An analytic-geometric model of the effect of spherically distributed injection errors for Galileo and Ulysses spacecraft - The multi-stage problemIn previous work the problem of injecting the Galileo and Ulysses spacecraft from low earth orbit into their respective interplanetary trajectories has been discussed for the single stage (Centaur) vehicle. The central issue, in the event of spherically distributed injection errors, is what happens to the vehicle? The difficulties addressed in this paper involve the multi-stage problem since both Galileo and Ulysses will be utilizing the two-stage IUS system. Ulysses will also include a third stage: the PAM-S. The solution is expressed in terms of probabilities for total percentage of escape, orbit decay and reentry trajectories. Analytic solutions are found for Hill's Equations of Relative Motion (more recently called Clohessy-Wiltshire Equations) for multi-stage injections. These solutions are interpreted geometrically on the injection sphere. The analytic-geometric models compare well with numerical solutions, provide insight into the behavior of trajectories mapped on the injection sphere and simplify the numerical two-dimensional search for trajectory families.
Document ID
19880063152
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Longuski, James M. (Jet Propulsion Lab., California Inst. of Tech. Pasadena, CA, United States)
Mcronald, Angus D. (California Institute of Technology Jet Propulsion Laboratory, Pasadena, United States)