A database of planar axisymmetric periodic orbits for the solar system. (English) Zbl 1447.70029
Summary: A multiple grid search strategy is implemented to generate a broad database of axisymmetric three-body periodic orbits for planets and main planetary satellites in the Solar system. The periodic orbit search is performed over 24 pairs of bodies that are well approximated by the circular restricted three-body problem (CR3BP), resulting in approximately 3 million periodic solutions. The periodic orbit generation is implemented in a two-level grid search scheme. First, a global search is applied to each CR3BP system in order to capture the global structure of most existing families, followed by a local grid search, centered around a few fundamental families, where useful, highly sensitive periodic orbits emerge. A robust differential corrector is implemented with a full second-order trust region method in order to efficiently converge the highly sensitive solutions. The periodic orbit database includes solutions that (1) remain in the vicinity of the secondary only; (2) circulate the primary only via inner or outer resonances; and (3) connect both resonance types with orbits bound to the secondary, approximating heteroclinic connections that leads to natural escape/capture mechanisms. The periodic solutions are characterized and presented in detail using a descriptive nomenclature. Initial conditions, stability indices, and other dynamical parameters that allow for the solution characterization are computed and archived. The data and sample scripts are made available online.
Keywords:
periodic orbits; circular restricted three-body problem; dynamical system theory; stability; solar system dynamicsReferences:
| [1] | Anderson, RL; Campagnola, S; Lantoine, G, Broad search for unstable resonant orbits in the planar circular restricted three-body problem, Celest. Mech. Dyn. Astron., 124, 177-199, (2016) · doi:10.1007/s10569-015-9659-7 |
| [2] | Barrabés, B; Gómez, G, Spatial p-q resonant orbits of the RTBP, Celest. Mech. Dyn. Astron., 84, 387-407, (2002) · Zbl 1026.70013 · doi:10.1023/A:1021137127909 |
| [3] | Barrabés, B; Mondelo, J; Ollé, M, Numerical continuation of families of homoclinic connections of periodic orbits in the RTBP, Nonlinearity, 22, 2901-2918, (2009) · Zbl 1290.70015 · doi:10.1088/0951-7715/22/12/006 |
| [4] | Barrabés, B; Mondelo, J; Ollé, M, Numerical continuation of families of heteroclinic connections between periodic orbits in a Hamiltonian system, Nonlinearity, 26, 274-2765, (2013) · Zbl 1274.70014 · doi:10.1088/0951-7715/26/10/2747 |
| [5] | Belbruno, E; Topputo, F; Gidea, M, Resonance transitions associated to weak capture in the restricted three-body problem in the restricted three-body problem, Adv. Space Res., 42, 1330-1351, (2008) · doi:10.1016/j.asr.2008.01.018 |
| [6] | Bradley, N; Russell, RP, A continuation method for converting trajectories from patched conics to full gravity models, J. Astronaut. Sci., 61, 227-254, (2014) · doi:10.1007/s40295-014-0017-x |
| [7] | Broucke, R.A.: Periodic orbits in the restricted three-body with Earth-Moon masses. Technical report 32-1168, JPL, Caltech (1968) |
| [8] | Broucke, RA, Stability of periodic orbits in the elliptic, restricted three-body problem, AIAA J., 7, 1003-1009, (1969) · Zbl 0179.53301 · doi:10.2514/3.5267 |
| [9] | Campagnola, S; Skerritt, P; Russell, RP, Flybys in the planar, circular, restricted, three-body problem, Celest. Mech. Dyn. Astron., 113, 343-368, (2012) · Zbl 1266.70011 · doi:10.1007/s10569-012-9427-x |
| [10] | Canalias, E; Masdemont, J, Homoclinic and heteroclinic transfer trajectories between planar Lyapunov orbits in the Sun-Earth and Earth-Moon systems, DCDS, 14, 261-279, (2006) · Zbl 1105.34027 |
| [11] | Conn, A.R., Gould, N.I.M., Toint, P.L.: Trust-Region Methods, chap 7. SIAM, Philadelphia (2000) · Zbl 0958.65071 · doi:10.1137/1.9780898719857 |
