The Center of Mass for a Binary System
If you think about it a moment, it may seem a little strange that in Kepler's Laws
the Sun is fixed at a point in space and the planet revolves around it. Why is the
Sun privileged? Kepler had rather mystical ideas about the Sun, endowing it
with almost godlike qualities that justified its special place. However Newton,
largely as a corollary of his 3rd Law, demonstrated that the situation actually
was more symmetrical than Kepler imagined and that the Sun does not occupy a
privileged postion; in the process he modified Kepler's 3rd Law.
Consider the diagram shown to the right. We
may define a point called the
center of
mass
between two objects through the
equations
where R is the total separation between the
centers of the two objects. The center of mass is familiar to anyone who has ever
played on a seesaw. The fulcrum point at which the seesaw will exactly balance
two people sitting on either end is the center of mass for the two persons sitting
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 Fall '10
 MonicaOyola
 Anthropology, Mass, Astronomical unit, Kepler's laws of planetary motion

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