Finite-burn Interplanetary Injection from Earth Orbit - OTB

Optimization Toolbox version of a MATLAB script that can be used to model finite-burn interplanetary injection from a circular Earth orbit.

This submission is a MATLAB script named fb_hyper_otb 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_otb 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. It uses the interior-point numerical method of the fmincon algorithm of the Mathworks™ Optimization Toolbox to solve this problem. It implements a simple shooting technique to propagate the trajectory and solve the boundary value mission constraints.