Centripetal Acceleration

Question

An undiscovered planet, many light years from Earth, has one moon in a periodic orbit. This moon takes 1.955 x 10^6 seconds (about 23 days) on average to complete one nearly circular revolution around the unnamed planet. The distance from the center of the moon to the surface of the planet is 245.0 x 10^6 m and the planet has a radius of 3.20 x 10^6 m, calculate the moon's centripetal acceleration.

Answer 1

a = v²/(R + r); v = 2π(R + r)/T; a = 4π²(R + r)/T² = 4π²(245·10⁶m + 3.2·10⁶m)/(1.995·10⁶s)² =.2.462·10^-3m/s²