significant difference between these mass choices. We therefore chose our prescription, Eq.\[eq:hpm\], which has a simpler physical interpretation: the mass entering Kepler’s third law is simply the interior mass.

Wisdom-Holman Mapping
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Our goal is to find a solution to the equations of motion for particles governed by the Hamiltonian in Eq. \[eq:H\]. No analytic solution exists to the full Hamiltonian and we thus need to find an approximate solution. There are many different ways to do that. Here, we describe the idea of constructing a symplectic integrator by means of splitting the Hamiltonian into smaller parts, each of which can be easily integrated.

The introduction of Jacobi coordinates led us to the Hamiltonian splitting described in Sect. \[sec:splitting\]. Analytic solutions can be found for the evolution of the system under each of the individual Hamiltonians $\operatorname{\mathcal{H}}_0$ and $\operatorname{\mathcal{H}}_{\rm Interaction}$. The solution to $\operatorname{\mathcal{H}}_0$ simply corresponds to motion along a straight line. The solution to $\operatorname{\mathcal{H}}_{\rm Interaction}$ is a kick step where the velocities change due the inter-particle accelerations but the position remain constant. The solution to $\operatorname{\mathcal{H}}_{\rm Kepler}$ is a set of two-body Kepler orbits, which can also be easily solved with an iterative algorithm. We discuss the details 