How did Newton make the law of universal gravitation?

Isaac newton formulated the law of universal gravitation by synthesizing his observations of celestial bodies and his mathematical insights. He proposed that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This idea emerged from his work on planetary motion, particularly observing the orbits of planets and the moon, and was mathematically expressed in his seminal work, "Mathematical Principles of Natural Philosophy" (1687). This law laid the groundwork for classical mechanics and transformed our understanding of gravity and motion.