QCE Physics - Unit 3 - Gravity and motion

Gravitational Fields and Kepler's Laws | QCE Physics

Learn QCE Physics gravitational fields, inverse-square gravity, field strength, orbital motion and Kepler's third law.

Updated 2026-06-17 - 4 min read

Gravity is more than a contact-free force between two masses. QCE Physics treats gravity as a field: a region around a mass where another mass would experience a force. This field idea links weight, satellite motion, orbital speed and Kepler's laws.

Universal gravitation

Newton's law of universal gravitation states that any two masses attract each other with a force:

$ F=\frac{GMm}{r^2} $

Here $M$ and $m$ are the two masses, $r$ is the distance between their centres, and $G$ is the universal gravitational constant. The force is attractive and acts along the line joining the centres of the masses.

The inverse-square part is important. If the distance between centres doubles, the gravitational force becomes one quarter as large:

$ F \propto \frac{1}{r^2} $

This is why distance matters so strongly in orbital and field-strength questions.

Gravitational field strength

Gravitational field strength is the force per unit mass:

$ g=\frac{F}{m} $

Substitute Newton's law of gravitation into this definition:

$ g=\frac{GM}{r^2} $

This equation gives the gravitational field strength at a distance $r$ from the centre of a spherical mass $M$. The object placed in the field does not affect the field strength in this model; it only experiences the field.

Gravitational field lines point toward the source mass because gravity is attractive. Around an isolated spherical mass, the field is radial and spreads over a larger area as distance increases, which matches the inverse-square decrease in $g$.

Weight is then:

$ F_g=mg $

Mass is the amount of matter in an object. Weight is the gravitational force on that mass. Mass stays the same when an astronaut moves from Earth to the Moon, but weight changes because $g$ changes.

Kepler's three laws

Kepler's laws describe planetary motion:

1. Planets move in elliptical orbits with the Sun at one focus.
2. A line from the Sun to a planet sweeps out equal areas in equal times.
3. The square of orbital period is proportional to the cube of orbital radius or semi-major axis.

For the circular-orbit model used in many QCE calculations, the third law is written:

$ \frac{T^2}{r^3}=\frac{4\pi^2}{GM} $

For two objects orbiting the same central mass:

$ \frac{T_a^2}{r_a^3}=\frac{T_b^2}{r_b^3} $

This comparison form is useful because $G$ and $M$ cancel.

Gravity as centripetal force

In a circular orbit, the object is accelerating toward the centre even if its speed is constant. The required centripetal force is:

$ F_c=\frac{mv^2}{r} $

For a satellite, gravity supplies that centripetal force:

$ \frac{GMm}{r^2}=\frac{mv^2}{r} $

The satellite's mass cancels, which means the orbital speed for a circular orbit depends on the central mass and radius, not on the satellite's mass:

$ v=\sqrt{\frac{GM}{r}} $

This is also why higher circular orbits have lower orbital speeds but longer periods. They move more slowly and have a larger path to complete.

Worked example

Interpreting orbital data

If a table gives orbital period and radius for several moons or planets orbiting the same central mass, check whether $T^2/r^3$ is approximately constant. Small differences can come from rounding, elliptical orbits, measurement uncertainty or using average radius rather than exact semi-major axis.

Quick check

Sources

• QCAA Physics subject page
• QCAA Physics 2025 syllabus
• QCAA Physics 2025 formula and data book
• OpenStax University Physics Volume 1: Newton's Law of Gravitation
• OpenStax University Physics Volume 1: Kepler's Laws