Question

An undiscovered planet, many lightyears from Earth, has one moon in a periodic orbit. This moon takes 1960 × 103 seconds (about 23 days) on average to complete one nearly circular revolution around the unnamed planet. If the distance from the center of the moon to the surface of the planet is 275.0 × 106 m and the planet has a radius of 3.20 × 106 m, calculate the moon's radial acceleration ?c.

Answer 1

Radial acceleration is v^2 / r.

v = distance traveled over time taken, that's (2 * pi * 3.20 * 10^6 m + 275 * 10^6 m)/(1960 * 10^3 seconds) = 150.56 m/s.

The acceleration then is v^2/r = (150.56 m/s)^2/(3.20 * 10^6 m + 275 * 10^6 m) = 8.15 ×10^-5 m/s^2