Calculating velocity of a spacecraft between moon and earth I'm in high school, I'm not very good at physics, and I have this project (year long). I'm trying to determine the accuracy of a simulator (Universe Sandbox 2) with theoretical velocities vs. the data on the simulator. 
How do I calculate the velocity of the spacecraft when it's in between the Earth and Moon? I've included an image of what the simulator got along with a total velocity vs. time graph of the spacecraft in the corner for you.

 A: 
I'm trying to determine the accuracy of a simulator (Universe Sandbox 2) with theoretical velocities

The problem is that, excepting the situation of a natural or artificial satellite orbiting a celestial body, the theoretical velocity of the satellite has a quite complicated expression or an analytical solution does not exist which means that only the simulator can find $v(t)$.
If you are in high school you can verify the accuracy of the software you use by comparing what the simulator outputs to the theoretical speed of a satellite in circular motion around the earth or any other planet in our solar system or you can verify the impact speed of a meteorite that strikes Jupiter, because for the circular motion and the impact speed there are well known and simple expressions.
For a more spectacular relatively simple situation (see the picture) you can try the case where two planets are on a collision course moving along a straight line and a spacecraft is pointing to the center of mass of the two celestial bodies, perpendicular to the line that unites their centers. The analytical relation for the speed of the spacecraft can be obtained and compared with what the simulator outputs.

