Abstract
With recent improvements in ground and space-based telescopes, a large number of binary systems have been observed both within the solar system and beyond. These systems can take the form of asteroid pairs or even binary stars, with each component possessing a similar mass. In this investigation, periodic motions near large mass ratio binaries are explored using the circular restricted three-body problem, which is modified to include an additional three-body interaction. Discrete variational mechanics is leveraged to obtain periodic orbits that exhibit interesting shape characteristics, as well as the corresponding natural parameters. Shape characteristics and structural changes are explained using the stability and existence of equilibrium points, enabling exploration of the effect of an additional three-body interaction and conditions for reproducibility in a natural gravitational environment.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bosanac, N.: Exploring the influence of a three-body interaction added to the gravitational potential function in the circular restricted three-body problem: a numerical frequency analysis. M.S. Thesis, School of Aeronautics and Astronautics, Purdue University, West Lafayette (2012)
Bosanac, N., Howell, K.C., Fischbach, E.: Exploring the impact of a three-body interaction added to the gravitational potential function in the restricted three-body problem. In: 23rd AAS/AIAA Space Flight Mechanics Meeting, Hawaii (2013)
Bosanac, N., Howell, K.C., Fischbach, E.: Stability of orbits near large mass ratio binary systems. Celest. Mech. Dyn. Astron. 122 (1), 27–52 (2014)
Bosanac, N., Howell, K.C., Fischbach, E.: A natural autonomous force added in the restricted problem and explored via stability analysis and discrete variational mechanics. In: AAS/AIAA Space Flight Mechanics Meeting, Williamsburg (2015)
Chappaz, L.: Exploration of bounded motion near binary systems comprised of small irregular bodies. Celest. Mech. Dyn. Astron. (2015). doi:10.1007/s10569-015-9632-5
Contopoulos, G.: Order and Chaos in Dynamical Astronomy. Springer, Berlin (2002)
Douskos, C.N.: Effect of three-body interaction on the number and location of equilibrium points of the restricted three-body problem. Astrophys. Space Sci. 356 (2), 251–268 (2014)
Fischbach, E.: Long-range forces and neutrino mass. Ann. Phys. 247, 213–291 (1996)
Greenwood, D.T.: Principles of Dynamics, 2nd edn. Prentice-Hall, Englewood Cliffs (1988)
Lanczos, C.: The Variational Principles of Mechanics. Courier Dover, Toronto (2012)
Marsden, J.E., West, M.: Discrete mechanics and variational integrators. Acta Numer. 10, 357–514 (2001)
Margot, J.L., Nolan, M.C., Benner, L.A.M., Ostro, S.J., Jurgens, R.F., Giorgini, J.D., Slade, M.A., Campbell, D.B.: Binary asteroids in the Near-Earth object population. Science 296 (5572), 1445–1448 (2002)
Moore, A.: Discrete mechanics and optimal control for space trajectory design. Ph.D Thesis, Control and Dynamical Systems, California Institute of Technology, Pasadena (2011)
Ober-Blobaum, S., Junge, O., Marsden, J.E.: Discrete mechanics and optimal control: an analysis. ESAIM Control Optim. Calc. Var. 17 (2), 322–352 (2011)
Raghavan, D., Henry, T.J., Masion, B.D., Subasavage, J.P., Jao, W., Beaulieu, T.H., Hambly, N.C.: Two suns in the sky: stellar multiplicity in exoplanet systems. Astrophys. J. 646, 523–542 (2006)
Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic, London (1967)
Acknowledgements
The authors wish to acknowledge support from the Zonta International Amelia Earhart Fellowship during this work, as well as from the School of Aeronautics and Astronautics at Purdue University.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Bosanac, N., Howell, K.C., Fischbach, E. (2016). Leveraging Discrete Variational Mechanics to Explore the Effect of an Autonomous Three-Body Interaction Added to the Restricted Problem. In: Gómez, G., Masdemont, J. (eds) Astrodynamics Network AstroNet-II. Astrophysics and Space Science Proceedings, vol 44. Springer, Cham. https://doi.org/10.1007/978-3-319-23986-6_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-23986-6_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-23984-2
Online ISBN: 978-3-319-23986-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)