Question

An undiscovered planet, many lightyears from Earth, has one moon in a periodic orbit. This moon takes 1810 × 10³ seconds (about 21 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 255.0 × 10⁶ m and the planet has a radius of 3.80 × 10⁶ m, calculate the moon's radial acceleration ?c in m/s².

Answer 1

Time period of revolution = 2* pi* r / velocity

r = distance between the centers of the planet and moon.

1810 x 10^3 = 2*3.14 * (258.80 x 10^ 6) / velocity

hence velocity = 897.9 m/s

now radial acceleration = v^2 /r

hence ac = 897.9^2 / (258.8 x 10^6)

ac =3.115 x 10^-3 m/s^2