Speeding up kepler solver

[ericagol]

Perhaps we could try the approach used in this paper:

https://arxiv.org/abs/2105.11671

[langfzac]

The AstroLib.jl kepler_solver appears to be ~2x faster.

[ericagol]

That's neat! The Kepler solver in NbodyGradient takes a different form that a typical Kepler solver - it's a universal solver, and it uses the difference in M and s over time steps, rather than their absolute values. So, these other approaches would need to be adapted and then tested.