Abstract:
We present and analyze the performance of a new algorithm for performing accurate simulations of the solar system when collisions between massive bodies and test particles are permitted. The orbital motion of all bodies at all times is integrated using a high-order variable-timestep explicit Runge–Kutta Nyström (ERKN) method. The variation in the timestep ensures that the orbital motion of test particles on eccentric orbits or close to the Sun is calculated accurately. The test particles are divided into groups and each group is integrated using a different sequence of timesteps, giving a multirate algorithm. The ERKN method uses a high-order continuous approximation to the position and velocity when checking for collisions across a step. We give a summary of the extensive testing of our algorithm. In our largest simulation—that of the Sun, the planets Earth to Neptune and 100,000 test particles over 100 million years—the relative error in the energy after 100 million years was of the order of 10−11.
