Explore Kepler’s three laws of planetary motion with interactive diagrams.
Every planet moves in an ellipse with the Sun at one focus.
Planet position: (, )
Distance to Sun (focus 1):
Distance to focus 2:
Total PF₁ + PF₂ =
This constant sum defines the ellipse.
A line from the planet to the Sun sweeps out equal areas in equal intervals of time.
Time step:
Area swept:
No matter where the planet is, equal time → equal area.
The square of a planet’s orbital period is proportional to the cube of its semi‑major axis:
T² ∝ a³
a =
T² = a³ → T =