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AS & A-Level Physics 13 — Gravity and Orbits

AS & A-Level Physics 13 — Gravity and Orbits

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Independent Deckloop revision aligned with the Cambridge International AS & A Level Physics (9702) syllabus, 2025–2027. Not affiliated with or endorsed by Cambridge International Education. Chapter 13 of 26: Gravity and orbits. Concepts, worked applications and misconception checks.

Physics EN A-Level
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Gravitational Fields and Field Strength

A gravitational field is a region of space where a mass experiences a force due to the presence of another mass. It is an example of a force field, meaning that a force acts on objects within it without direct contact. The strength of this field at any point is defined as the gravitational force experienced per unit mass placed at that point. Mathematically, this is expressed as g=F/mg = F/m, where gg is the gravitational field strength, FF is the gravitational force, and mm is the test mass. Gravitational field strength is a vector quantity, meaning it has both magnitude and direction. Its direction is the direction of the force on a mass, always towards the source of the field. The SI unit for gravitational field strength is Newtons per kilogram (N kg−1^{-1}), which is dimensionally equivalent to metres per second squared (m s−2^{-2}), representing the acceleration of free fall.

Key points

  • A gravitational field is a region where a mass experiences a force.
  • Gravitational field strength (gg) is force per unit mass: g=F/mg = F/m.
  • It is a vector quantity, directed towards the source mass.
  • Units are N kg−1^{-1} or m s−2^{-2} (acceleration of free fall).

Worked example

Question

A probe of mass 550 kg experiences a gravitational force of 1.25×1031.25 \times 10^3 N when orbiting a distant asteroid. Calculate the gravitational field strength at the probe's location.

Solution

1. The gravitational field strength gg is defined as the force per unit mass, g=F/mg = F/m.
2. Given force F=1.25×103F = 1.25 \times 10^3 N and mass m=550m = 550 kg.
3. Substitute the values into the formula: g=(1.25×103 N)/(550 kg)g = (1.25 \times 10^3 \text{ N}) / (550 \text{ kg}).
4. Calculate the result: g=2.2727...g = 2.2727... N kg−1^{-1}.
5. Round to an appropriate number of significant figures (e.g., 3 s.f. based on input data).

The gravitational field strength at the probe's location is 2.27 N kg−1^{-1}.

Common pitfalls

  • Confusing gravitational field strength (g) with gravitational force (F). Remember F=mgF=mg, so gg is the force per unit mass.
  • Incorrectly stating the units. While N kg−1^{-1} and m s−2^{-2} are equivalent, ensure consistency with the context (force per mass vs. acceleration).

Prerequisites

  • Understanding vector quantities like force and field strength.
  • Knowledge of force, mass, and acceleration (F=ma).
  • Understanding weight as the effect of a gravitational field on a mass.
Further resources