Calculator for Kepler's 3rd law
Calculates the square of the ratio of the orbital periods and the cube of the ratio of the semimajor axes of two planets and compares them with each other.
The formula for Kepler's third law is
Please enter three or four values or select planets, the fourth value and the two ratios will be calculated. The more distant planet should be selected first, otherwise the ratio may become 0 by rounding. Due to rounding, the ratios may differ slightly from one another.
Kepler's first law states that planets orbit their stars in elliptical paths, with the Sun, respectively the star, situated at one of the foci. In the case of the eight planets in our solar system, these ellipses are nearly circular, though not perfectly so. There are exoplanets with highly eccentric orbits, and Pluto, too, has an orbit that differs significantly from a perfect circle. Before Kepler, it was assumed that planets followed circular paths (and, prior to Copernicus, it was even thought they orbited the Earth), but this could not be reconciled with observational data.
Kepler's second law states that a planet sweeps out equal areas in equal intervals of time. These areas are known as Kepler sectors. Due to the elliptical orbit, the planet is sometimes closer to its star and sometimes farther away. Consequently, to sweep out the same area within a given timeframe, it must move faster when it is closer to the star.
Although Kepler discovered these laws for planets, they also apply to other celestial bodies, such as moons and asteroids. Comets can also follow hyperbolic trajectories and then become one-time visitors to the solar system.
Last updated on 08/11/2026. Author: Jürgen Kummer
Calculators for Planets and Astronomy
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