===== 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