# Efficient design of direct low-energy transfers in multi-moon systems

## Abstract

In this contribution, an efficient technique to design direct (i.e., without intermediate flybys) low-energy trajectories in multi-moon systems is presented. The method relies on analytical two-body approximations of trajectories originating from the stable and unstable invariant manifolds of two coupled circular restricted three-body problems. We provide a means to perform very fast and accurate computations of the minimum-cost trajectories between two moons. Eventually, we validate the methodology by comparison with numerical integrations in the three-body problem. Motivated by the growing interest in the robotic exploration of the Jovian system, which has given rise to numerous studies and mission proposals, we apply the method to the design of minimum-cost low-energy direct trajectories between Galilean moons, and the case study is that of Ganymede and Europa.

## Keywords

Spacecraft trajectories Low-energy transfers Circular restricted three-body problem Restricted two-body problem Galilean moons## Notes

### Acknowledgments

The authors wish to thank Roberto Flores, Martin Ozimek and Andrea Viale for useful discussions and the anonymous referee for his/her valuable suggestions.

## References

- Campagnola, S., Russell, R.P.: Engame problem part 2: multibody technique and the Tisserand–Poincaré Graph. J. Guid. Control. Dyn.
**33**(2), 476–486 (2010)ADSCrossRefGoogle Scholar - Campagnola, S., Boutonnet, A., Schoenmaekers, J., Grebow, D.J., Petropoulos, A.E., Russell, R.P.: Tisserand-leveraging transfers. J. Guid. Control. Dyn.
**37**(4), 1202–1210 (2012)ADSCrossRefGoogle Scholar - Campagnola, S., Buffington, B.B., Petropoulos, A.E.: Jovian tour design for orbiter and lander missions to Europa. Acta Astronautica
**100**, 68–81 (2014)ADSCrossRefGoogle Scholar - Castelli, R.: Regions of prevalence in the coupled restricted three-body problems approximation. Commun. Nonlinear Sci. Numer. Simul.
**17**(2), 804–816 (2012)ADSMathSciNetCrossRefMATHGoogle Scholar - Colasurdo, G., Zavoli, A., Longo, A., Casalino, L., Simeoni, F.: Tour of Jupiter galilean moons: winning solution of GTOC6. Acta Astronaut.
**102**, 190–199 (2014)ADSCrossRefGoogle Scholar - ESA (2014). JUICE JUpiter ICy moons Explorer, vol. 1. ESAGoogle Scholar
- Fantino, E., Gómez, G., Masdemont, J.J., Ren, Y.: A note on libration point orbits, temporary capture and low-energy transfers. Acta Astronaut.
**67**(9–10), 1038–1052 (2010)ADSCrossRefGoogle Scholar - Gómez, G., Koon, W.S., Lo, M.W., Marsden, J.E., Masdemont, J.J., Ross, S.D.: Invariant manifolds, the spatial three-body problem and space mission design. Adv. Astronaut. Sci.
**109**, 3–22 (2001)Google Scholar - Gómez, G., Koon, W.S., Lo, M.W., Marsden, J.E., Masdemont, J.J., Ross, S.D.: Connecting orbits and invariant manifolds in the spatial restricted three-body problem. Nonlinearity
**17**(5), 1571 (2004)ADSMathSciNetCrossRefMATHGoogle Scholar - Gómez, G., Masdemont, J.J., Mondelo, J.: Libration point orbits: a survey from the dynamical point of view. In: Gómez, G., Lo, M.W., Masdemont, J.J. (eds.) Libration point orbits and applications. World Scientific Publishing Company, Singapore (2003)CrossRefGoogle Scholar
- Grover, P., Ross, S.: Designing trajectories in a planet-moon environment using the controlled keplerian map. J. Guid. Control Dyn.
