Summary: Planetary motion.
This material comes from an article by Robert Osserman in the American Mathematical Monthly of
Part One. Suppose we have an inertial frame of reference in which a body of constant mass m is
concentrated at the point p and another body of constant mass M is concentrated at the point P. Suppose
there are no other masses in our universe and that Newton's law of gravitation holds; this amounts to
(1) mĘp =
|P - p|3
(P - p) and M ĘP =
|p - P|3
(p - P)
where G is Newton's gravitational constant in appropriate units.
m + M
(mp + MP)
be the center of mass of our two body system. A simple calculation shows that