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:
[tex]F=G\frac{m_1m_2}{r^2}[/tex] (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:
[tex]F=G\frac{M_em}{r_1^2}-G\frac{M_mm}{r_2^2}[/tex] (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):
[tex]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[/tex]
The net force exerted over the rocket is 4.48N
The net gravitational force on the rocket from the earth and moon is 4.48N.
The gravitational force between two objects is:
F = Gm₁m₂/r²
Where m₁, m₂, are masses, r is the distance between them and G is gravitational constant = 6.67 * 10⁻¹¹ Nm²/kg²
Let us assume that the rocket is at the origin with the Moon to the left and the Earth to the right. Hence:
[tex]F=G[\frac{m_em}{r_1^2} -\frac{m_mm}{r_2^2} ][/tex]
Where me is the mass of earth = 5.98 × 10^24 kg,
r₁ is the distance from earth to rocket = 3.0 × 10^8 m,
m is the mass of rocket = 1200 kg,
mm is the mass of moon = 7.35 × 10^22 kg,
r₂ is the distance from moon to rocket = 3.84 × 10^8 m - 3.0 × 10^8 m = 0.84 × 10^8 m
Hence:
[tex]F=6.67*10^{-11}[\frac{1200*5.98*10^{24}}{3*10^8}-\frac{1200*3*10^{22}}{0.84*10^8} ]\\\\F=4.48\ N[/tex]
The net gravitational force on the rocket from the earth and moon is 4.48N.
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