Teach Astronomy - Gravity and Calculus

http://www.teachastronomy.com/ The universal law of gravity applies between two point masses, and it is exact. However in any real situation, such as a solar system with more than two objects, or in calculating the gravity between extended objects, the simple law of gravity will not suffice. Newton invented the calculus to do the more complicated calculations of the gravity of extended objects or more than two objects. Gravity is not deterministic in this situation and must be approximated with increasing mathematical precision and computational power, so the metaphor of a clockwork universe in inappropriate. Using this extended formalism of the calculus you can calculate, for example, that the gravity exerted on yourself by the Earth is roughly 100 million times larger than the gravity exerted by someone sitting next to you. Newton argued bitterly with Leibnitz over who first invented the calculus.