Solar System Lab

How orbital mechanics works

The planets orbit the Sun in ellipses, not circles, obeying the three laws Johannes Kepler distilled from decades of observations in the early 1600s. His first law says each orbit is an ellipse with the Sun at one focus. His second law says a planet sweeps out equal areas in equal times, so it moves faster when nearer the Sun and slower when farther away. His third law ties a planet's orbital period to its distance: the period squared is proportional to the semi-major axis cubed.

Newton later showed that all three laws follow from a single inverse-square law of gravity. This simulator uses real eccentricity values and solves Kepler's equation numerically for each planet, so the positions you see are faithful to the actual geometry of the solar system rather than idealized circles.

Experiments to try in this simulation

1. Verify Kepler's third law: open the T²/a³ table below the canvas. For every planet that ratio comes out to essentially the same number — the fingerprint of a single gravitational law governing them all.

2. Speed and distance: fast-forward the simulation and watch Mercury race around while Neptune barely creeps. Inner planets have far shorter years because they are both closer and moving faster.

3. Eccentric orbits: click a planet with a stretched orbit, such as Mercury or Pluto, and watch it speed up near the Sun and slow down far away — Kepler's second law in motion.

4. Compare the data: click each planet to read its semi-major axis, eccentricity, and period, and see how sharply orbital period grows with distance from the Sun.

Key laws

Kepler's third law, T² ∝ a³, is the quantitative heart of the simulation: a planet's year (T) depends only on its average distance from the Sun (the semi-major axis a), not on its mass. Double the distance and the period grows by a factor of 2^(3/2) ≈ 2.8. Kepler's second law is equivalent to the conservation of angular momentum, which forces a planet to trade speed for distance as it orbits.

Newton's law of universal gravitation, F = G·m₁m₂/r², underlies all of it — the inverse-square dependence on distance is exactly what produces closed elliptical orbits and Kepler's tidy relationships.

Real-world applications

The same orbital mechanics that place the planets guide every satellite and spacecraft we launch. Mission designers use Kepler's and Newton's laws to plan orbits, timing, and the gravitational slingshots that let probes reach the outer planets on limited fuel. Kepler's third law is also how astronomers weigh distant objects: measuring the period and size of an orbit reveals the mass at its centre — a technique used to find exoplanets and to infer the supermassive black holes at the hearts of galaxies.