Abstract
A small, but by no means negligible, fraction of the small bodies of the Solar System is on planet-crossing orbits, including Earth-crossing ones. The dynamics of planet-crossing asteroids/comets is strongly controlled by the occurrence of close approaches. The node crossing cycle, resulting from the secular evolution of the orbital elements, especially the argument of perihelion, is apparent in the evolution of all the elements, including the semimajor axis. The most common type of orbits defines the Geographos class, in which close approaches occur at random whenever they are made possible by the distance of the orbits. Other orbits are protected from close approaches either by mean motion resonances (Toro class) or by secular perturbations (Kozai class). The Alinda class is defined by the presence of a mean motion resonance with Jupiter, which can change over a comparatively short time the eccentricity and therefore the crossing behavior. In all cases the orbits are chaotic, and in the long run transitions between the different orbit types can occur. This paper summarizes the experimental evidence, resulting from numerical integrations, and the semianalytical theories (based upon the adiabatic invariant and upon the Kozai approximation) which can explain in a satisfactory way most of the dynamical behaviors found in the experiments.
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References
Arnold, V.: 1976, Les méthodes mathématiques da la mécanique classique, Editions MIR, Moscou.
Bailey, M.E., Chambers, J.E., Hahn, G: 1992, ‘Origin of sungrazers: a frequent cometary end state’, Astron. Astropys. 257, 315–322.
Bottke, W. F. Jr., Nolan, M.C., Greenberg, R., Kolvoord, R. A.: 1994, ‘Collisional lifetimes and impact statistics of near-Earth asteroids’, in Hazards due to comets and asteroids, T. Gehrels ed., Univ. of Arizona press, 337–358
Farinella, P., Froeschlé, Ch., Froeschlé, C., Gonczi, R., Hahn, G., Morbidelli, A., Valsecchi, G.B.: 1994, ‘Asteroids falling into the Sun’, Nature 371, 314–317
Froeschlé, Ch., Hahn, G., Gonczi, R., Morbidelli, A., Farinella, P.: 1995, ‘Secular resonances and the dynamics of Mars-crossing and near-Earth asteroids’, Icarus 117, 45–61
Greenberg, R.: 1982, ‘Orbital interactions: a new geometrical formalism’, Astr. J 87, 184–195
Gronchi, G.F., Milani, A.: 1998, ‘Averaging on Earth-crossing orbits’, submitted. 8. Henrard J.:1993, ‘The adiabatic invariant in classical mechanics’, Dynamics Reported 2
Janiczek, P. M., Seidelmann, P. K. and Duncombe, R. L.: 1972, ‘Resonances and encounters in the inner Solar System’, Astron. J. Vol. 77, pp. 764–773
Kessler, D.J., Cour-Palais, B.G.: 1978, ‘Collision frequency of artificial satellites: the creation of a debris belt’ J. Geophys. Res 83, 2637–2646
Kessler, D.J.: 1981, ‘Derivation of the collision probability between orbiting objects: The lifetimes of Jupiter’s outer moons’, Icarus 48, 39–48
Kozai, Y.: 1962, ‘Secular perturbation of asteroids with high inclination and eccentricity.’, Astron.J. 67, 591–598
Michel, P., Thomas, F. C.: 1996, ‘The Kozai resonance for near-Earth asteroids with semimajor axes smaller than 2 AU’, Astron. Astrophys. 307, 310–318
Michel, P., Froeschlé, Ch.: 1997, ‘The location of linear secular resonances for semimajor axes smaller than 2 AU’, Icarus 128, 230–240
Michel, P., Froeschlé, C., Farinella, P.: 1996, ‘Dynamical evolution of two nearEarth asteroids to be explored by spacecraft: (433) Eros and (4660) Nereus’, Astron.Astrophys. 313, 993–1007
Michel, P., Farinella, P., Froeschlé, C.: 1996, ‘Dynamics of Eros’, submitted.
Milani, A.: 1993, ‘The Trojan asteroid belt: proper elements, stability, chaos and families’, Celestial.Mechanics 57 59–94
Milani, A. : 1994, ‘Proper elements and stable chaos’, in From Newton to chaos: modern techniques for understanding and coping with chaos in N-body dynamical systems, A. E. Roy & B.A. Steves eds., Plenum, New York, pp. 47–78.
Milani, A., Baccili, S.: 1998, ‘Dynamical classsification of Earth-crossing orbits: the dance of the Toro asteroids’, submitted.
Milani, A., Carpino, M., Hahn, G. and Nobili, A. M.: 1989, ‘Dynamics of Planetcrossing Asteroids: Classes of Orbital Behavior’, Icarus Vol. 78, pp. 212–269
Milani, A., Carpino, M. and Marzari, F.: 1990, ‘Statistics of Close Approaches between Asteroids and Planets:’, Icarus Vol. 88, pp. 292–335
Moons, M., Morbidelli, A. : 1995, ‘Secular resonances in mean motion commensurabilities; the 4/1, 3/1, 5/2 and 7/3 cases’, Icarus 114, 33–50
Morbidelli, A., Moons, M. ; 1993, ‘Secular resonances in mean motion commensurabilities; the 2/1 and 3/2 case’, Icarus 102, 316–332
Morbidelli, A.; 1993, ‘Asteroid secular resonant proper elements’, Icarus 105, 48–66
Opik, E. J.: 1951, ‘Collision probabilities with the planets and the distribution of interplanetary matter’, Proc. R. Ir. Acad. 54A, 165–199
Steel, D.I., Baggaley, W.J.: 1985, ‘Collisions in the solar system-I. Impacts of Apollo-Amor-Aten asteroids upon the terrestrial planets’ Mon. Not. R. Astr. Soc. 212, 817–836
Tancredi, G.: 1998f, ‘Chaotic dynamics of planet-encountering bodies’, Celestial Mechanics, in press.
Valsecchi, G.B., Morbidelli, A., Gonczi, R., Farinella, P., Froeschlé, Ch., Froeschlé, C.: 1995, ‘The dynamics of objects in orbits resembling that of P/Encke’, Icarus 118, 169–180
Wetherill, G.W. : 1967, ‘Collisions in the asteroid belt’, J. Geophys. Res. 72, 2429–2444.
Whipple, A.: 1995, ‘Lyapounov times of the Inner Asteroids’, Icarus 115, 347–353
Williams, J.G., Faulkner, J.: 1981, ‘The position of secular resonance surfaces’, Icarus 46, 390–399.
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Milani, A. (1999). Dynamics of Planet-Crossing Asteroids. In: Steves, B.A., Roy, A.E. (eds) The Dynamics of Small Bodies in the Solar System. NATO ASI Series, vol 522. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9221-5_13
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DOI: https://doi.org/10.1007/978-94-015-9221-5_13
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