Abstract
In this paper the authors provide a study of the phenomenon of the gravitational capture by using the models of the circular and elliptic restricted three-body problem. In the first part the inadequacy of the circular restricted three-body problem in the study of the phenomenon of the capture in the case of NEAs is shown. In the model of the spatial elliptic restricted three-body problem criteria of the capture are deduced by using the pulsating Hill-regions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Astakhov, S. A., Burbanks, A. D., Stephen, W. and Farrelly. D.: 2003, ‘Chaos-assisted capture of irregular moons’, Nature 423, 464–467.
Belbruno, E.: 1999, ‘Hopping in the Kuiper Belt and significance of the 2:3 resonance'. In: Bonnie A. Steves and Archie E. Roy (eds), The Dynamics of Small Bodies in the Solar System, A Major Key to Solar System Studies, Kluwer Academic Publishers, pp. 37–49.
Belbruno, E. and Marsden, B. G.: 1997, ‘Resonance hopping in comets’, Astron. J. 113(4), 1433–1444.
Brunini, A.: 1996, ‘On the satellite capture problem. Capture and stability regions for planetary satellites’, Celestial Mech. Dyn. Astr. 64, 79–92.
Brunini, A., Giordano, C. M. and Orellana, R. B.: 1996, ‘Capture conditions in the restricted three-body problem’, Revista Mexicana de Astronomia y Astrofisica Serie de Conferencais 4, 111–116.
Murison, M. A.: 1989, ‘The fractal dynamics of satellite capture in the circular restricted three-body problem’, Astron. J. 98(6), 2346–2386.
Szebehely, V.: 1967, Theory of orbits, Academic Press, New-York.
Vieira, N. E. and Winter, O. C.: 2001, ‘Time analysis for temporary gravitational capture: satellites of Uranus’, Astronom. J. 122(1), 440–448.
Wisdom, J. and Holman, M.: 1991, ‘Symplectic maps for the N-body problem’, Astron. J. 102, 1528–1538.
Wisdom J. and Holman, M.: 1992, ‘Symplectic maps for the N-body problem: Stability analysis’, Astron. J. 104, 2022–2029.
Yu, Q. and Tremaine, S.: 2001, ‘Resonant capture by inward-migrating planets’, Astron. J. 121(3), 1736–1740.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Makó, Z., Szenkovits, F. Capture in the Circular and Elliptic Restricted Three-Body Problem. Celestial Mechanics and Dynamical Astronomy 90, 51–58 (2004). https://doi.org/10.1007/s10569-004-5899-7
Issue Date:
DOI: https://doi.org/10.1007/s10569-004-5899-7