Understanding Keplerian Orbits: Equations and Time Dependence

[holtto]

Just curious, does anyone know what are the equations for the displacement-time graph of a Keplerian orbit?

The horizontal displacement-time graph should be somewhat sinusoidal, the vertical one cosinusoidal, or vice versa.

 

[voko]

There is a formula relating the orbital angle and the orbital radius, and so one can easily get the x/y components versus the angle. Dependence on time, however, is implicit.

 

[holtto]

There is a formula relating the orbital angle and the orbital radius, and so one can easily get the x/y components versus the angle. Dependence on time, however, is implicit.

and it involves really complicated D.E.s