Labs / Astronomy
Kepler's Equal Areas
A planet is orbiting the Sun, which sits at one focus of the ellipse. Each colored slice is swept out in the same amount of time — yet the planet moves far faster near the Sun than far away. Watch the areas come out equal anyway, and read off the speed, distance, and swept area as it goes. That is Kepler's second law.
v —r —swept —each —
What to try
- Set the orbit to "Extreme" and pause near the Sun. How much faster is the planet at perihelion than at aphelion?
- Every wedge takes the same time to sweep — so why are the thin ones stretched long and the fat ones stubby and short?
- Compare the "swept" readout as each slice finishes. Does the area really land on the same number every time, whatever the eccentricity?
- Switch to a perfect "Circle". Does the planet still speed up and slow down, or does it glide at one constant pace?
- Change the sweep interval from T ÷ 4 to T ÷ 12. What stays the same about each slice, and what changes?