AIAA-13095-511

AIAA-13095-511 - JOURNAL OF SPACECRAFT AND ROCKETS Vol. 41,...

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JOURNAL OF SPACECRAFT AND ROCKETS Vol. 41, No. 5, September–October 2004 Shape-Based Algorithm for Automated Design of Low-Thrust, Gravity-Assist Trajectories Anastassios E. Petropoulos and James M. Longuski Purdue University, West Lafayette, Indiana 47907-1282 Given the beneFts of coupling low-thrust propulsion with gravity assists, techniques for easily identifying candi- date trajectories would be extremely useful to mission designers. The computational implementation of an analytic, shape-based method for the design of low-thrust, gravity-assist trajectories is described. Two-body motion (cen- tral body and spacecraft) is assumed between the ±ybys, and the gravity-assists are modeled as discontinuities in velocity arising from an instantaneous turning of the spacecraft’s hyperbolic excess velocity vector with respect to the ±yby body. The method is augmented by allowing coast arcs to be patched with thrust arcs on the transfers between bodies. The shape-based approach permits not only rapid, broad searches over the design space, but also provides initial estimates for use in trajectory optimization. Numerical examples computed with the shape-based method, using an exponential sinusoid shape, are presented for an Earth–Mars–Ceres rendezvous trajectory and an Earth–Venus–Earth–Mars–Jupiter ±yby trajectory. Selected trajectories from the shape-based method are successfully used as initial estimates in an optimization program employing direct methods. Nomenclature a = thrust acceleration normalized by local gravitational acceleration a 0 P = zeroth-order constant coef±cient for out-of-plane a b 0 = ±rst-order constant coef±cient for out-of-plane a d i = difference in inverse radii, m 1 F = thrust acceleration, ms 2 f h = thrust acceleration along spacecraft’s orbital angular momentum, ms 2 h x = spacecraft speci±c orbital angular momentum, x component, m 2 s 2 h y = spacecraft speci±c orbital angular momentum, y component, m 2 s 2 I sp = speci±c impulse, s i = inclination, rad k 0 = scale parameter for the exponential sinusoid, m k 1 = dynamic range parameter for the exponential sinusoid k 2 = winding parameter for the exponential sinusoid k 12 s = k 1 k 2 2 s ˙ m = propellant mass ²ow rate, mg/s n = integer P =p ower, kW p = semilatus rectum, m r = radial distance from the central body, m r B = radial distance of ²yby body (or switch point) from central body at time of ²yby (or thrust switch on/off), m s = sin ( k 2 θ + φ) Presented as Paper 2001-467 at the AAS/AIAA Astrodynamics Special- ists Conference, Qu´ebec City, QC, Canada, 30 July–2 August 2001; re- ceived 5 June 2002; revision received 28 July 2003; accepted for publication 1 August 2003. Copyright c ° 2003 by Anastassios E. Petropoulos and James M. Longuski. Published by the American Institute of Aeronautics and Astro- nautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 0022-4650/04 $10.00 in correspondence with the
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AIAA-13095-511 - JOURNAL OF SPACECRAFT AND ROCKETS Vol. 41,...

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