Question

During a solar eclipse, the moon, Earth, and sun lie on the same line, with the moon between Earth and the sun. (a) What force is exerted on the moon by the sun? N (b) What force is exerted on the moon by the Earth? N (c) What force is exerted on the Earth by the sun? N

(Average Earth-moon distance = 3.84 ✕ 108 m, Average Earth-sun distance = 1.5 ✕ 1011 m, mass of the moon = 7.35 ✕ 1022 kg, mass of the Earth = 5.97 ✕ 1024 kg, mass of the sun = 1.99 ✕ 1030 kg)

Answer 1

We can use the law of universal gravitational law of Newton to find the force between the two bodies of mass M and m sepated by a distance R.

F= GMm/R^2, G is the gravitational constant, M and m are the masses of the bodies.

A) Between Earth and sun:

M= mass of sun =1.99x10^30 kg), m=mass of earth= 5.98x10^24kg) and R = 1.496 x 10^11 m, G=6.673 x 10^-11 N times m^2/ kg^2,

F = (6.673 x 10^-11 N times m^2/ kg^2,)(1.99x10^30 kg)(5.98x10^24kg)/(1.496 x 10^11 m)^2

= 3.54233552*10^22 N is the force between earth and sun.

B) Between moon and sun:

M = sun's mass above, m = moon's mass = 7.36x10^22kg and R = Sun moon distance = Earth sun distance - Earth moon distance as both sun and moon and earth are on the same line= 1.496 x 10^11 m. - 3.84 x 10^8 m = 1.49214*10^11 meter.

F= (6.673 x 10^-11*1.99x10^30 *7.36x10^22)/(1.49214*10^11)^2

=4.38968*10^20 N is the force between sun and moon.

C) Between earth and moon:

F = (6.673 x 10^-11*5.98x10^24*7.36x10^22)/(3.84 x 10^8)^2

=1.991763064*10^20 N is gravitational force between earth and the moon