How did the Principia help explain Kepler’s laws of planetary motion?

In his seminal work, the Principia, Isaac Newton provided the physical foundation for Johannes Kepler’s empirical laws of planetary motion by demonstrating that they were a direct consequence of his own laws of motion and the law of universal gravitation.12

Newton explained these laws through the following applications:

• Inverse Square Law: By applying his second law of motion to Kepler’s third law, Newton mathematically demonstrated that the centripetal force holding planets in their orbits must decrease with the square of their distance from the Sun.32
• Elliptical Orbits: Newton proved that an elliptical path is the natural result of an inverse-square gravitational attraction toward a central focus. He further showed that bodies subject to this force could also follow parabolic or hyperbolic paths, depending on their total energy.4256
• Conservation of Angular Momentum: Newton’s framework confirmed that Kepler’s second law—which states that a planet sweeps out equal areas in equal times—is a direct result of the conservation of angular momentum in the presence of a central force.56