Is there an effective mathematical way to predict the orbit of a spaceship or planet?

This is, of course, assuming I have a few known parameters:

  1. velocity of the object in the time $\tau$.

  2. Velocity angle angle relative to the primary in time $\tau$.

  3. Distance from the primary in time $\tau$.

  4. the primary object mass.

Note: I do not mean by time $\tau$ here anything specific, I used it to note that these parameters describe the movement of the body at the time named “$\tau$”.

  • $\begingroup$ Are you asking what initial conditions are needed to uniquely determine an orbit? $\endgroup$
    – Sandejo
    Nov 10, 2021 at 21:37

1 Answer 1


Under the additional assumptions that the given velocities are relative to the planet, and the object is much less massive than the planet, these are sufficient conditions to determine the trajectory of the orbit, up to some rotation of the axes, since they provide ample initial conditions (position and velocity) for the second-order linear PDE of motion (Newton's second law).

If you want to solve for the orbit yourself, the easiest way is to calculate angular momentum and total energy from the position and velocity information. Then, the shape of the orbit is given by the orbit equation.


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