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How does Kepler’s second law use equal areas to describe a planet’s motion?
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Celestial mechanics
Ptolemaic diagram of a geocentric system, from the star atlas Harmonia Macrocosmica by the cartographer Andreas Cellarius, 1660.
Kepler’s second law states that a radius vector joining a planet to the Sun sweeps out equal areas in equal intervals of time.123
This geometric principle describes how a planet's orbital speed changes as it moves along its elliptical path. Because the planet must cover the same area in the same amount of time, its velocity is not constant:1
- Near perihelion: When the planet is closest to the Sun, it must travel at a higher-than-average velocity to sweep out the required area.12
- Near aphelion: When the planet is farthest from the Sun, it moves at a lower-than-average velocity.12
This law is fundamentally linked to the conservation of angular momentum, as the angular momentum of a planet remains constant throughout its orbit. By demonstrating that planets do not move at uniform speeds, this law provided essential evidence for Isaac Newton in the development of his law of gravitation.23