Answer:
F = 4.48N
Explanation:
In order to calculate the net gravitational force on the rocket, you take into account the formula for the gravitational force between two objects, which is given by:
(1)
G: Cavendish's constant = 6.674*10^-11 m^3kg^-1s^-2
r: distance between the objects
You have a rocket at the middle of the distance between Earth and Moon, then, you have opposite forces on the rocket.
If you assume the origin of a system of coordinates at the rocket position, with the Moon to the left and the Earth to the right, you have:
(2)
Me: mass of the Earth = 5.98*10^24 kg
Mm: mass of the Moon = 7.35*10^22 kg
m: mass of the rocket = 1200kg
r1: distance from the rocket to the Earth = 3.0*10^8m
r: distance between rocket and Moon = 3.84*10^8m - 3.0*10^8m = 8.4*10^7m
You replace the values of the parameters in the equation (2):
![F=Gm[\frac{M_e}{r_1^2}-\frac{M_m}{r_2^2}]\\\\F=(6.674*10^{-11}m^3kg^{-1}s^{-2})(1200kg)[\frac{5.98*10^{24}kg}{(3.0*10^8m)^2}-\frac{7.35*10^{22}kg}{(8.4*10^7m)^2}]\\\\F=4.48N](https://tex.z-dn.net/?f=F%3DGm%5B%5Cfrac%7BM_e%7D%7Br_1%5E2%7D-%5Cfrac%7BM_m%7D%7Br_2%5E2%7D%5D%5C%5C%5C%5CF%3D%286.674%2A10%5E%7B-11%7Dm%5E3kg%5E%7B-1%7Ds%5E%7B-2%7D%29%281200kg%29%5B%5Cfrac%7B5.98%2A10%5E%7B24%7Dkg%7D%7B%283.0%2A10%5E8m%29%5E2%7D-%5Cfrac%7B7.35%2A10%5E%7B22%7Dkg%7D%7B%288.4%2A10%5E7m%29%5E2%7D%5D%5C%5C%5C%5CF%3D4.48N)
The net force exerted over the rocket is 4.48N