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===== Pre-lecture: Gravitation ===== * Earlier we talked about mg * It turns out that is an approximate form for the interaction between two objects with mass, which i'll describe now * Consider the Earth and the Moon. * Certainly, you've heard the Earth and Moon are attracted to each other * That attraction is how the Earth and Moon interact -- through the gravitational force -- it is a force that involves no contact * Newton developed the model for universal gravitation by studying data collected by Brahe and Kepler * Used it to predict the motion of astronomical objects * Here's Earth and Moon * The force that the Moon exerts on the Earth * Write out equation * Describe all the bits (G, separation vector, minus sign, unit vector) * What about Earth on Moon? different separation vector * This force is really weak; astronomical objects are affected by gravity * On Earth, most objects are unaffected by the gravitational interaction with other objects, because overwhelming affected by interaction with Earth. * But we already have a model for that - mg = GMEm/RE^2 * Motion? Objects move in elliptical orbits (special case circular) * Predicting the motion of astronomical objects in general requires computation