The entire trajectory is integrated using a Runge-Kutta 7/8, variable step integrator. The tolerance is set to E-14, giving a consistent accuracy in determination of the flight path of 14 to 16 significant digits. Five features of the trajectory can be modified by the user, specified in context as follows.
The program first optimizes the Earth to conjunction part of the trajectory. An escape hyperbola from Earth is found that begins at the designated parking orbit. A mission design parameter can be set that (1) instructs the program to find an escape trajectory that takes advantage of a small gravity assist on flyby, and/or (2) allows the flight path to briefly drop below the parking orbit to get even more of a gravity assist.
The conjunction to Mars flight path is calculated after applying a (3) user-defined thrust at conjunction. A capture hyperbola is then found that ends at the designated parking orbit. A mission design parameter can be set that (4) instructs the program to find a gravity assisted capture trajectory, and/or (5) allows the flight path to drop below the parking orbit height.
Given these flight plan modifications and the extra thrusts, the program finds a complete trajectory that minimizes the total thrust for the mission. The objective is to get to Mars in as little time as possible, but using the least amount of fuel. All the orbits begin from a 200 Km parking orbit around Earth, and end at a 100 Km parking orbit around Mars. Although these parking orbits are themselves usually a mission design parameter, this is an optimization program so if several missions are to be compared on equal terms they must have the same beginning and end points.
Some definitions:
Integrated trajectory - The program begins with initial velocities for all the bodies. The forces on the spacecraft from the Sun and planets are calculated, and then all the bodies are moved a time increment. At this point all the forces are recalculated, and the bodies are moved another time step, etc...
Variable step integrator - A special integration method that varies the time step so the trajectory can be calculated most accurately. Accuracy is lost when time steps are short because of roundoff and truncation errors, so the integrator determines the longest possible time increment at each step of the integration and so is able to generate the most accurate trajectory possible given the limitations of the model and of the computer.
Parking orbit - A circular orbit, say around Earth, into which an interplanetary mission is sometimes placed before beginning the escape trajectory. This is helpful in timing the first major thrust to coincide with the optimal flight path designed on the computer.
Gravity assisted flyby - When a spacecraft passes close to a major celstial body, it's velocity is accelerated by the gravity of the central body. This is a small affect in the present context, but every bit of fuel that can be saved is critical to a successful mission.
