We want to compute the orbits numerically for some fixed energy level. The fixed energy level is the noise. There are N! equations of mass on mass with G, the summation of these equations at any step is the signal. You step all radius with some common step value such that the divergence along the way does not break Shannon separability. Check the -iLog(i) along the way with you computer, or just scale up.
The amplitude is some 2^(k* quant). You want to compute the quants for each step from k=0 to k = Nmax. Compute the mass on mass signal at each step, use Shannon to get the quant.
What does this get you? You have simply counted up the group with respect to some fixed point of symmetry. You have created the Kepler group. Does this find you the central Lagrange, or is there one? I have not done this, but if you lay out the radii on a complete sequence, they should count out the potential energy. The kinetic energy makes that phase flat. When the potential energy is maximum they are closest together, and visa versa. So, use a little ingenuity and fins a common Lagrange.
For example:
On the complete symmetry group of the classical Kepler system
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