Maths in physics and engineering · Solid · Dissertation

Kepler's third law from Newton: a maths EPQ idea

Why it works as an EPQ

A short derivation for circular orbits, then a log–log test on real data, then an evaluation of the approximations.

Scope and difficulty

Solid. Solid. Circular orbits derived; elliptical orbits discussed.

The maths

Builds on these A Level topics: Forces and Newton's laws · Kinematics · Exponentials and logarithms · Sampling and data.

You would learn:

• Circular motion
• Newton's law of gravitation
• Log–log graphs

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

1. Derive T² ∝ r³ for circular orbits.
2. Collect orbital data from a reliable source.
3. Fit a power law on a log–log graph.
4. Evaluate the circular-orbit assumption and the role of the central mass.

Pitfalls

• Data without units or sources.
• Calling the fit a proof.

Where to start reading

• NASA planetary fact sheets
• Search for: Kepler third law derivation circular orbit

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

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All maths in physics and engineering ideas · all 93 ideas

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