Abstract
We study the motion of grains in orbit around asteroids under the influence of radiation pressure originating in the flux of solar photons. Of interest is the possibility of initially bound grains becoming unbound and leaving the vicinity of the asteroid. The analysis extends the two-degree-of-freedom results of (Dankowicz, 1995) to three-degree-of-freedom motions. In particular, we use a Melnikov-type approach for finding transversal points of intersection between high-dimensional perturbed stable and unstable manifolds. As a consequence, the system is shown to be nonintegrable and the resulting homoclinic tangles are suggested as a means for phase space transport along resonance layers, so-called Arnol'd diffusion. We discuss the implications of the diffusion on the depletion of asteroid-bound particles and attempt to estimate the diffusion rate for physical comparison. For particular values of physical parameters the time scale is shown to be on the order of hundreds of orbital revolutions of the asteroid around the sun.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnol'd, V. I.: 1988, Dynamical Systems III, Springer-Verlag, Berlin.
Arnol'd, V. I.: 1989, Mathematical Methods of Classical Mechanics, 2nd Edition, Springer-Verlag, New York.
Bernard, P.: 1996, Perturbation d'un Hamiltonien Partiellement Hyperbolique, C.R. Acad. Sci. Paris, t. 323, Sèrie I, pages 189–194.
Burns, J. A. and Lamy, P. L. and Soter, S.: 1979, Radiation Forces on Small Particles in the Solar System, Icarus, 40:1–48.
Byrd, P. F. and Friedman, M. D.: 1971, Handbook of Elliptic Integrals for Scientists and Engineers, Springer-Verlag, New York.
Chamberlain, J. W. and Bishop, J.: 1993, Radiation Pressure Dynamics in Planetary Exospheres. II. Closed Solutions for the Evolution of Orbital Elements, Icarus, 106:419–427.
Chierchia, L. and Gallavotti, G.: 1994 Drift and Diffusion in Phase Space, Ann. H. Poincarè (Physique Theorique), 60(1):1–144.
Dankowicz, H.:1994, Some Special Orbits in the Two-body Problem with Radiation Pressure, Celes. Mech., 58:353–370.
Dankowicz, H.: 1995, The Two-Body Problem with Radiation Pressure in a Rotating Reference Frame, Celes. Mech, 61(3):287–313.
Dankowicz, H.: 1996, Analytical Expressions for Stable and Unstable Manifolds in Higher Degree of Freedom Hamiltonian Systems, International Journal of Bifurcation and Chaos, 6(11):1997–2013.
Deprit, A.: 1983, Dynamics of Orbiting Dust under Radiation Pressure. In A. Berger, editor, The Big Bang and Georges Lemaître, pages 151–180. D. Reidel Publishing Company, Dordrecht.
Graff, S. M.: 1974, On the Conservation of Hyperbolic Invariant Tori for Hamiltonian Systems. J. Diff. Eqs.,15:1–69.
Haller, G.: 1995, Diffusion at Intersecting Resonances in Hamiltonian Systems. Physics Letters A, 200:34–42.
Hamilton, D. P. and Burns, J. A.: 1992, Orbital Stability Zones about Asteroids. II. The Destabilizing Effects of Eccentric Orbits and of Solar Radiation, Icarus, 96:43–64.
Holmes, P. J. and Marsden, J. E.: 1982, Melnikov's Method and Arnold Diffusion for Perturbations of Integrable Hamiltonian Systems, J. Math. Phys., 23(4):669–675.
Lichtenberg, A. J. & Lieberman, M. A.: 1982, Regular and Stochastic Motion. Springer-Verlag, New York.
Lochak, P.: 1996, Arnold Diffusion: a Compendium of Remarks and Questions. In Hamiltonian Systems with Three or More Degrees of Freedom, Dordrecht, Holland. NATO Adv. Sci. Inst. C Math. Phys. Sci., Kluwer.
Mignard, F.: 1982, Radiation Pressure and Dust Particle Dynamics, Icarus, 49:347–366.
Mignard, F.: 1984, Effects of Radiation Forces on Dust Particles in Planetary Rings. In R. Greenberg and A. Brahic, editors, Planetary Rings, pages 333–366. The University of Arizona Press, Tucson, Arizona.
Moser, J.: 1973, Stable and Random Motions in Dynamical Systems. Princeton University Press.
NSSDC.: 1996, Asteroids and Comets. http//nssdc.gsfc.nasa.gov/planetary/planets/asteroidpage. html.
Robinson, C.: 1988, Horseshoes for Autonomous Hamiltonian Systems using the Melnikov Integral. Ergod. Th. & Dynam. Sys, 8:395–409.
Shu, F. H.: 1984, Waves in Planetary Rings. In R. Greenberg and A. Brahic, editors, Planetary Rings, pages 513–561. The University of Arizona Press, Tucson, Arizona.
Stiefel, E. and Scheifele, G.:, Linear and Regular Celestial Mechanics. Springer-Verlag, Berlin-Heidelberg.
Treshev, D. V.: 1994, Hyperbolic Tori and Asymptotic Surfaces in Hamiltonian Systems. Russian J. Math. Phys., 2(1):93–110.
Wiggins, S.: 1988, Global Bifurcations and Chaos. Analytical Methods. Springer-Verlag, New York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
DANKOWICZ, H. ESCAPE OF PARTICLES ORBITING ASTEROIDS IN THE PRESENCE OF RADIATION PRESSURE THROUGH SEPARATRIX SPLITTING. Celestial Mechanics and Dynamical Astronomy 67, 63–85 (1997). https://doi.org/10.1023/A:1008201916186
Issue Date:
DOI: https://doi.org/10.1023/A:1008201916186