Kepler's laws of planetary motion

Three rules describe planetary orbits: planets follow ellipses with the Sun at one focus, sweep equal areas in equal times, and obey a period–orbit-size scaling law.

Kepler's first law: A planet moves on an ellipse with the Sun at one focus. This law fixes the geometric shape shared by idealized planetary orbits.
Tycho Brahe: A Danish astronomer whose precise pre-telescopic observations greatly improved measurements of planetary positions. His observations gave Kepler the data needed to test competing orbit shapes.
Ellipse: A closed curve whose points have a constant sum of distances from two foci. The first law identifies this curve as the ideal planetary path.
Isaac Newton: An English mathematician and physicist who formulated classical mechanics and universal gravitation. Newton showed how inverse-square gravity yields Kepler's orbital relationships.
Circular orbit: An orbit whose distance from its central body remains constant. A circle is only a special zero-eccentricity case of the first law's ellipse.
Kepler's second law: A line from a planet to the Sun sweeps equal areas in equal time intervals. This law explains why orbital speed increases near the Sun and decreases farther away.
Rudolphine Tables: Astronomical tables published in 1627 that predicted planetary positions using Kepler's methods. They applied Kepler's orbital theory to practical astronomical prediction.
Focus (geometry): One of two fixed points that define an ellipse and help determine its shape. The Sun occupies one focus in the first law, not the ellipse's center.
Newton's laws of motion: Three principles relating force, mass, and motion in classical mechanics. Combined with gravitation, they turn Kepler's empirical patterns into consequences of dynamics.
Two-body problem: The mathematical problem of predicting the motion of two mutually gravitating bodies. Kepler's laws describe the idealized solution when only the Sun and one planet interact.

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