**32**(2), 436–443 (2009)ADSCrossRefGoogle Scholar - Izzo, D., Simoes, L.F., Martens, M., de Croon, G. C. H. E., Heritier, A., Yam, C.: Search for a grand tour of the Jupiter galilean moons. In: Proceedings of the 15th annual conference on Genetic and evolutionary computation, pp. 1301–1308, Amsterdam, The Netherlands. ACM (2013)Google Scholar
- Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics. Chaos
**10**(2), 427–469 (2000)ADSMathSciNetCrossRefMATHGoogle Scholar - Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Low energy transfer to the moon. Celest. Mech. Dyn. Astron.
**81**, 63–73 (2001)ADSMathSciNetCrossRefMATHGoogle Scholar - Koon, W. S., Lo, M. W., Marsden, J. E. and Ross, S. D.: Constructing a low energy transfer between jovian moons. Celestial Mechanics, Dedicated to Donald Saari for his 60th Birthday, p 129 (2002)Google Scholar
- Koon, W.S., Lo, M.W., Marsden, J.E., Ross, S.D.: Dynamical systems, the three-body problem and space mission design. Marsden Books, (2011)Google Scholar
- Lam, T., Camacho, J.A., Buffington, B.: The Europa mission: multiple europa flyby trajectory design trades and challenges. In: AAS/AIAA Astrodynamics Specialist Conference, Vail, Colorado, number Paper No. AAS 15-657 (2015)Google Scholar
- Lantoine, G., Russell, R.P.: Near Ballistic Halo–to–Halo transfers between planetary moons. J. Astronaut. Sci.
**58**(3), 335–363 (2011)ADSCrossRefGoogle Scholar - Lantoine, G., Russell, R.P., Campagnola, S.: Optimization of low-energy resonant hopping transfers between planetary moons. Acta Astronaut.
**68**, 1361–1378 (2011)ADSCrossRefGoogle Scholar - Lo, M.W., Williams, B.G., Bollman, W.E., Han, D., Hahn, Y., Bell, J.L., et al.: Genesis mission design. J. Astronaut. Sci.
**49**, 169–184 (2001)Google Scholar - Lo, M.W., Anderson, R.L., Lam, R. and Marsden, J.E.: The role of invariant manifolds in low thrust trajectory design (part III). In: AAS/AIAA Spaceflight Mechanics Meeting, Tampa, Florida, vol. AAS 06–190 (2006)Google Scholar
- Parker, J.S., Anderson, R.L.: Low-energy lunar trajectory design. Wiley, Hoboken, New Jersey (2014)Google Scholar
- Petropoulos, A.: Problem description for the 6th global trajectory optimisation competition. (2012) http://www.esa.int/gsp/ACT/doc/MAD/ACT-RPT-MAD-GTOC6-problem_stmt (last viewed 20/04/2016)
- Ross, S.D., Koon, W.S., Lo, M.W., Marsden, J.E.: Design of a multi-moon orbiter. In: 13th AAS/AIAA Space Flight Mechanics Meeting. Ponce, Puerto Rico, vol. AAS 03–143 (2003)Google Scholar
- Roy, A.E.: Orbital motion, 3rd edn. Adam Hilger, Bristol (1988)Google Scholar
- Sims, J.A.: Jupiter icy moons orbiter mission design overview. In: AAS/AIAA SpaceFlight Mechanics Meeting, Tampa, Florida. Pasadena, CA : Jet Propulsion Laboratory, National Aeronautics and Space Administration (2006)Google Scholar
- Szebehely, V.: Theory of orbit: the restricted problem of three bodies. Elsevier, Amsterdam (2012)Google Scholar
- Zanzottera, A., Mingotti, G., Castelli, R., Dellnitz, M.: Intersecting invariant manifolds in spatial restricted three-body problems: design and optimization of Earth-to-halo transfers in the Sun-Earth-moon scenario. Commun. Nonlinear Sci. Numer. Simul.
**17**(2), 832–843 (2012)ADSMathSciNetCrossRefMATHGoogle Scholar