Kepler's Laws of Planetary Motion
Johannes Kepler published his three empirical laws between 1609 and 1619, based on Tycho Brahe's naked-eye observations of Mars. Newton later showed that all three follow from his law of universal gravitation in a two-body system.
First law: the law of ellipses
The orbit of every planet is an ellipse with the Sun at one of the two foci. The shape of an ellipse is set by its semi-major axis a (half the longest diameter) and its eccentricity e (a number between 0 and 1). The simulator uses these two numbers to draw any bound orbit: e = 0 gives a circle, while e close to 1 gives a long, narrow ellipse.
Second law — equal areas in equal times
The line joining a planet to the Sun sweeps out equal areas in equal intervals of time. This is a direct statement of conservation of angular momentum under a central force. The practical consequence is that a body moves fastest at periapsis (its closest approach to the central body) and slowest at apoapsis (its farthest point). This is exactly what you see when the simulator's eccentricity slider is increased.
Third law: the harmonic law
The square of the orbital period T is proportional to the cube of the semi-major axis a. For any object orbiting a body of mass M, T² = (4π²/μ)·a³, with μ = G·M. This single relation lets you compute the period of a low Earth orbit (~90 min), of geostationary orbit (~24 h), and of the Moon (~27.3 days) from the same formula.
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