Why was Kepler's second law important to Isaac Newton's study of gravity?

Kepler’s second law, which states that a radius vector joining a planet to the Sun sweeps out equal areas in equal lengths of time, was crucial to Isaac Newton during his formulation of the law of gravitation in 1684–85.12

The law was important for several key reasons:

• Conservation of Angular Momentum: Kepler’s second law implies that the angular momentum of a planet remains constant as it orbits the Sun. This principle provided a foundational physical constraint for Newton’s work on celestial mechanics.12
• Central Force Motion: By analyzing this law, Newton was able to demonstrate that the motion of bodies is governed by a central gravitational force directed toward the Sun. This helped him establish that the same gravitational principles applying to objects on Earth also govern the motion of planets and the Moon.13
• Generalizing Orbits: While Kepler’s first law focused on elliptical orbits, the second law helped Newton show that objects subject to central gravitational forces could follow other paths, such as parabolic or hyperbolic orbits, depending on their total energy.12

Ultimately, Newton’s law of gravity is mathematically derivable from Kepler’s laws when combined with Newton’s own laws of motion.3