Value of the Hamiltonian εℬ_q(r) in Eq. (35) as a function of the parametrisation point, q, and the star’s instantaneous position, r. The value of εℬ_q(r) is shown by the colour shades and black level curves. By definition of q, the value of εℬ_q(r) is zero along the diagonal (i.e. for r = q). An example of the periapsis, r_p, apoapsis, r_a, and best parametrisation point, q_⋆, are shown in red and blue. In this system of units, the Plummer characteristic radius, κ, lies at r = 1.