Question

Mass of the Sun is 1.99 × × 1030 kg, mass of the Earth is 5.98 × × 1024 kg, mass of the Moon is 7.35 × × 1022 kg. Orbit radius of the Earth is 1.50 × × 1011 m, orbit radius of the Moon is 3.84 × × 108 m. 1) Determine the magnitude of the net force of gravity acting on the Moon during an eclipse when it is directly between Earth and the Sun. (Express your answer to three significant figures.)

Answer 1

The force between earth and moon is

F_EM = GMm/r^2
= 6.67*10^-11*5.98*10^24*7.35*10^22/(3.84*10^8)^2

=1.98 * 10^20 N

The force between sun and moon is

F_ SM = 6.67*10^-11*7.36*10^22*1.99*10^30/(1.50* 10^11)^2

=4.34 * 10^20 N

Fnet = FEM - FSM = - 2.36*10^20 N

Fnet = 2.36*10^20 N in direction to the sun.
The sun pulls about twice as strongly at the moon as the earth does.