Proposal for extension of ORSA to include phasing in to prove successive encounters of an asteroid between Earth and Mars

Ben Jolitz 2/6/10 Proposal for extension of ORSA to include phasing in to prove successive encounters of an asteroid between Earth and Mars Phasing is the act of changing the phase angle between two sinusoidal functions. In the case of orbits, which are ellipses drawn by sinusoidal functions, phasing is the act of matching one orbit to another. Finding the phasing parameters of a captured asteroid, a non-Keplarian object, in a resonant bi-elliptic orbit and simulation thereof is rather difficult without specialized and esoteric applications. However, open source in the last ten years has made incredible advance-ments, and some projects originally designed for orbital reconstruction have been released to the public on an AS IS basis; one such project is ORSA -Orbital Reconstruction, Simulation, Analysis. ORSA, however, does not have methods for evaluating the relative changes to a phase angle of a bi-elliptic orbit in a recursive manner for successive encounters. For years, space shuttles and other celestial transport vessels have been faced with the difficulty of docking with the International Space Station, a task which involves matching the craft to the unique elliptical orbit of the ISS such that the shuttle will meet the ISS with the appropriate orbital parameters. However, calculation of such requires consideration of only the Earth and it's effect on rather small, man-made objects. In electrical engineering, the concept of a phase lock loop is used to match the frequency and phase of a controlled oscillator with a given set of input signals. In our test case, we wish compute the successive bi-elliptic half orbits of a captured asteroid that traverses between Earth and Mars using gravitational interactions with the intent of computing the relative phase angle between the desired half orbit and current orbit such that a timed encounter with Earth or Mars is possible. The goal of this proposal is to extend ORSA to maintain relative phase angle between bi-elliptic orbits for successive encounters.