Celestial Mechanics and Dynamical Astronomy

, Volume 109, Issue 3, pp 241–264

# Optimal transfers between unstable periodic orbits using invariant manifolds

• Kathryn E. Davis
• Rodney L. Anderson
• Daniel J. Scheeres
• George H. Born
Original article

## Abstract

This paper presents a method to construct optimal transfers between unstable periodic orbits of differing energies using invariant manifolds. The transfers constructed in this method asymptotically depart the initial orbit on a trajectory contained within the unstable manifold of the initial orbit and later, asymptotically arrive at the final orbit on a trajectory contained within the stable manifold of the final orbit. Primer vector theory is applied to a transfer to determine the optimal maneuvers required to create the bridging trajectory that connects the unstable and stable manifold trajectories. Transfers are constructed between unstable periodic orbits in the Sun–Earth, Earth–Moon, and Jupiter-Europa three-body systems. Multiple solutions are found between the same initial and final orbits, where certain solutions retrace interior portions of the trajectory. All transfers created satisfy the conditions for optimality. The costs of transfers constructed using manifolds are compared to the costs of transfers constructed without the use of manifolds. In all cases, the total cost of the transfer is significantly lower when invariant manifolds are used in the transfer construction. In many cases, the transfers that employ invariant manifolds are three times more efficient, in terms of fuel expenditure, than the transfer that do not. The decrease in transfer cost is accompanied by an increase in transfer time of flight.

## Keywords

Three-body problem Unstable periodic orbits Invariant manifolds Dynamical systems theory Transfer trajectories Primer vector theory Libration point orbits

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## Authors and Affiliations

• Kathryn E. Davis
• 1
• Rodney L. Anderson
• 1
• Daniel J. Scheeres
• 1
• George H. Born
• 1