Interplanetary Injection from a Circular Earth Orbit

PDF document and script for computing the coplanar single impulse transfer from a circular Earth orbit to a hyperbolic orbit.

This submission is a MATLAB script named hyper1 which can be used to determine the characteristics of a single coplanar 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 an interplanetary mission.

The hyper1 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 for two possible interplanetary injection opportunities. This information can be used as an initial guess for other trajectory simulations.