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@davidr@hachyderm.ioSo apparently in #orbit #mechanics (both large and #quantum #physics) there are the obvious conservation laws of energy and angular momentum, but also a conservation of the Hermann-Bernoulli-Laplace-Hamilton-Runge-Lenz #vector (I'm not even joking about that name, although Laplace-Runge-Lenz aka LRL is more common).
I'm not sure if this will help the problem I'm working on, but it'll be fun trying to find out.
@davidr that vector is really only useful for the Kepler or Coulomb potential, so if that's your problem you're in luck.
@paulmasson #Kepler. I'm not 100% clear what happens with the #vector outside of a two body problem though. Iin particular, not modeling the Earth as a simple point mass, but having some extent. Central inverse square...with N centers?
But my problem can be point-mass during some parts and during those parts I have another perturbation that I'm trying to tease out. Think something like solar radiation pressure, although it isn't #physics based like that.
@davidr @paulmasson I think that, to the extent the earth is round, you can model it as a point mass even though it isn't because of the shell theorem https://en.m.wikipedia.org/wiki/Shell_theorem and ultimately because of Gauss Law for gravity
@nfsmithca @paulmasson Point-mass modeling is out of my hands. The data already exists. I'm analyzing it afterwards. I'm just trying to figure out what effect the non-point-mass segments of the data will have on the LRL vector.