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Article Summaries:
- John Baez’s draft for the Notices of the American Mathematical Society revisits Newton’s lesser‑known insight into the inverse‑cube force law. Baez explains that a central force proportional to (1/r^{3}) can rescale a particle’s angular velocity by a constant factor without altering its radial motion, a property Newton derived in the 17th century but only fully appreciated in the 1990s. He shows how the centrifugal force-also an inverse‑cube term-competes with attractive forces, leading to three distinct orbital regimes (spiral, bounded, or unbounded) analogous to the classic elliptical, parabolic, and hyperbolic orbits of the inverse‑square law. These trajectories, known as Cotes spirals, highlight the subtle dynamics of inverse‑cube forces.
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