The purpose of the "Mars Pathfinder" computer program is to find a faster, more efficient trajectory from Earth to Mars. The program is an exact model of the 2001 Mars mission, within a few small variations as described in the Assumptions section.
The most efficient trajectory between Earth and mars is the
Hohmann Transfer
. The spacecraft escapes from Earth on a hyperbolic trajectory, then goes to a heliocentric ellipse where it intercepts Mars at apoapse in a hyperbolic capture path. The Hohmann Transfer is based on a two body model, whereas the program simulates forces from three bodies on the spacecraft. Hence, it is a four body problem.
The Hohmann Transfer, then, is theoretically not defined in the complex model used to generate the flight path in the program, because it is based on a much simpler system of forces. However, it is a good place to start in seeking an efficient trajectory. So the program assumes the Hohmann Transfer is the "nominal" trajectory, and tries slight deviations from this path, seeking a faster and more efficient way to get to Mars.
The calculations are all done to 16 significant digits (ideally, down to less than a millimeter accuracy) in metric units. Despite this great accuracy, though, the program is intended to be used as a mission planning tool. The idea is to find a better trajectory from the perspective of the whole project using this program. Then once the global parameters are defined - e.g. the total fuel allowance and time of flight - the resulting trajectory is submitted to an exhaustive analysis on a powerful mainframe computer, to work out the minute by minute particulars of the flight path; versus the day by day details, as examined here.
There are a number of parameters that can be selected by the mission designer within this program, each of which has a significant impact upon the trajectory. The actual design of the trajectory can be specified, as well as thrusts at specific points in the mission. The critical parameter is fuel, so the designer is most concerned with minimizing the total thrust to reach Mars. Time is also important, but to a lesser extent. Each mission is rated by the criteria, or "performance index":
Rating = (Time in days*1 + total thrust*40)/5 = +/- 100 units
This shows just how important thrust is!
Normally, all of these variables would be identified and the whole problem analyzed on a mainframe computer. However, this particular problem is so non linear that it cannot be optimized by numerical methods. It must be studied analytically, and solved by trial and error. The mission designer is charged with finding the best way to get there! The computer cannot solve the problem - it can only apply your mission criteria and use them to generate an efficient trajectory.
Some definitions:
Ellipse - a conic section with the central body at one focus - i.e. an Earth satellite has Earth at the main focus; Earth itself moves in an ellipse with the Sun at one focus.
Ellipse - a conic section with the central body at one focus - i.e. an Earth satellite has Earth at the main focus; Earth itself moves in an ellipse with the Sun at one focus.
Apoapse - the most distant point from the central body on an elliptical orbit (the closest point is the periapse)
Hohmann Transfer - in this problem, it's an ellipse with the Sun at the focus and the apoapse is equal to Earth's orbit; the peripase equal to Mars' orbit. The spacecraft moves along half of an ellipse in transit from Earth to Mars.
