A Semi-relativistic Approach To The Circular Restricted Three-body Problem And A Numerical Experiment Around The 3:2 Resonance

A Hamiltonian that approaches the study of the three-body problem in general relativity is obtained. We use it to study the relativistic version of the circular restricted three-body problem in which the first body is the heaviest and the third body is a test particle. We focus on the orbits around the 3:2 resonance. We show that, in spite of the notable difference between the relativistic and Newtonian orbits, most of the resonant region is preserved. Nevertheless, differently from the Newtonian case, the frequencies between the second and the third body are no longer commensurable. © 2006 IOP Publishing Ltd.233673682Danby, J.M.A., (1988) Fundamentals of Celestial MechanicsMurray, C.D., Dermott, S.F., (1999) Solar System DynamicsMorbidelli, A., (2002) Modern Celestial Mechanics: Dynamics in the Solar SystemHenon, M., (1966) Int. Astron. Union Symp., 25, p. 157Lemaitre, A., Henrard, J., (1989) Celest. Mech., 43 (1-4), p. 91Wisdom, J., (1982) Astron. J., 87 (3), p. 577Hannay, J., (1985) J. Phys. A: Math. Gen., 18 (2), p. 221Spallicci, A., Morbidelli, A., Metris, G., (2005) Nonlinearity, 18 (1), p. 45Chenciner, A., Montgomery, R., (2000) Ann. Math., 152, p. 881De Sitter, W., (1916) Mon. Not. R. Astron. Soc., 77, p. 155De Sitter, W., (1917) Mon. Not. R. Astron. Soc., 77, p. 481Shapiro, I.I., Reasenberg, R.D., Chandler, J.F., Babcock, R.W., (1988) Phys. Rev. Lett., 61 (23), p. 2643Krefetz, E., (1967) Astron. J., 72, p. 471Rosswog, S., Trautmann, D., (1996) Planet. Space Sci., 44 (4), p. 313Brumberg, V.A., (2003) Celest. Mech., 85 (3), p. 269Wardell, Z.E., (2003) Mon. Not. R. Astron. Soc., 341 (2), p. 423Guéron, E., Letelier, P.S., (2004) Gen. Rel. Grav., 36 (9), pp. 2107-2122Campanelli, M., Dettwyler, M., Hannam, M., Lousto, C.O., (2005)Ghez, A.M., Morris, M., Becklin, M.E.E., Tanner, A., Kremenek, T., (2000) Nature, 407 (6802), p. 349Wisdom, J., Holman, M., (1991) Astron. J., 102 (4), p. 1528Laskar, J., Robutel, P., (2001) Celest. Mech. Dyn. Astron., 80 (1), p. 39Wald, R.M., (1984) General RelativityBertschinger, E., (2002) Hamiltonian Dynamics of Particle MotionKramer, D., Neugebauer, G., (1980) Phys. Lett., 75 (4), p. 259Gueron, E., Letelier, P.S., Weyl solutions: Solitons, strings and struts (1994) Proc. Silarg VIII, 75, pp. 259-261Cooperstock, F.I., Booth, D.J., (1969) Phys. Rev., 187 (5), p. 1796Hulse, R.A., Taylor, J.H., (1975) Astrophys. J., 195, p. 51Barack, L., Burko, L.M., (2000) Phys. Rev., 62 (8), p. 084040Barack, L., Lousto, C.O., (2002) Phys. Rev., 66 (6), p. 061502Quinn, T.C., Wald, R.M., (1997) Phys. Rev., 56 (6), p. 3381Mino, Y., Sasaki, M., Tanaka, T., (1997) Phys. Rev., 55 (6), p. 3457Spallicci, A., Aoudia, S., (2004) Class. Quantum Grav., 21 (5), p. 563Quevedo, H., (1989) Phys. Rev., 39 (10), pp. 2904-2911Boisseau, B., Letelier, P.S., (2002) Gen. Rel. Grav., 34 (7), pp. 1077-1096Abramowicz, M.A., Bulik, T., Bursa, M., Kluźniak, W., (2003) Astron. Astrophys., 404 (1), pp. 21-L24Lecar, M., Aarseth, S.J., (1986) Astrophys. J., 305 (1), p. 564Ioka, K., Chiba, T., Tanaka, T., Nakamura, T., (1998) Phys. Rev., 58 (6), p. 063003Burnell, F., Malecki, J.J., Mann, R.B., Oht, T., (2004) Phys. Rev., 69, p. 01621