Universal Law of Gravitation problem

[MiniOreo1998]

Homework Statement

The Earth has a mass of 5.98 x 10²⁴ kg and the moon has a mass of 7.35 x 10²⁴ 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 Moon.

Find the net gravitational force on the rocket from the Earth and Moon.

If anyone spots any mistakes (or clearer ways that I could have written things out) let me know!

Thanks in advance, coming to this site and reading through some of the threads has started to boost my confidence.

Homework Equations

Fg = m1 m2 / r²

The Attempt at a Solution

Fg = m1 m2 / r²

Earth & Rocket: Fg (6.67 x 10^-11) (5.98 x 10²⁴) (1200) / (3.0 x 10⁸)²

Fgnet_rocket = 5.318 N

Moon & Rocket: Fg (6.67 x 10^-11) (1200) (7.35 x 10²²) / (8.4 x 10⁷)²

Fgnet_rocket = -0.8337 N

Adding together to get:

Fgnet_{Rocket, Earth} 5.318 N + Fgnet_{Rocket, Moon} (0.8337 N) = 4.48

Fgnet_rocket = 4.48 N

 

[Simon Bridge]

You seem to be doing fine - though I did not check your arithmetic.
I have some tweaks for you:

Fg = m1 m2 / r2

Since you want to use SI units, that should be $F_g=GMm/r^2$ ... since force is a vector, maybe: $$\vec F = -\frac{Gm_1m_2}{r_{12}^3}\vec r_{12}$$ where r12 is the vector pointing from m1 to m2. This would give the force on m2 due to m1.

Fgnetrocket = 4.48 N

Good including the units - lots of people forget.
Don't forget to specify the direction the force acts in the answer ... you have implied earlier that a positive force is in the direction of the Earth, but you should say that in the answer too.

Since the only forces being considered are gravitational, you don't need the g subscript.
In the 1st two cases you don't need the net" either - the gravitational force on the rocket due to the Earth would be $\vec F_E$, due to the Moon would be $F_M$ and the total gravitational force (from these two) is $F_{net}$ or $F_{tot}$ ... that approach avoids having to write out huge long subscripts all the time.

Confidence booster: You can also figure out what distance the rocket needs to be from the Earth for the two forces to be equal and opposite.

You are going to have to figure out how to tell if you have the right answers - you are training to solve problems where nobody knows the right answer after all.