Calculating Orbital Trajectories for Spaceflight Simulators

[flyingdutchman]

Hi!

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?

 

[Fred Wright]

If you have some knowledge of polar coordinates and how to solve second order homogeneous differential equations, I suggest you study this: https://www.ucl.ac.uk/~ucahad0/1302week3Polar08.pdf. Follow the technique used in the two examples.

 

[hilbert2]

It can be done with finite difference method, but then it may be necessary to adjust the length of timestep during the simulation to correspond to the magnitude of speed and acceleration at a particular time. Sometimes there can also be problems with numerical stability.

http://physics.bu.edu/py502/lectures3/cmotion.pdf

 

[sophiecentaur]

If you want to make a passable simulation then a step-by-step approach can work very well and produce an orbit that 'looks' stable and with no 'creep'. Small enough steps, using Initial Velocity and Position and a Gravitation Force vector to produce a final position and velocity. In 2D, it's very easy to produce a very convincing looking elliptical path.