Hyperbolic Injection from a Circular Earth Park Orbit SNOPT

MATLAB script for modeling interplanetary injection from an Earth escape hyperbolic orbit using the SNOPT programming method.

This submission is a MATLAB script named hyper2_snopt which can be used to determine the characteristics of the single impulsive maneuver required to transfer a spacecraft from an initial circular Earth park orbit to a departure hyperbola. The algorithm implemented in this script is based on the equations derived in Chapter 4 of Richard Battin’s classic text, Astronautical Guidance, and Chapter 11 of An Introduction to the Mathematics and Methods of Astrodynamics, also written by Professor Battin and published by the American Institute of Aeronautics and Astronautics (AIAA).

The Earth departure trajectory for interplanetary missions is usually 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 interplanetary missions.

The hyper2_snopt MATLAB script determines the orbital elements and state vectors of the park orbit and departure hyperbola at injection, and the injection delta-v vector and magnitude. This information can be used as initial guesses for other trajectory simulations.

This script is valid for coplanar and non-coplanar from a circular Earth orbit.

This script uses the SNOPT nonlinear programming (NLP) method for optimizing the problem implemented in this script. MATLAB versions of SNOPT mex and support m-files for several computer platforms can be found at Professor Philip Gill’s web site which is located at http://scicomp.ucsd.edu/~peg/. Professor Gill’s web site also includes a PDF version of the SNOPT software user’s guide.