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Analyzing the structure of periodic orbit families that exist around asteroid (101955) Bennu. (English) Zbl 1535.70041

(101955) Bennu is a small, near-Earth asteroid that passes close to Earth about every six years. It was the target of NASA’s OSIRIS-REx mission to collect an asteroid sample and bring it to Earth.
This work focuses on periodic orbits in the vicinity of the asteroid (101955) Bennu. These orbits were computed and analyzed using a constant-density polyhedron model based on measurements from the OSIRIS-REx mission. Moreover the planar retrograde and direct families, orbit families emanating from equilibria, and families emanating from bifurcation points in other families were identified and analyzed. The authors claim that portions of the orbit families presented in this work were first identified by the second author et al. in [The dynamics about asteroid (101955) Bennu. Techn. Rep. AIAA 2022–2468, AIAA SCITECH 2022 Forum (2022; doi:10.2514/6.2022-2468)], but they were incomplete. Additionally, with respect to the aforementioned paper, here the authors consider slight modifications to the Bennu shape model.
One of the new features of this work is the use of the estimates of Bennu’s characteristics and shape based on measurements from the OISRIS-REx mission. The specific shape model used by the authors is the image-based stereophotoclinometry (SPC) v42 model (see [O. S. Barnouin et al., Nat. Geosci. 12, No. 4, 247–252 (2019; doi:10.1038/s41561-019-0330-x)]), which can be found in the JHUAPL Small Body Mapping Tool (SBMT).
Overall, there were many similarities to the structures identified using this model and the structures identified using simplified models like the homogeneous rotating gravitating tri-axial ellipsoid. While the asteroid does not have any perfect symmetry, a number of the orbit structures identified were nearly symmetric. Furthermore, many of the structures identified in this analysis were very similar to each other, and one expects a number of these structures evolve in similar ways. Ten distinct families were identified in this set, and many of the orbit structures were similar (e.g., the vertical families emanating from the equilibria behaved in similar ways), and several of these structures were connected to each other. By using numerical continuation, the authors identified 12 distinct families emanating from bifurcation points in the initial families. These 12 families could be classified into four types. Even though the model of Bennu had no exact symmetry, many nearly symmetric structures were identified. There were also many similarities to structures identified using simplified models like the homogeneous rotating gravitating triaxial ellipsoid.

MSC:

70F15 Celestial mechanics
70K42 Equilibria and periodic trajectories for nonlinear problems in mechanics
70K50 Bifurcations and instability for nonlinear problems in mechanics
70-08 Computational methods for problems pertaining to mechanics of particles and systems
Full Text: DOI

References:

