A satellite orbiting at a distance R from the center of the earth follows the circular path x(t) = R cosωt, y(t) = R sinωt.
(a) Show that the period T (the time of one revolution) is T = 2π/ω.
(b) According to Newton’s Laws of Motion and Gravity,

where G is the universal gravitational constant and me is the mass of the earth. Prove that R³/T² = Gme/4π².
Thus, R³/T² has the same value for all orbits (a special case of Kepler’s Third Law).

Transcribed Image Text:

x' (t) = -Gme X R³⁹ y"(t) = -Gme R³