Many of the important algorithms we use today in the space business have their origins in NASA’s Apollo program. For example, the Runge-Kutta methods with stepsize control developed by Erwin Fehlberg (1911-1990). These are still used today for propagating spacecraft trajectories. Fehlberg was a German mathematician who ended up at Marshall Spaceflight Center in Huntsville, Alabama. Many of the original reports documenting these methods are publicly available on the NASA Technical Reports Server (see references below). Modern Fortran implementations of Fehlberg’s RK7(8) and RK8(9) methods (and others) can be found in the Fortran Astrodynamics Toolkit.
- Fehlberg, E., “Classical Fifth-, Sixth-, Seventh-, and Eighth-Order Runge–Kutta Formulas with Stepsize Control“, NASA-TR-R-287, 1968
- Fehlberg, E., “Low-order classical Runge–Kutta formulas with stepsize control and their application to some heat transfer problems“, NASA-TR-R-315, 1969
- Fehlberg, E., “Classical eight- and lower-order Runge–Kutta-Nystrom formulas with stepsize control for special second-order differential equations“, NASA-TR-R-381, M-533, 1972
- Fehlberg, E., “Classical eighth- and lower-order Runge-Kutta-Nystrom formulas with a new stepsize control procedure for special second-order differential equations“, NASA-TR-R-410, M-544, 1973
- Fehlberg, E., “Classical seventh-, sixth-, and fifth-order Runge-Kutta-Nystrom formulas with stepsize control for general second-order differential equations“, NASA-TR-R-432, M-546, 1974