Can Numerical Simulations Accurately Predict Orbital Precession?

[oq123]

If we had a literal two body system (point masses M and m), with one orbiting the other according to Newton's Law of gravitation, would there be orbital precession? Or would they map out the same ellipse each time?

 

[A.T.]

If we had a literal two body system (point masses M and m), with one orbiting the other according to Newton's Law of gravitation, would there be orbital precession?

No

 

[oq123]

Perfect A.T. Thank you! That is what I thought, but running a simulation I wrote, there appeared to be precession. I thought that it was an artifact, but wanted to be sure.

 

[dipole]

numerical simulations can be unstable - you accumulate errors over time. You should check that the total energy of the system remains constant in your simulations.

Note that any kind of perturbations which deviate from a 1/r potential will lead to precession.

 

[DrDu]

There would be no orbital precession. The deeper reason is the hamiltonian of the system having a dynamical symmetry so that the direction of the axis of the ellipsis is a constant of motion, the Runge Lenz vector.
http://en.wikipedia.org/wiki/Laplace–Runge–Lenz_vector

 

[oq123]

numerical simulations can be unstable - you accumulate errors over time. You should check that the total energy of the system remains constant in your simulations.

Note that any kind of perturbations which deviate from a 1/r potential will lead to precession.

I was somewhat surprised that the simulation would lead to precession, though. I would have expected the orbit to wobble, but it the type of error introduced in these simulations tend to always go the same way...