| [12] | Dichmann, D.J., Doedel, E.J., Paffenroth, R.C.: The computation of periodic solutions of the 3-body problem using the continuation software AUTO. In: International Conference on Libration Points Orbits and Applications, Aiguablava, Spain (2002) |
| [13] | Eberle, J; Cuntz, M; Musielak, ZE, The instability transition for the restricted 3-body problem, Astron. Astrophys., 489, 1329-1335, (2008) · Zbl 1156.85301 · doi:10.1051/0004-6361:200809758 |
| [14] | Farquahar, RW; Kamel, AA, Quasi-periodic orbits about the translunar libration point, Celest. Mech., 7, 458-473, (1973) · Zbl 0258.70011 · doi:10.1007/BF01227511 |
| [15] | Folta, DC; Bosanac, N; Guzzetti, D; Howell, KC, An Earth-Moon system trajectory design reference catalog, Acta Astronaut., 110a, 341-353, (2015) · doi:10.1016/j.actaastro.2014.07.037 |
| [16] | Fuente, Marcos C; Fuente, Marcos R, Asteroid (469219) 2016 \({\text{HO}}_3\), the smallest and closest Earth quasi-satellite, MNRAS, 462, 3441-3456, (2016) · doi:10.1093/mnras/stw1972 |
| [17] | Goudas, CL, Three-dimensional periodic orbits and their stability, Icarus, 2, 1-18, (1963) · Zbl 0116.15302 · doi:10.1016/0019-1035(63)90003-4 |
| [18] | Guzzetti, D; Bosanac, N; Haapala, A; Howell, KC; Folta, DC, Rapid trajectory design in the Earth-Moon ephemeris system via an interactive catalog of periodic and quasi-periodic orbits, Acta Astronaut., 126, 439-455, (2016) · doi:10.1016/j.actaastro.2016.06.029 |
| [19] | Haapala, AF; Howell, KC, A framework for constructing transfers linking periodic libration point orbits in the spatial circular restricted three-body problem, Int. J. Bifurc. Chaos, 26, 1630013, (2016) · Zbl 1343.70015 · doi:10.1142/S0218127416300135 |
| [20] | Haapala, A.F., Vaquero, M., Pavlak, T.A., Howell, K.C., Folta, D.C.: Trajectory selection strategy for tours in the Earth-Moon system. In: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference, Hilton Head, SC (2013) |
| [21] | Hénon, M, Numerical exploration of the restricted problem. V. hill’s case: periodic orbits and their stability, Astron. Astrophys., 1, 223-238, (1969) · Zbl 0177.27703 |
| [22] | Hénon, M, Vertical stability of periodic orbits in the restricted problem I. equal masses, Astron. Astrophys., 28, 415-426, (1973) · Zbl 0272.70023 |
| [23] | Hénon, M, Vertical stability of periodic orbits in the restricted problem II. hill’s case, Astron. Astrophys., 30, 317-321, (1974) · Zbl 0359.70021 |
| [24] | Hénon, M.: Generating families in the restricted three-body problem. In: Lecture Notes in Physics, vol. 52. Springer, Berlin (1997) · Zbl 0882.70001 |
| [25] | Hénon, M, New families of periodic orbits in hill’s problem of three bodies, Celest. Mech. Dyn. Astron., 85, 223-246, (2003) · Zbl 1062.70018 · doi:10.1023/A:1022518422926 |
| [26] | Howell, KC, Three-dimensional, periodic, ‘halo’ orbits, Celest. Mech., 32, 53-71, (1984) · Zbl 0544.70013 · doi:10.1007/BF01358403 |
| [27] | Howell, KC; Marchand, B; Lo, MW, Temporary satellite capture of short-period Jupiter family comets from the perspective of dynamical systems, J. Astronaut. Sci., 49, 539-557, (2001) |
| [28] | Keller, H.B.: Numerical Solution of Bifurcation and Nonlinear Eigenvalue Problems. Springer, Berlin (1986) |
| [29] | Koon, WS; Lo, MW; Marsden, JE; Ross, SD, Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics, Chaos, 10, 427-469, (2000) · Zbl 0987.70010 · doi:10.1063/1.166509 |
| [30] | Koon, WS; Lo, MW; Marsden, JE; Ross, SD, Resonance and capture of Jupiter comets, Celest. Mech. Dyn. Astron., 81, 27-38, (2001) · Zbl 1013.70011 · doi:10.1023/A:1013398801813 |
| [31] | Kotoulas, TA; Voyatzis, G, Three dimensional periodic orbits in exterior mean motion resonances with neptune, Astron. Astrophys., 441, 807-814, (2005) · Zbl 1093.70007 · doi:10.1051/0004-6361:20052980 |
| [32] | Lam, T., Whiffen, G.J.: Exploration of distant retrograde orbits around Europa. In: 15th AAS/AIAA Space Flight Mechanics Conference, Copper Mountain, CO (2005) |
| [33] | Lara, M; Pelaez, J, On the numerical continuation of periodic orbits, an intrinsic, 3-dimensional, differential, predictor-corrector algorithm, Astron. Astrophys., 389, 692-701, (2002) · Zbl 1214.70002 · doi:10.1051/0004-6361:20020598 |
