ROCKET SCIENCE ISN'T EASY, especially the orbital dynamics part. Maneuvering in space is fundamentally different and more difficult than normal flight. Usually, such things would not be of concern to you, but I've thrown together a little program to let you experience the joys of Keplerian motion and issue you two challenges: dock while in orbit and get a vehicle from the Earth to the Moon.
This task is simple. Get any two satellites in similar orbits such that they maintain constant distance from each other.
Movement in orbit is significantly different than typical flight because objects in orbit aren't under power — they are falling towards the earth, but they have enough tangential velocity that, in the words of Douglas Adams, they keep missing the ground.
Consider that you are trying to dock with another spacecraft in orbit. If the craft is ahead, you may be tempted to accelerate towards it. Normally this would work, but a tangential acceleration in orbit causes the orbit to become more elliptic with the point of acceleration being a new perigee. If you were to accelerate again at the new apogee, you would yet again be in a circular orbit, but at a higher altitude. Congratulations, you've performed a Hohmann transfer orbit.
The dismaying part of this whole story is not that you are now higher than the other craft (although that is unfortunate), it's that the craft is now pulling away from you. Being in a higher orbit, your craft has a lower velocity. Worse yet, you have a much larger circumference to trace, so you will invariably fall behind the other craft. This is similar to how Pluto completes one revolution around the sun in 248 years at 4.5 km/s while Mercury completes a rotation in 88 days at a fleet-footed 47 km/s.
If you've made it this far, you're probably looking for an explanation as to how it is done. In reality, spacecraft have very little fuel for orbital maneuvering and nothing near what you have in this simulator. During the Gemini program where NASA experimented with the mechanics of orbital rendezvous, the Gemini spacecraft's entire fuel store could move it sideways about one mile. If an orbital rendezvous is required today, the launch is timed so that the two orbits line up. That's why you'll often hear about "launch windows." If they don't launch at a certain time, the vehicle will not have enough fuel to catch up. Of course, once they are up there, they still have to dock, but then they whip out their cruise control, and life is relatively easy.
Getting two craft into similar orbit requires finesse, which eludes my ability to describe in words. First, clear the screen of all but two satellites (comma key). Select one of them. You will be transferred to the satellite tracking camera mode. Use the left and right thrusters to get the two satellites into the same orbital plane. Next, change the camera mode to the perpendicular mode. You should see two ellipses. Perform a couple of Hohmann transfers to see how they change the shape and position of your orbit. Try to get into a smaller circular orbit than the other satellite. Wait for your craft to be slightly ahead of the other and perform a forward acceleration. You should transfer to a higher orbit and fall back to meet the other craft. I've only been able to perform this a handful of times, so don't spend too much time trying.
The previous task may have been impossibly difficult, but you should certainly be able to perform a transfer from an earth parking orbit to a lunar orbit as done by the Apollo crews on their voyages to the moon.
First, clear the screen of all but one satellite. Click on the satellite to select it and move it into an orbit around the equator — pressing the p key will reveal the poles. Now, change the camera into the Z-look mode and pull way, way back until you see the moon. It should be a gray sphere on the left side of the screen. Wait until the satellite is rounding the earth and moving towards the moon. Apply a significant forward acceleration, and you should see your satellite break away from the earth. This may or may not be escape velocity, the speed at which your satellite will fly off into outer space and force you to start over with a new satellite.
You can do some in orbit maneuvers to correct your trajectory. Aim your vehicle towards the edge of the moon and let the gravity field of the moon catch your craft. Your craft should spiral towards it and eventually be in a stable orbit around the moon as shown in Figure 3. Don't run into the moon. It will kill you. You can use the 'm' key to alter the mass of the moon. With higher mass, it will be easier for the moon to "catch" your vehicle. I've never been able to transfer in the realistic mode.
In the mid 1960s, NASA performed all of this perfectly with limited fuel on the first try using slide rules.