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Basically I am developing a spaceflight simulator specifically for the space shuttle. Coding the Shuttles Systems etc. is not actually the hardest part, as I had thought before.

The real problem is the physics engine

The main problem I have is, that with all the Equations for the different orbital elements every one of them depends on another.

So I thought it would be a great idea to have some "easy" beginning and moved on to think about how to calculate the Apoapsis right after the engines had shutten off, as it would only change a very small amount during ascent. If you then have the current speed and radius of the apoapsis it becomes quite easy to calculate the radius of the periapsis. From there on everything should be preatty straightforward.

However, I don't have a clue how to calculate the trajectoy itself. On a small scale (eg. throwing a baseball) its easy. But for these distances and speeds, the downward accelleration because of gravity would constantly change direction as you fly along the trajectory.

So does anybody know a way to calculate this?