Kepler's Laws
Watch a planet trace an exact elliptical orbit with the star at one focus, its equal-time sectors shaded to show equal-area sweeps, and a second comparison planet whose period and semi-major axis satisfy the same T^2/a^3 ratio.
Preview — sign up free to change the numbers yourself
What you can adjust
- Planet 1 semi-major axis
- 0.3 – 5 AU
- Planet 1 eccentricity
- 0 – 0.9
- Central star mass
- 0.2 – 5 solar masses
- Planet 2 (comparison) semi-major axis
- 0.3 – 5 AU
- Equal-time sectors
- 4 – 12
The orbit's average distance from the star, in astronomical units (Earth = 1 AU). Sets the ellipse's overall size.
0 is a perfect circle; higher values stretch the ellipse — the star always sits at one focus, never the center.
A heavier star pulls harder, shortening both planets' orbital periods for the same semi-major axis.
A second, independent planet (near-circular) orbiting the same star — compare its period against planet 1's to see T^2/a^3 come out equal for both.
How many equal-TIME slices of planet 1's orbit to shade. Kepler's second law says every one of these sectors sweeps out the SAME area, even though they cover very different arcs of the ellipse.
About this simulation
What it shows
A planet follows an elliptical orbit with the star at one focus, with equal-time sectors shaded in. A second planet orbits the same star for comparison.
The key idea
Planets sweep out equal areas in equal times, so they move fastest when closest to the star. The square of the period is proportional to the cube of the average distance (T² ∝ a³), the same for every planet around one star.
Try this
Set Planet 1 semi-major axis to 1 AU and Planet 2 (comparison) semi-major axis to 4 AU: planet 2's period is 8 times longer, yet T²/a³ is the same for both.