Why Orbits Work: Kepler's Three Laws in Plain Language
Between 1609 and 1619, Johannes Kepler extracted three simple statements from Tycho Brahe's careful naked-eye observations of Mars. Those three laws still describe every orbit in the solar system — and every planet Kepler-the-spacecraft has since found around other stars.
First law: orbits are ellipses
Every planet moves on an ellipse with the Sun at one of the two foci. The other focus is mathematically important and physically empty.
This was the surprise. For 2,000 years Greek and Islamic astronomers had assumed orbits were combinations of perfect circles — Ptolemy stacked more than 40 of them to fit the observed motion of the planets. Kepler showed you need exactly one ellipse per planet.
How elliptical? For most planets, barely. Earth's eccentricity is 0.017 — you would not be able to tell its orbit from a circle in a drawing. Mars is 0.093, noticeably out-of-round. Mercury is 0.206. Comets are the extreme case: Halley's has eccentricity 0.967.
Second law: equal areas in equal times
Draw a line from a planet to the Sun. As the planet moves, that line sweeps out area. Kepler's second law says the area swept per unit time is constant — so the planet moves faster near perihelion (closest to the Sun) and slower near aphelion (farthest).
This is a statement about angular momentum being conserved, though Kepler had no way to know that yet. Earth is a real example: we are at perihelion in early January (147 million km) and aphelion in early July (152 million km). At perihelion Earth is moving at 30.3 km/s; at aphelion, 29.3 km/s.
Third law: period squared, distance cubed
The square of a planet's orbital period is proportional to the cube of its average distance from the Sun. In units where distance is in astronomical units (AU) and period is in Earth years, the constant of proportionality is exactly 1: P² = a³.
| Planet | a (AU) | P² / a³ |
|---|---|---|
| Mercury | 0.387 | 1.000 |
| Venus | 0.723 | 1.000 |
| Earth | 1.000 | 1.000 |
| Mars | 1.524 | 1.000 |
| Jupiter | 5.203 | 1.000 |
| Saturn | 9.537 | 1.000 |
| Uranus | 19.19 | 1.000 |
| Neptune | 30.07 | 1.000 |
That last column is not a coincidence — it's the law. Earth at 1 AU takes 1 year; Neptune at 30 AU takes ≈165 years, and 30³ ≈ 27,000 ≈ 165². The whole solar system dances to the same relation.
Where the laws come from
Kepler found the laws empirically. Half a century later, in his Principia (1687), Newton derived all three from a single premise: a force proportional to 1/r² between any two masses. Kepler's laws are what an inverse-square gravitational attraction looks like when one mass is much larger than the other.
Why this is still useful
Kepler's laws are what make orbital predictions cheap. Given one good position measurement plus a velocity, you can predict where a planet, a comet, or a satellite will be for centuries. NASA plots interplanetary spacecraft trajectories on the same framework Kepler wrote down before the telescope was fifteen years old.
Frequently asked
- Do the laws work for satellites?
- Yes. Any orbit of one small object around a much more massive one obeys the same three laws. GPS satellites, the ISS, and the Moon all follow them; only the constant in the third law changes with the central mass.
- Where is Earth's aphelion?
- About July 4th each year, at roughly 152.1 million km from the Sun. Perihelion is around January 3rd at 147.1 million km. The difference doesn't drive the seasons — axial tilt does.
- What happens for near-circular orbits?
- The math still applies, but the two foci sit almost on top of each other and the ellipse looks like a circle. The second law reduces to constant speed, which is what you'd expect.