Kepler's Second Law says that a planet sweeps out equal areas in equal times as it orbits the Sun.
In this demo, the Sun sits at one focus of an ellipse. The planet moves faster when close to the Sun
and slower when farther away, but each highlighted sector corresponds to the same time interval and has nearly the same area.
Watch how the planet speeds up near perihelion and slows down near aphelion, while equal-time shaded sectors stay nearly equal in area.
For an ellipse with eccentricity e, position can be parameterized by the eccentric anomaly E:
x = a(cos E - e), y = b sin E, where b = a√(1-e²).
Kepler's equation: M = E - e sin E. Equal time means equal increments in mean anomaly M,
which produce equal swept areas.
Sector
Time Interval
Approx. Swept Area
Planet Distance from Sun
Angular Motion During Interval
Status
This app uses equal increments of mean anomaly to represent equal times, then computes sector areas numerically.
Small differences shown are due to polygon approximation and screen discretization.