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The 75 pages that link to Kepler's laws of planetary motion, each with the reason it gives.

• Isaac NewtonRelated: Newton’s gravitational theory explained why the planetary patterns Kepler had found hold.

• Orbital mechanicsRelated: They summarize the geometry and timing of ideal gravitational orbits.

• Newton's law of universal gravitationRelated: Newton derived these orbital patterns from universal gravitation and motion.

• Radial velocity methodNarrower topic: The method’s orbital interpretation relies on the same period, shape, and distance relations.

• Celestial mechanicsRelated: They summarize the regular patterns that gravitational mechanics explains.

• Johannes KeplerBroader topic: These laws are Kepler’s best-known account of planetary motion.

• Binary starRelated: They connect a binary's orbital period and separation to the stars' combined mass.

• Conic sectionRelated: The first law identifies planetary orbits as ellipses with the Sun at one focus.

• Tycho BraheRelated: Kepler extracted these laws from the planetary positions Brahe had recorded.

• Astronomical unitRelated: Their period–distance relation is commonly expressed with orbital distances in astronomical units.

• Orbital periodNarrower topic: The period relation belongs to this broader description of orbital motion.

• Milankovitch cyclesNarrower topic: They provide the orbital geometry underlying eccentricity and seasonal timing.

• Geostationary orbitRelated: They relate orbital period and distance, fixing the orbit’s radius.

• Newtonian gravityBroader topic: Newtonian gravity explains these regularities as consequences of an inverse-square force.

• Earth's orbitRelated: They describe the shape and speed variation of Earth's orbit.

• AstronomyRelated: They provide a foundational description of orbital motion in planetary systems.

• HeliocentrismRelated: Elliptical orbits replaced the Copernican system’s circles and improved its predictions.

• Three-body problemCompared with: They describe ideal two-body motion, not the full mutual interaction of three bodies.

• Stellar massRelated: Orbital periods and separations yield component masses in binary stars.

• EphemerisRelated: They provide a foundational approximation for predicting planetary positions.

• Copernican heliocentrismRelated: They corrected Copernicus’s circular orbits while retaining the Sun-centered framework.

• Edmond HalleyRelated: Kepler’s rules supplied the orbital framework Halley applied to comet observations.

• EllipseRelated: Kepler’s first law identifies planetary orbits as ellipses with the Sun at one focus.

• Philosophiæ Naturalis Principia MathematicaRelated: Newton derived these orbital regularities from his laws and gravitational force.

• Vis-viva equationCompared with: They describe orbital geometry and timing, while vis-viva specifies speed at a given radius.

• Mercury's perihelion precessionRelated: In an ideal two-body Newtonian system, Keplerian ellipses do not rotate.

• Kepler Space TelescopeRelated: Transit timing and orbital periods connect Kepler detections to the geometry of planetary orbits.

• SiriusRelated: They connect Sirius A and B’s orbital period to their separation and masses.

• Hohmann transfer orbitNarrower topic: They provide the orbital framework for estimating transfer time and motion.

• Semimajor axisRelated: Kepler’s third law links a body's orbital period to its semimajor axis.

• Apollonius of PergaRelated: Kepler identified planetary orbits as ellipses, a major later use of conic geometry.

• Circular motionCompared with: Planetary orbits are generally elliptical, showing why circular motion is an approximation in orbital mechanics.

• EquantCompared with: Kepler replaced circle-based constructions like the equant with elliptical orbits and changing orbital speed.

• Alpha CentauriRelated: They provide a starting point for describing the A–B orbit.

• Conservation of angular momentumRelated: Equal areas in equal times express angular momentum conservation for a planet under central gravity.

• Copernican RevolutionBroader topic: Kepler replaced Copernicus’s circles with elliptical orbits that fit observations.

• History of astronomyBroader topic: They replaced circular planetary paths with a precise description grounded in Tycho Brahe's observations.

• PeriapsisRelated: The equal-area law explains why orbital speed peaks at periapsis.

• PerihelionRelated: The equal-area law predicts that an orbiting body moves fastest near perihelion.

• Uniform circular motionCompared with: They replaced uniform circular motion as a more accurate account of planetary motion.

• Kirkwood gapRelated: They connect an asteroid’s distance from the Sun to its orbital period.

• Lunar librationNarrower topic: The Moon’s variable orbital speed follows the same orbital geometry that drives longitudinal libration.

• OrbitRelated: They relate an orbit’s shape, speed, and period to the central body.

• Orbital rendezvousNarrower topic: They explain why an object in a lower orbit can catch one in a higher orbit.

• Tidal accelerationNarrower topic: They describe orbital motion at a given moment, while tidal acceleration changes the orbit over time.

• Gravitational parameterRelated: The third law relates an orbit's period and size to the central body's gravitational parameter.

• LibrationRelated: An elliptical orbit makes orbital speed vary, producing longitudinal optical libration.

• Transit timing variationRelated: They provide the idealized orbital predictions against which timing departures are measured.

• Circular orbitNarrower topic: Circular motion is a special case of the orbital patterns these laws describe.

• Rudolphine TablesRelated: These laws supplied the orbital model used to calculate planetary positions.