A Continuation Method for Converting Trajectories from Patched Conics to Full Gravity Models

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A Continuation Method for Converting Trajectories from Patched Conics to Full Gravity Models

Bradley, Nicholas / Russell, Ryan P.

Abstract A method is introduced to transition space trajectories from low fidelity patched conics models to full-ephemeris n-body dynamics. The algorithm incorporates a continuation method that progressively re-converges solution trajectories in systems with incremental changes in the dynamics. Continuation is accomplished through the variation of a control parameter, which is tied to body ephemeris locations and masses, minimum flyby altitudes, and sphere of influence sizes. The intermediate models provide a continuous and differentiable path between solutions in the simplified and n-body dynamics, and the boundary values of the control parameter replicate the patched conics and full-ephemeris models exactly. Each successive step preserves the qualitative properties of the initial guess by successively altering flyby states and body masses. A similar approach to this methodology may be taken with any simplified starting guess, such as a restricted three-body model. Trajectories computed using the patched conics conversion method presented here may include gravity assists and rendezvous with any number of target bodies, so the method is ideal for constructing interplanetary or intermoon tour missions, and is amenable to patching shorter segments together to form longer tours.