Question

Calculate (separately) the gravitational force that the Earth exerts on the Moon, and that the Sun exerts on the Moon. Please take the masses and distances from the Appendix section of your textbook. When you compare these two forces, which body should the Moon orbit around do you think? Explain the reason if you find a contradiction between what you find from your calculation and what you observe.

Answer 1

M_e = mass of earth = 5.98 x 10²⁴ kg

m = mass of moon = 7.35 x 10²² kg

r = distance between earth and moon = 3.8 x 10⁸ m

gravitational force between earth and moon is given as

F_e = G M_e m/r² = (6.67 x 10^-11) (5.98 x 10²⁴) (7.35 x 10²²)/(3.8 x 10⁸)² = 2.03 x 10²⁰ N

M_s = mass of sun = 1.989 x 10³⁰ kg

m = mass of moon = 7.35 x 10²² kg

r = distance between sun and moon = 1.5 x 10¹¹ m

gravitational force between earth and moon is given as

F_s = G M_e m/r² = (6.67 x 10^-11) (1.989 x 10³⁰) (7.35 x 10²²)/(1.5 x 10¹¹)² = 4.3 x 10²⁰ N