Advertisement

Leveraging Discrete Variational Mechanics to Explore the Effect of an Autonomous Three-Body Interaction Added to the Restricted Problem

Conference paper
Part of the Astrophysics and Space Science Proceedings book series (ASSSP, volume 44)

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.

Keywords

Periodic Orbit Equilibrium Point Constrain Optimization Problem Dynamical System Theory Reference Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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.

References

  1. 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)Google Scholar
  2. 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)Google Scholar
  3. 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)ADSMathSciNetCrossRefGoogle Scholar
  4. 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)Google Scholar
  5. 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 MathSciNetGoogle Scholar
  6. Contopoulos, G.: Order and Chaos in Dynamical Astronomy. Springer, Berlin (2002)CrossRefzbMATHGoogle Scholar
  7. 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)ADSCrossRefGoogle Scholar
  8. Fischbach, E.: Long-range forces and neutrino mass. Ann. Phys. 247, 213–291 (1996)ADSCrossRefGoogle Scholar
  9. Greenwood, D.T.: Principles of Dynamics, 2nd edn. Prentice-Hall, Englewood Cliffs (1988)Google Scholar
  10. Lanczos, C.: The Variational Principles of Mechanics. Courier Dover, Toronto (2012)zbMATHGoogle Scholar
  11. Marsden, J.E., West, M.: Discrete mechanics and variational integrators. Acta Numer. 10, 357–514 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 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)ADSCrossRefGoogle Scholar
  13. Moore, A.: Discrete mechanics and optimal control for space trajectory design. Ph.D Thesis, Control and Dynamical Systems, California Institute of Technology, Pasadena (2011)Google Scholar
  14. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 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)ADSCrossRefGoogle Scholar
  16. Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic, London (1967)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Aeronautics and AstronauticsPurdue UniversityWest LafayetteUSA
  2. 2.Department of Physics and AstronomyPurdue UniversityWest LafayetteUSA

Personalised recommendations