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Planetary motion. This material comes from an article by Robert Osserman in the American Mathematical Monthly of
 

Summary: Planetary motion.
This material comes from an article by Robert Osserman in the American Mathematical Monthly of
July 2001.
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 =
GmM
|P - p|3
(P - p) and M ĘP =
GmM
|p - P|3
(p - P)
where G is Newton's gravitational constant in appropriate units.
Let
C =
1
m + M
(mp + MP)
be the center of mass of our two body system. A simple calculation shows that

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics