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We present WHFast, a fast and accurate implementation of a Wisdom-Holmansymplectic integrator for long-term orbit integrations of planetary systems.WHFast is significantly faster and conserves energy better than all otherWisdom-Holman integrators tested. We achieve this by significantly improvingthe Kepler-solver and ensuring numerical stability of coordinatetransformations to and from Jacobi coordinates. These refinements allow us toremove the linear secular trend in the energy error that is present in otherimplementations. For small enough timesteps we achieve Brouwer's law, i.e. theenergy error is dominated by an unbiased random walk due to floating-pointround-off errors. We implement symplectic correctors up to order eleven thatsignificantly reduce the energy error. We also implement a symplectic tangentmap for the variational equations. This allows us to efficiently calculate twowidely used chaos indicators the Lyapunov characteristic number (LCN) and theMean Exponential Growth factor of Nearby Orbits (MEGNO). WHFast is freelyavailable as a flexible C package, as a shared library, and as an easy-to-usepython module.

WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations