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How did Newton use gravity to explain the motion of planets and their moons?

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gravitational lens — gravity A galactic cluster, about five billion light-years away, produces a tremendous gravitational field that “bends” light around it. This lens produces multiple copies of a blue galaxy about twice as distant. Four images are visible in a circle surrounding the lens; a fifth is visible near the center of the picture, which was taken by the Hubble Space Telescope.

Isaac Newton explained the motion of planets and their moons by applying his laws of motion and his law of universal gravitation to the empirical observations of Johannes Kepler.123

Newton recognized that, according to the law of inertia, a body in motion would travel in a straight line unless acted upon by an external force. He concluded that a centripetal force—which he identified as gravity—must be acting on planets and moons to continuously divert them from a straight path into their observed orbits.4523

By mathematically analyzing Kepler’s third law, Newton demonstrated that this gravitational force must decrease with the square of the distance between bodies. He further confirmed this by comparing the acceleration of the Moon in its orbit to the acceleration of objects falling freely on Earth, showing that the same force governs both. This synthesis allowed him to describe planetary motion as a result of gravitational attraction between massive bodies, proportional to the product of their masses and inversely proportional to the square of the distance between them.2341