How did Isaac Newton explain why Kepler's laws work?

Isaac Newton explained the physical basis for Johannes Kepler's empirical laws by formulating his laws of motion and the law of universal gravitation.1

While Kepler described planetary motion, he did not define the underlying physical processes. Newton demonstrated that these laws were consequences of a central gravitational force acting between bodies. Specifically:1

• Inverse-Square Law: By applying his second law of motion to Kepler’s third law, Newton deduced that the force keeping planets in orbit must vary inversely with the square of the distance ($1/r^2$) from the Sun.1
• Universal Gravitation: Newton showed that this force is proportional to the product of the masses of the two bodies and acts as if the mass were concentrated at the center of the sphere.12
• Derivability: Kepler’s laws can be mathematically derived from Newton’s laws of motion and his law of gravity.1

Newton’s synthesis proved that the same gravitational force governing falling objects on Earth also dictates the motion of planets in space, replacing earlier, incomplete models of celestial mechanics.13