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Tsien's Method For Generating Non-Keplerian Trajectories Part 11 - The Question of Thrust to Orbit a Sphere and the Restricted Three-Body Problem
Paul A. Murad*
Abstract
Orbit prediction of a body undergoing accelerations/decelerations is examined by extending Tsien's method.A solution for the generalized case is discussed for a body undergoing both azimuthal and radial thrust and the simplified case of azimuthal thrust alone. Judicious selection of thrust can generate either an elliptic or hyperbolic trajectory regardless of initial conditions. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended to treat vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation produce hyperbolic trajectories through eigenvalue decomposition. Since eigenvalues for no-thrust can be imaginary, thrust can generate real eigenvalues and hyperbolic trajectories. Keplerian dynamics repre-sents a small subset of a much larger non-Keplerian domain that includes thrust effects. Consequently, the need for high thrust long-duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated.
*Aerospace Engineer. Defense Intelligence Agency, Washington, D.C. The views expressed in this article are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government