Lecture 72: Newton and the Apple (Universal Gravitation)

In this video, I delve into Newton's universal gravitation, showcasing his profound insight that the same mechanics governing celestial bodies, such as the moon, apply to terrestrial objects, like an apple. Building upon the previous lesson's exploration of the centripetal force for orbiting bodies obeying an inverse square law, I demonstrate that this force is also proportionate to the product of the masses of the gravitating objects. Utilizing the assumption of a circular orbit with the force centered on a significantly more massive star, I elucidate this fundamental principle. Additionally, I discuss Galileo's observation that the gravitational acceleration experienced by an object is independent of its mass, further solidifying the foundational concepts of gravitational theory. Through this exploration, viewers will gain a deeper understanding of Newton's groundbreaking contributions to our understanding of gravity and celestial mechanics.