Finding the net gravitational force on a rocket....

[Specter]

Homework Statement

The Earth has a mass of 5.98 x 10²⁴ kg and the moon has a mass of 7.35 x 10²² kg. The distance from the centre of the moon to the centre of the Earth is 3.84 x 10⁸ m. A rocket with a total mass of 1200 kg is 3.0 x 10⁸ 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 the moon.

Homework Equations

Fnet = Gm1m2/r²

The Attempt at a Solution

m1 (earth)=5.98 x 10²⁴ kg
m2 (moon)=7.35 x 10²² kg
m3 (rocket)=1200kg

m1 is 3.85 x 10⁸m from the centre of m2
m3 is 3.0 x 10⁸ m from the centre of m1

My problem is trying to figure out how far the rocket(m3) is from the moon(m2). The question says that the rocket is directly in between the Earth and the moon, so does that mean that the distance is 3.0 x 10⁸ m to the centre of the moon and to the centre of the earth?

Next I would use Fnet = Gm₁m₃/r₁₃ + Gm₂m₃/r₂₃ and solve the question. In the example I read it said "add their magnitudes since both forces act in the same direction". In this question the forces would be acting in different directions, one toward the moon and the other toward earth. Does this mean I subtract the magnitudes instead of adding?

 

[jbriggs444]

The question says that the rocket is directly in between the Earth and the moon, so does that mean that the distance is 3.0 x 108 m to the centre of the moon and to the centre of the earth?

It is saying that the rocket is somewhere on the line connecting the two centers. Not necessarily at the midpoint of that line.

Does this mean I subtract the magnitudes instead of adding?

That will give you the magnitude of the result. If you want to know its direction, you will have to decide which pull is stronger.

 

[Specter]

It is saying that the rocket is somewhere on the line connecting the two centers. Not necessarily at the midpoint of that line.

That will give you the magnitude of the result. If you want to know its direction, you will have to decide which pull is stronger.

The pull of the Earth would be stronger. So if the Earth's pull is stronger than the moons the rocket would be closer to the Earth than the moon, right? But how can I figure out the distance knowing this?

 

[jbriggs444]

So if the Earth's pull is stronger than the moons the rocket would be closer to the Earth than the moon, right?

The position of the rocket is what it is regardless of the force it is subject to.

 

[Specter]

The position of the rocket is what it is regardless of the force it is subject to.

I think I figured it out. I was making it way harder then it needed to be...

3.84 x 10⁸-3.0 x 10⁸=8.4 x 10⁷

 

[jbriggs444]

I think I figured it out. I was making it way harder then it needed to be...

3.84 x 10⁸-3.0 x 10⁸=8.4 x 10⁷

Yep. That's the distance of the rocket from the center of the moon.