Gravitational field strength (A-level only) — AQA A-Level Physics

Gravitational field strength is a fundamental concept in A-level Physics that quantifies the gravitational force per unit mass at any point in a gravitational field. It explains why objects fall with the same acceleration regardless of mass and is essential for understanding planetary motion, satellite orbits, and the behaviour of masses in fields. The topic builds on Newton's law of gravitation and introduces the inverse square law for radial fields, linking to gravitational potential and energy.

In the AQA A-Level specification, this topic is part of the 'Fields and their consequences' unit. It provides the foundation for analysing orbits, escape velocity, and the motion of planets and satellites. Mastery of gravitational field strength is crucial for tackling synoptic questions that combine mechanics, energy, and fields, and it frequently appears in exam calculations and explanations.

• →Gravitational field strength (g) is defined as the gravitational force per unit mass on a small test mass, g = F/m, and is a vector quantity measured in N kg^-1.
• →For a radial gravitational field produced by a point mass or spherically symmetric body, g = GM/r^2, where M is the mass of the body and r is the distance from its centre.
• →Near the Earth's surface, the field is approximately uniform, with g ≈ 9.81 N kg^-1, and gravitational force is F = mg.
• →Inside a uniform solid sphere, g is directly proportional to the distance from the centre (g ∝ r), while outside it follows an inverse square law (g ∝ 1/r^2).
• →The gravitational field strength is the negative gradient of gravitational potential: g = -dV/dr, linking field strength to potential.

• Draw gravitational field lines pointing radially inwards towards the centre of a spherical mass.
• Use the spacing of field lines to represent the magnitude of gravitational field strength, with closer lines indicating a stronger field.
• Explain that field lines show the direction of the gravitational force on a small test mass placed in the field.
• Recognise that field lines do not cross and that the field is radial near an isolated spherical mass.
• Interpret field-line diagrams for more than one mass, showing the resultant field direction at a point.

• 💡Use arrows on field lines to show direction clearly, and make the lines meet the surface at right angles for a spherical mass.
• 💡When comparing two points, refer to the spacing of field lines to justify which has greater gravitational field strength.
• 💡For two masses, sketch the resultant field pattern and mark the neutral point if it exists, showing where fields cancel.
• 💡Always write the defining equation and substitute values with units before calculating. This secures method marks even if the final answer is wrong.
• 💡When explaining field strength, use precise terminology: 'force per unit mass' not 'force per mass' or 'gravitational pull'. Avoid saying 'gravity' when you mean 'gravitational field strength'.
• 💡For graph questions, label axes with quantities and units, and indicate key features such as the surface value, the inverse square decrease outside, and the linear increase inside a solid sphere.

• Drawing field lines pointing outwards from a mass; correction: gravitational field lines point inwards because gravity is attractive.
• Drawing field lines crossing each other; correction: field lines never cross because the field has a single direction at any point.
• Using evenly spaced lines everywhere around a planet; correction: spacing should increase with distance to show decreasing field strength.
• Students often think gravitational field strength and gravitational potential are the same thing. Correction: g is force per unit mass (N kg^-1), while V is work done per unit mass (J kg^-1); they are related by g = -dV/dr.
• Many believe that g is always 9.81 N kg^-1 everywhere on Earth. Correction: g varies with altitude, latitude, and local geology; it decreases with height above the surface according to the inverse square law.
• Students sometimes assume that inside a planet, g continues to increase as you go deeper. Correction: Inside a uniform sphere, g decreases linearly with distance from the centre, reaching zero at the centre.

1. 1Day 1-2: Review Newton's law of gravitation and the definition of gravitational field strength. Learn the equation g = GM/r^2 and its derivation from F = mg and F = GMm/r^2.
2. 2Day 3-4: Practice calculations for g at the surface and at altitude for different planets. Include unit conversions and standard form.
3. 3Day 5-6: Study the variation of g inside and outside a uniform sphere. Sketch and interpret g-r graphs, noting the linear and inverse square regions.
4. 4Day 7-8: Work through exam-style questions on gravitational field strength, including those linking to gravitational potential and orbital motion. Mark your answers using the mark scheme.
5. 5Day 9-10: Create a summary sheet with key definitions, equations, graphs, and common pitfalls. Test yourself with active recall prompts and past paper questions.

• 📋Calculation of gravitational field strength: Use g = GM/r^2 to find g at a planet's surface or at a given altitude. Remember to add the altitude to the planet's radius to find r.
• 📋Explanation of field strength variation: Describe and explain how g changes inside and outside a planet, often requiring a graph. Use the shell theorem and the concept of enclosed mass.
• 📋Comparison of gravitational field strength on different planets: Calculate g for two planets and compare, or explain why g differs based on mass and radius.
• 📋Link to gravitational potential: Given a graph of potential against distance, determine g from the gradient, or vice versa. Use g = -dV/dr.