Kepler's Laws
Planets move on ellipses, sweep equal areas in equal times, and obey T² ∝ a³.
About this topic
Kepler's three laws describe planetary motion. First: orbits are ellipses with the Sun at one focus. Second: a line from the Sun to a planet sweeps out equal areas in equal times, so planets move faster when closer. Third: T² is proportional to a³, the square of the period to the cube of the average orbital distance. Kepler found them from Tycho Brahe's careful observations of Mars.
The second law is really conservation of angular momentum: when a planet is near the Sun its speed rises, and when far away it slows. Earth is closest to the Sun in early January and travels slightly faster then. The third law follows directly from Newton's gravitation, and for the Sun gives T² = a³ when T is in years and a is in astronomical units.
Worked example: Jupiter orbits at 5.2 AU, so T² = 5.2³ ≈ 140.6 and T ≈ 11.9 years, which matches observation. If an asteroid has T = 8 years then a³ = 64, so a = 4 AU.
The laws apply to moons around planets and satellites around Earth too, with a different constant. Astronomers use them to find the masses of stars and the orbits of exoplanets. A misconception is that planetary orbits are very elongated; most are almost circular, and seasons come from Earth's axial tilt, not from its distance from the Sun.
Key ideas
- Law 1: ellipse with Sun at a focus
- Law 2: faster near the Sun
- Law 3: T² = a³ for AU and years
Quick check
Use cases: where Kepler's Laws helps
- Homework: review the key idea behind Kepler's Laws before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Kepler's Laws without notes.
- Visual learning: play with the interactive lab to see how Kepler's Laws changes when you adjust its inputs.
- Teaching a friend: explain Kepler's Laws in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Kepler's Laws?
Planets move on ellipses, sweep equal areas in equal times, and obey T² ∝ a³.
What will I learn in Kepler's Laws?
Law 1: ellipse with Sun at a focus. Law 2: faster near the Sun. Law 3: T² = a³ for AU and years.
Is Kepler's Laws part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Kepler's Laws lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Kepler's Laws?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.