Education Principle Animation:Kepler’s Laws Lab

Tie a string to two pins and trace around it: the pen’s distances to the pins always add up to the string length 2a. A planet’s orbit is such an ellipse with the Sun at one focus and nothing at the other. Drag eccentricity to 0 and it becomes a circle.

The red and blue sectors take the same time—a tenth of a period. Near perihelion the sector is short and wide, near aphelion long and thin, and computed from the true orbit their areas match. The whole ellipse splits into ten equal-area slices, each crossed in the same time.

Falling toward the Sun, part of gravity points along the motion and speeds the planet up; climbing away, gravity pulls back and slows it. Each pair of dots is the same time apart, so they spread out near perihelion. Kinetic and potential energy trade off while their sum stays constant.

Mercury takes 88 days, Mars almost two years. Square the period, cube the semi-major axis, and every planet gives the same ratio; on log axes they line up on a slope of 3/2. Double the star’s mass and every period shrinks to 0.71 of its value.