Kepler's First Law of Planetary Motion

Johannes Kepler discovered that planets follow elliptical orbits after analyzing Tycho Brahe's detailed observations of Mars. While Copernicus proposed circular orbits, Kepler's analysis revealed that planetary orbits deviate from perfect circles. This elliptical shape, with the Sun at one focus, better matched astronomical data and became Kepler's first law of planetary motion.

Perihelion is the point where a planet is closest to the Sun, while aphelion is where it is farthest. At perihelion, the planet's potential energy is lower due to reduced distance. These two points represent the extremes of a planet's radial distance throughout its orbital year.

A planet moves faster when closer to the Sun at perihelion and slower when farther away at aphelion. This occurs because total orbital energy is conserved. As potential energy decreases near the Sun, kinetic energy increases, causing the planet to accelerate in its orbit.

Eccentricity measures the degree of elongation of an ellipse, expressed as the ratio of the minor axis to the major axis. For a circle, eccentricity equals zero. Earth's orbit has eccentricity 0.0167, while Mars has 0.0935, indicating Mars follows a more elongated elliptical path than Earth.

The semi-major axis of an elliptical orbit equals the planet's average distance from the Sun. This fundamental parameter characterizes the size and shape of each planetary orbit. The semi-major axis, combined with eccentricity, fully describes a planet's elliptical path around the Sun.

Following the energy conservation principle, a planet's total orbital energy remains constant. As a planet approaches the Sun at perihelion, its gravitational potential energy decreases. To maintain constant total energy, kinetic energy must increase proportionally, causing the planet to accelerate in its orbit.

Tycho Brahe's precise observations of Mars contradicted Copernicus's circular orbit model. When Kepler analyzed this data, he discovered Mars followed an elliptical path with the Sun at one focus. This finding, combined with observations of other planets, led him to establish Kepler's first law of planetary motion.