Revisiting high-order Taylor methods for astrodynamics and celestial mechanics

ABSTRACT We present heyoka, a new, modern and general-purpose implementation of Taylor’s integration method for the numerical solution ordinary differential equations. Detailed tests focused on difficult high-precision gravitational problems in astrodynamics celestial mechanics show how our integrator is competitive with often superior to state-of-the-art specialized symplectic non-symplectic integrators both speed accuracy. In particular, we Taylor methods are capable satisfying Brouwer’s law conservation energy long-term integrations planetary systems over billions dynamical time-scales. also close encounters modelled accurately during simulations formation Kirkwood gaps Apophis’ 2029 encounter Earth (where heyoka surpasses accuracy domain-specific methods). can be used from C++ python, it publicly available as an open-source project.