Acceleration on Rocket

HELP! I'm trying to write a computer program (C) to plot the trajectory of the rocket as it flies from Earth to Moon. In the information sheet it says:

ax = -GMe*(1/rr^2)*(xr/|rr|) - GMm*(1/[rr-rm]^2)*([xr - xm]/[|rr - rm|])

Where:
ax = acceleration in x-direction (we're working in xy coords)
rr = a vector from the Earth to the Rocket
rm = a vectore from the Earth to the Rocket
xr = Rocket's x coordinate
xm = Moon's x coordinate
Me = Earth's Mass
Mm = Moon's Mass

Now, in order to input this acceleration in the x direction into my program I have to resolve the vector's into their x-direction BUT also be aware that their y co-ords will have an effect on the gravitational force felt in the x direction.

Could some-one explain to me what I actually have to compute then (not how to write the program, but help with the Physics!!!)? Also, when it says "rr^2" does this mean the modulus squared?!

Please help, I'm really stuck!!! Thanks
Chloé
xxx

Is rm vector from the Earth to the Moon, not to the rocket?

Therefore, if we consider the force acts on the Rocket by the Earth due to x axis
Fe = [GMem/rr^2] .cos(rr, Ox) = [GMem/rr^2].xr/|rr|
where m is mass of the Rocket

I think the remain is the same.

Yes sorry! Was in a mad rush trying to type it out before my tute!