Center 4 CM

Optimizing the Earth to Mars Trajectory

The Earth-to-Mars flight path is set up in a computer simulation with the planets in elliptical two body motion and the spacecraft (s/c) in motion about a central body, perturbed by the other two. The trajectory is integrated using a variable step Runge Kutta 7/8 integrator which determines the path accurate to 14 significant digits. The path is seamlessly integrated from hyperbolic escape from a 200 km Earth parking orbit to a heliocentric transfer ellipse, then hyperbolic capture at Mars and transition into a 100 km parking orbit there. The simulation provides for a mid-course correction, approximately at conjunction. Given an input of magnitude and direction of this thrust, the trajectory is then optimized for total energy usage and transit time with a total of five independent thrusts (two inside Earth' sphere of influence; two near Mars; one at conjunction). The complete analysis takes less than 30 seconds on a 300 mHz PC. Using the thrust used for a minimum energy two-body Hohmann transfer, the program generated a 215 day mission profile using the actual ephemerides for the 2001 Mars mission. Actual Mars missions to date use 20% more energy, to reach Mars 40 days slower.

You can download the complete paper in PDF format here. Also available in PDF format are two multi chapter reports on Orbital Mechanics and Modeling Interplanetary Trajectories.