High Speed Solution of Spacecraft Trajectory Problems Using Taylor Series Integration

Abstract

Taylor series integration is implemented in a spacecraft trajectory analysis code-the Spacecraft N-body Analysis Program (SNAP) - and compared with the code s existing eighth-order Runge-Kutta Fehlberg time integration scheme. Nine trajectory problems, including near Earth, lunar, Mars and Europa missions, are analyzed. Head-to-head comparison at five different error tolerances shows that, on average, Taylor series is faster than Runge-Kutta Fehlberg by a factor of 15.8. Results further show that Taylor series has superior convergence properties. Taylor series integration proves that it can provide rapid, highly accurate solutions to spacecraft trajectory problems.