Hyperbolic Injection from a Circular Earth Park Orbit – OTB

Determine delta-v required for coplanar and non-coplanar impulsive hyperbolic orbit transfers

This submission is a MATLAB script named hyper2_otb 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_otb 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 uses the fminconalgorithm of the Optimization Toolbox to find the optimal coplanar or non-coplanar transfer maneuver.