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How did Newton’s laws provide a physical explanation for Kepler’s laws of planetary motion?

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A diagram of a cylindrical vessel containing gas, with a movable piston held down by a weight. Countless small dots beneath the piston represent gas particles in rapid, random motion, illustrating Bernoulli's model of gas pressure. — physics As conceived by Daniel Bernoulli in *Hydrodynamica* (1738), gases consist of numerous particles in rapid random motion. He assumed that the pressure of a gas is produced by the direct impact of the particles on the walls of the container.

Johannes Kepler’s laws of planetary motion were empirical, meaning they described how planets move without explaining the underlying physical causes. Isaac Newton provided this physical foundation by applying his three laws of motion and his law of universal gravitation to celestial dynamics.12

Newton demonstrated that Kepler’s laws are a direct consequence of a central gravitational force that decreases with the inverse square of the distance ( $1 / r^{2}$ ) between the Sun and a planet. Specifically:1

Kepler’s Second Law: Newton showed that this law, which states that a planet sweeps out equal areas in equal times, is a result of the conservation of angular momentum under a central force.34
Kepler’s Third Law: By applying his second law of motion to circular orbits, Newton proved that if the period of revolution varies as $r^{3 / 2}$ , the required centripetal force must vary as $1 / r^{2}$ .1
Kepler’s First Law: Newton used his laws to show that an object subject to an inverse-square gravitational force follows a path defined by a conic section—an ellipse, parabola, or hyperbola—depending on the object's total energy.341

By quantifying force and mass, Newton transformed planetary motion into a precise, predictable system of classical mechanics.21