The motion of a planet in a circular orbit about a star obeys the equations of simple harmonic motion. If the orbit is observed edge-on, so the planet’s motion appears to be one- dimensional, the analogy is quite direct: The motion of the planet looks just like the motion of an object on a spring.
a) Use Kepler’s Third Law of planetary motion to determine the “spring constant” for a planet in circular orbit around a star with period T.
b) When the planet is at the extremes of its motion observed edge-on, the analogous “spring” is extended to its largest displacement. Using the “spring” analogy, determine the orbital velocity of the planet.
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