With the advent of modern high-speed personal computers, why do we still teach astrodynamics/orbital mechanics using Kepler’s equations?  When I taught astrodynamics 40 years ago at the USAF Academy, we used the Bate, Mueller, and White book Fundamentals of Astrodynamics. It presented space flight using highly complex, mathematical gymnastics based on Kepler’s equations of planetary motion.

In fact, it can be taught using basic physics and the equation of motion for the spacecraft under the acceleration of Earth gravity with perturbations from other sources such as Sun, Moon, Earth bulge, Earth atmosphere, solar pressure, and thrust (see image below).  Since equations are available for the position of the Sun and Moon relative to the Earth-centered Inertial (ECI) coordinate system, you don’t need to do an n-body equation of motion.

This spacecraft equation of motion can easily be solved by computer using a double numerical integrator with small time steps making it very accurate.  Missions that require months can now be solved accurately and quickly using your laptop computer in less than 10 seconds. You can even propagate spacecraft backward in time.

This is how we do orbit simulations using SOS. It’s designed for education and allows you to do the simulations with or without any of the perturbations so you can see the effects of perturbations.

Andrew Motes