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A MATLAB Script for Ballistic Interplanetary Trajectory Design and Optimization
This document describes a MATLAB script called ipto_matlab that can be used to design and optimize “patched conic” ballistic interplanetary trajectories between any two planets of our solar system. It can also be used to find two-body trajectories between a planet and an asteroid or comet. A patched-conic trajectory ignores the gravitational effect of both the launch and arrivals planets on the heliocentric transfer trajectory. This technique involves the solution of Lambert's problem relative to the Sun. Patched-conic trajectories are suitable for preliminary mission design. This script uses the SNOPT nonlinear programming (NLP) algorithm to solve this classic astrodynamics problem. The ipto_matlab MATLAB script also performs a graphical primer vector analysis of the solution. This program feature displays the behavior of the primer vector magnitude and primer derivative magnitude as a function of mission elapsed time in days from departure. User interaction with script The software will ask the user for an initial guess for the launch and arrival calendar dates as well as the launch and arrival celestial bodies. The script will also ask the user for a search boundary, in days, on the launch and arrival dates. The algorithm will restrict its search for the optimum launch date DL and arrival date DA as follows:
DLg  DL  DL  DLg  DL DAg  DA  DA  DA  DA

where DLg and DAg are the user’s initial guess for launch and arrival dates, and DL , DA , are the user-specified search boundaries for the launch and arrival dates, respectively. The following is typical user interaction with this MATLAB application. This example is an Earth-toMars mission that minimizes the launch delta-v. The user inputs for this example are in bold font. departure conditions - start date please input the calendar date