Impulsive Hyperbolic Injection from a Circular Earth Park Orbit

[cdeaglejr]

Updated October 16, 2022

This HP Prime computer program 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 an interplanetary mission.

The demo_hyper1 software 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.

A PDF document which describes the orbital mechanics of this classic astrodynamics problem is included in the attached zip archive.