How to play Kepler's Clock
- Choose an orbit and read the central mass, the distances, and any known period on the card.
- Use T = 2π·√(r³ ÷ G·M), or compare two bodies around the same centre with T² ∝ r³.
- Type your answer and press Run. A period runs the clock for that many days; a mass sets Jupiter; a distance places Mars.
- If you are right, the marked body comes back exactly to the start mark. Then read the graph: every body lies on the line T² ∝ r³.
What is Kepler's third law?
Johannes Kepler found that the farther a planet is from the Sun, the longer it takes to go around, with T² proportional to r³. Newton's law of universal gravitation explains why: for a circular orbit, gravity supplies the centripetal force, G·M·m ÷ r² = m·(2π ÷ T)²·r, so T² = 4π²·r³ ÷ (G·M). The orbiting body's mass cancels, and the constant 4π² ÷ (G·M) is the same for every body around the same centre. That lets you compare two moons or planets with a simple ratio, find a distance from a period, or even weigh a planet or a star from the orbit of something going around it.
A focused learning model
Each orbit is a circle around a fixed central body, and the orbiting bodies do not pull on each other. Real orbits are slightly elliptical, and the central body also moves a little, so the Moon's measured month is 27.32 d rather than 27.45 d. Completed orbits and the end of each run are found exactly. Orbits are drawn to scale; the time per second on screen is shown on the canvas.