# Net gravitational force on the moon?

http://img301.imageshack.us/img301/6962/problem98j...

The drawing (not to scale) shows one alignment of the sun, earth, and moon. The gravitational force that the sun exerts on the moon is perpendicular to the force that the earth exerts on the moon. The masses are: mass of sun=1.99 × 1030 kg, mass of earth=5.98 × 1024 kg, mass of moon=7.35 × 1022 kg. The distances shown in the drawing are rSM = 1.50 × 1011 m and rEM = 3.85 × 108 m. Determine the magnitude of the net gravitational force on the moon.

If you know how to do this problem, please help me, I can't figure it out :-\

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I have calculated the gravitational force of attraction Sun/Moon using Newton's Law:

F = G*M1*M2/r² M1 = mass sun, M2 = mass moon r = distance

F = (6.67*10^-11 * 1.99*10^30 * 7.35*10^22 ) / (1.50*10^11)²

F =(6.67*10^-11 * 1.99*10^30 * 7.35*10^22 ) /2.25*10^22

F = (6.67*1.99*7.36*10^19) / 2.25

F = 4.342*10^20N

I have then calculated the gravitational force of attraction, Earth/Moon using same law:

F = G*M1M2/r² where M1 = Mass earth M2 = Mass moon, r = distance

F = (6.67*10-11 * 5.98*10^24* 7.35*10^22) / (3.85*10^8)²

F = 6.67*5.98*7.35*10^18 /1.482

F = 1.98*10^20

Find the angle between these forces:

Direction of resultant force:

Tan Θ = 1.98/4.342

Tan Θ = 0.4560

Θ = 24.51° from the Sun/Moon direction line

Magnitude of resultant force:

Fres = 1.98/sin 24.50°

Fres = 4.773*10^20N

I have double checked my calculations, in view of the numerous indices. I hope there are no mistakes, but the principle is correct, to find the individual forces via Newton, and then resolve to a rwesultant force.

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