Numerical errors on the computation of ∂_rεℬ using double precision arithmetic. The red curve shows the relative error obtained when using Eq. (D.2); the blue curve shows the relative error obtained when using Eq. (D.3). Errors are computed from a reference value obtained in quadruple precision. Panel a, b, and c show the error as a function of the distance r of the particle for the Orbits #1, #2, and #3 considered in Sect. 6, with parametrisation point q = r_⋆. The values of r shown range from periapsis to apoapsis.