  Newton's Theorem of Revolving Orbits derives the force that is necessary to
explain a particular precession that leaves the shape of an orbit unchanged.
Newton showed that for an orbiting body that is already subject to any central
force, the inclusion of an additional inverse-cube central force will change
that body's angular speed without affecting its radial motion; this leads to
the orbit's precession. After reviewing the relevant concepts of Kepler orbits,
we present a full description and explanation of Newton's theorem using modern
physical and mathematical approaches aimed at a general audience. We
specifically highlight the use of the transformation between a rotating
reference frame and an inertial reference frame, making this a suitable topic
for an upper-level undergraduate mechanics course.
