Kepler's Laws
Solar system builder. Builds on Orbits & Escape Velocity.
A comet orbits the Sun in a highly elliptical orbit. At its closest approach (perihelion), it's 1 AU from the Sun and moving at 40 km/s. At its farthest point (aphelion), it's 10 AU from the Sun.
How fast is the comet moving at aphelion?
Exactly 4 km/s — 10× slower at 10× the distance! This is Kepler's area law: the line from Sun to comet sweeps equal areas in equal times.
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Watch the comet sweep out equal areas in equal times. It races at perihelion and crawls at aphelion.
T² = (4π²/GM) a³
Farther orbits are slower — both in speed AND in period. Jupiter takes 12 years to orbit!
Speeds past the Sun at 54 km/s but crawls at aphelion at just 0.9 km/s
GPS satellites at higher orbits move slower than the ISS
Earth is actually slightly closer to the Sun in January — and moves slightly faster
“The planets dance to the same music — Kepler heard the melody, Newton wrote the score.”
Orbit Designer
Create custom orbits and watch Kepler's laws in action. See the area sweeping, the speed changing, and the period relationship.
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Make a very eccentric orbit (drag the planet close to the star). Watch how the area-sweep stays constant even as the speed varies wildly. Then make two orbits — one at 1 AU and one at 4 AU. How do their periods compare?
Kepler's third law (T² ∝ a³) means a planet at 4× the distance takes 8× as long to orbit. These laws, once mysterious patterns, are natural consequences of gravity.