| [34] | Lara, M; Russell, RP, On the family g of the restricted three-body problem, Monogr. Real Acad. Cienc. Zaragoza, 30, 51-66, (2007) · Zbl 1316.70009 |
| [35] | Lara, M; Russell, RP; Villac, B, Classification of the distant stability regions at europa, JGCD, 30, 409-418, (2007) |
| [36] | Lo, M.W., Parker, J.S.: Unstable resonant orbits near Earth and their applications in planetary missions. In: AIAA/AAS Conference, vol. 14, Providence, RI (2004) |
| [37] | Lo, M; Williams, BG; Bollman, WE; Han, D; Hahn, Y; Bell, JL; etal., Genesis mission design, J. Astronaut. Sci., 49, 145-167, (2001) · doi:10.2514/6.1998-4468 |
| [38] | Michalodimitrakis, M, On the continuation of periodic orbits from the planar to the three-dimensional general three-body problem, Celest. Mech., 19, 263-277, (1979) · Zbl 0404.70004 · doi:10.1007/BF01230218 |
| [39] | Moons, M; Morbidelli, A, Secular resonances inside mean-motion commensurabilities: the 4/1, 3/1, 5/2 and 7/3 cases, Icarus, 114, 33-50, (1995) · doi:10.1006/icar.1995.1041 |
| [40] | Morais, MHM; Namouni, F, Asteroids in retrograde resonance with Jupiter and saturn, MNRAS, 436, l30-l34, (2013) · doi:10.1093/mnrasl/slt106 |
| [41] | Morbidelli, A, An overview on the Kuiper belt and on the origin of Jupiter-family comets, Celest. Mech. Dyn. Astron., 72, 129-156, (1999) · Zbl 0925.70136 · doi:10.1023/A:1008322915678 |
| [42] | Murray, C., Dermott, S.: Solar System Dynamics. Cambridge University Press, Cambridge (1999) · Zbl 0957.70002 |
| [43] | Ocampo, C.A., Rosborough, G.W.: Transfer trajectories for distant retrograde orbiters of the Earth. In: Proceedings of the 3rd Annual Spaceflight Mechanics Meeting, vol. 82, No. 2, pp. 1177-1200 (1993) |
| [44] | Papadakis, K; Zagouras, C, Bifurcation points and intersections of families of periodic orbits in the three-dimensional restricted three-body problem, Astrophys. Space Sci., 199, 241-256, (1993) · Zbl 0767.70008 · doi:10.1007/BF00613198 |
| [45] | Parker, JS; Davis, KE; Born, GH, Chaining periodic three-body orbits in the Earth-Moon system, Acta Astronaut., 67, 623-638, (2010) · doi:10.1016/j.actaastro.2010.04.003 |
| [46] | Pellegrini, E; Russell, RP, On the acuracy of state transition matrices, J. Guid. Control Dyn., 39, 2485-2499, (2016) · doi:10.2514/1.G001920 |
| [47] | Pellegrini, E., Russell, R.P.: A multiple-shooting differential dynamic programming algorithm. In: AAS/AIAA Space Flight Mechanics Meeting, Paper AAS 17-453, San Antonio (2017) |
| [48] | Poincare, H.: Les Méthodes Nouvelles de la Mécanique Céleste, vol. 2. Gauthier-Villars, Paris (1892) · JFM 24.1130.01 |
| [49] | Restrepo, R.L., Russell, R.P.: Patched periodic orbits: a systematic strategy for low-energy transfer design. In: AAS/AIAA Astrodynamics Specialist Conference, AAS 17-695, Stevenson, WA (2017) |
| [50] | Robin, IA; Markellos, VV, Numerical determination of three-dimensional periodic orbits generated from vertical self-resonant satellite orbits, Celest. Mech., 4, 395-434, (1980) · Zbl 0426.70012 · doi:10.1007/BF01231276 |
| [51] | Russell, RP, Global search for planar and three-dimensional periodic orbits near europa, J. Astronaut. Sci., 54, 199-226, (2006) · doi:10.1007/BF03256483 |
| [52] | Szebehely, V.: Theory of Orbits: The Restricted Problem of Three Bodies. Academic Press, New York (1967) · Zbl 1372.70004 |
| [53] | Szebehely, V; Nacozy, P, A class of e. strömgren’s direct orbits in the restricted problem, AJ, 72, 184-190, (1967) · doi:10.1086/110215 |
| [54] | Zagouras, CG, Three-dimensional periodic orbits about the triangular equilibrium points of the restricted problem of three bodies, Celest. Mech., 37, 27-46, (1985) · Zbl 0591.70010 · doi:10.1007/BF01230339 |
| [55] | Zagouras, CG; Markellos, VV, Axi-symmetric periodic orbits of the restricted problem in three dimensions, Astron. Astrophys., 59, 79-89, (1977) · Zbl 0364.70012 |
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