Question

The earth has a mass of 5.98 × 10^24 kg and the moon has a mass of 7.35 × 10^22 kg. The distance from the centre of the moon to the centre of the earth is 3.84 × 10^8 m. A rocket with a total mass of 1200 kg is 3.0 × 10^8 m from the centre of the earth and directly in between the earth and the moon. Find the net gravitational force on the rocket from the earth and moon.

Answer 1

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:

$F=G\frac{m_1m_2}{r^2}$         (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:

$F=G\frac{M_em}{r_1^2}-G\frac{M_mm}{r_2^2}$       (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):

$F=Gm[\frac{M_e}{r_1^2}-\frac{M_m}{r_2^2}]\\\\F=(6.674*10^{-11}m^3kg^{-1}s^{-2})(1200kg)[\frac{5.98*10^{24}kg}{(3.0*10^8m)^2}-\frac{7.35*10^{22}kg}{(8.4*10^7m)^2}]\\\\F=4.48N$

The net force exerted over the rocket is 4.48N