Finite-burn Interplanetary Injection from Earth Orbit SNOPT

A MATLAB script for optimizing finite-burn interplanetary injection trajectories from an initial circular Earth orbit using SNOPT.

This submission a MATLAB script named fb_hyper_snopt which can be used to determine the characteristics of the optimal finite-burn maneuver required to transfer a spacecraft from an initial circular Earth park orbit to a departure hyperbola. The simulation assumes the propulsive maneuver is continuous, co-planar and modeled as a series of optimal discretized steering angles. This script attempts to minimize the thrust duration of the finite-burn while solving for user-defined hyperbolic boundary conditions at burnout.

The Earth departure trajectory for interplanetary missions is often defined by a “targeting specification” which consists of twice the specific (per unit mass) orbital energy C3, and the right ascension (RLA) and declination (DLA) of the outgoing asymptote. These targets may be supplied by a spacecraft customer or determined with a patched-conic or more sophisticated trajectory analysis computer program that solves Lambert’s problem for an interplanetary mission.

The fb_hyper_snopt MATLAB script determines the Earth-centered-inertial (ECI) orbital elements and state vector of the park orbit at ignition and the departure hyperbola at burnout. The optimization of the maneuver steering angles is performed using the SNOPT nonlinear programming (NLP) algorithm. MATLAB versions of SNOPT for several computer platforms can be requested/purchased at Professor Philip Gill’s web site which is located at http://scicomp.ucsd.edu/~peg/.