTRE of the mass, not the surface. If given altitude h, use r = Rₑₐᵣₜₕ + h.
- Work Done: Work done moving from A to B is m(φ_B - φ_A). Watch the signs carefully!
- Weightlessness: Astronauts in orbit are NOT weightless (gravity acts on them). They feel weightless because they are in free fall (normal reaction is zero).
- Escape speed: It depends on the source mass and starting radius, not the spacecraft mass. v_esc = square root of (2GM/r) under the stated ideal assumptions.
Practice
Test your understanding of Gravitation, then reinforce orbit mechanics and mixed-topic setup:
A Level Gravitation QuizGravitation Structured SetA Level Circular Motion QuizA Level Physics Quiz HubNext hub: Oscillations
Continue with the next resource in this course.
Course and syllabus information
- Course
- GCE A-Level H2 Physics
- Edition
- GCE A-Level H2 Physics 2027