Kepler’s Third Law
Lesson notes
Overview
The square of a planet’s orbital period is proportional to the cube of its distance. This topic is rated advanced and is number 32 of 98 in Earth & Space. Deeper models, formal results and harder reasoning.
What you are seeing
The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.
In depth
Kepler’s third law states that the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit. In units of years and AU, T² = a³, so a planet at 4 AU takes 8 years. Newton showed the constant depends on the mass of the central body, which lets astronomers weigh stars and planets from the orbits of their companions, including the moons of Jupiter and exoplanets.
Reading the relationship
The expression "T² = a³ (years, AU)" is a compact summary of the idea. It uses the symbols T, a, y, e, r, s; name what each one stands for before you start. Notice that it contains a squared term, so doubling that quantity changes the result by a factor of four. Then use the sliders to see how changing one quantity changes the others.
A guided exploration
1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.
Try this
Try to explain why the pattern holds, not just what it is. Look for limiting cases and what happens at the edges.
Common pitfalls
Earth and space systems work on very different scales of time and distance. Check which scale a number refers to before comparing it with another.
How it connects
It builds on “Surface Gravity of the Planets”, the topic before it in Earth & Space. Once you are comfortable, continue with “The Habitable Zone”.
Why it matters
Earth and space science helps us understand our planet, its climate and the wider universe.
Where you might use it
- Revising “Kepler’s Third Law” before a class, exam or certification
- Forecasting weather and understanding climate records and their uncertainty
- Planning for earthquakes, floods and other natural hazards in cities
- Interpreting satellite images, space missions and the age of rocks and stars
Frequently asked questions
What is Kepler’s Third Law?
The square of a planet’s orbital period is proportional to the cube of its distance. It is an advanced topic in Earth & Space.
How do I use the Kepler’s Third Law simulation?
The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression T² = a³ (years, AU) packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Deeper models, formal results and harder reasoning. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Surface Gravity of the Planets”, the previous topic in Earth & Space. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.
Quick quiz
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