[1] Barnouin, O.; Daly, M.; Palmer, E., Shape of (101955) Bennu indicative of a rubble pile with internal stiffness, Nat. Geosci., 12, 4, 247-252 (2019) · doi:10.1038/s41561-019-0330-x
[2] Benner, L.A.M., Busch, M.W., Giorgini, J.D., et al: Radar observations of near-earth and main-belt asteroids. In: Michel, P., DeMeo, F.E., Bottke, W.F. (eds) Asteroids IV. University of Arizona Press, pp. 165-182 (2015)
[3] Broucke, RA, Stability of periodic orbits in the elliptic. Restricted three-body problem, AIAA J., 7, 6, 1003-1009 (1969) · Zbl 0179.53301 · doi:10.2514/3.5267
[4] Brown, G.M., Scheeres, D.J.: A global method to compute asteroid equilibrium points for any spin rate. In: 33rd AAS/AIAA Space Flight Mechanics Meeting (2023a)
[5] Brown, G.M., Scheeres, D.J.: Studying the temporal evolution of the dynamical environment around asteroid (101955) Bennu. Icarus (2023b)
[6] Bury, L.: Low-Energy Secondary-Body Landing Trajectories in the Three-Body Problem. PhD thesis, University of Colorado Boulder (2021)
[7] Campbell, E.T.: Bifurcations from families of periodic solutions in the circular restricted problem with application to trajectory design. PhD thesis, Purdue University (1999)
[8] Chappaz, L.P.: The dynamical environment in the vicinity of small irregularly-shaped bodies with application to asteroids. Master’s thesis, Purdue University (2011)
[9] Doedel, E.J., Romanov, V.A., Paffenroth, R.C., et al.: Elemental periodic orbits associated with the libration points in the circular restricted 3-body problem. Int. J. Bifurc. Chaos 17(8) (2007) · Zbl 1139.70006
[10] Hénon, M., Generating Families in the Restricted Three-Body Problem (1997), Berlin: Springer, Berlin · Zbl 0882.70001
[11] Hergenrother, C., Maleszewski, C., Nolan, M., et al.: The operational environment and rotational acceleration of asteroid (101955) Bennu from OSIRIS-REx observations. Nat. Commun. 10(1291) (2019)
[12] Hou, X.; Xin, X.; Feng, J., Genealogy and stability of periodic orbit families around uniformly rotating asteroids, Commun. Nonlinear Sci. Numer. Simul., 56, 93-114 (2018) · Zbl 1510.70071 · doi:10.1016/j.cnsns.2017.07.004
[13] Howard, J.E., MacKay, R.S.: Linear stability of symplectic maps. J. Math. Phys. 28(5) (1987) · Zbl 0628.58012
[14] Hu, WD; Scheeres, DJ, Periodic orbits in rotating second degree and order gravity fields, Chin. J. Astron. Astrophys., 8, 1, 108-118 (2008) · doi:10.1088/1009-9271/8/1/12
[15] Jiang, Y., Baoyin, H.: Periodic orbit families in the gravitational field of irregular-shaped bodies. Astrono. J. 152(5) (2016)
[16] Jiang, Y.; Baoyin, H., Annihilation of relative equilibria in the gravitational field of irregular-shaped minor celestial bodies, Planet. Space Sci., 161, 15, 107-136 (2018) · doi:10.1016/j.pss.2018.06.017
[17] Jiang, Y.; Baoyin, H., Periodic orbits related to the equilibrium points in the potential of Irregular-shaped minor celestial bodies, Results Phys., 12, 368-374 (2019) · doi:10.1016/j.rinp.2018.11.049
[18] Jiang, Y.; Li, H., Equilibria and orbits in the dynamical environment of asteroid 22 Kalliope, Open Astronomy, 28, 1, 154-164 (2019) · doi:10.1515/astro-2019-0014
[19] Jiang, Y.; Baoyin, H.; Li, J., Orbits and manifolds near the equilibrium points around a rotating asteroid, Astrophys. Space Sci., 349, 1, 83-106 (2014) · doi:10.1007/s10509-013-1618-8
[20] Jiang, Y., Baoyin, H., Li, H.: Periodic motion near the surface of asteroids. Astrophys. Space Sci. 360(2) (2015a)
[21] Jiang, Y.; Yu, Y.; Baoyin, H., Topological classifications and bifurcations of periodic orbits in the potential field of highly irregular-shaped celestial bodies, Nonlinear Dyn., 81, 1-2, 119-140 (2015) · Zbl 1347.37096 · doi:10.1007/s11071-015-1977-5
[22] Kang, H., Jiang, Y., Li, H.: Convergence of a periodic orbit family close to asteroids during a continuation. Results Phys. 19 (2020)
[23] Karydis, D.; Voyatzis, G.; Tsiganis, K., A continuation approach for computing periodic orbits around irregular-shaped asteroids. An application to 433 Eros, Adv. Space Res., 68, 11, 4418-4433 (2021) · doi:10.1016/j.asr.2021.08.036
[24] Lan, L., Yang, H., Baoyin, H., et al.: Retrograde near-circular periodic orbits near equatorial planes of small irregular bodies. Astrophys. Space Sci. 362(9) (2017)
[25] Lara, M.; Scheeres, DJ, Stability bounds for three-dimensional motion close to asteroids, J. Astronaut. Sci., 50, 4, 389-409 (2002) · doi:10.1007/BF03546245
[26] Lauretta, D.; DellaGiustina, D.; Bennett, C., The unexpected surface of asteroid (101955) Bennu, Nature, 568, 55-60 (2019) · doi:10.1038/s41586-019-1033-6
[27] Li, X., Gao, A., Qiao, D.: Periodic orbits, manifolds and heteroclinic connections in the gravity field of a rotating homogeneous dumbbell-shaped body. Astrophys. Space Sci. 362(4) (2017)
[28] Liu, Y., Jiang, Y., Li, H.: Bifurcations of periodic orbits in the gravitational field of irregular bodies: applications to bennu and steins. Aerospace 9(3) (2022)
[29] Llanos, P., Miller, J., Hintz, G.: Orbital evolution and environmental analyses around asteroid 2008 EV5. In: Spaceflight mechanics meeting 2014 (2014)
[30] MacMillan, WD, Theory of the Potential (1958), New York: Dover Publications Inc, New York · Zbl 0088.15803
[31] McMahon, J.; Scheeres, D.; Chesley, S., Dynamical evolution of simulated particles ejected from asteroid Bennu, J. Geophys. Res. Planets, 158, 8, 1-18 (2020)
[32] Ni, Y., Baoyin, H., Junfeng, L.: Orbit dynamics in the vicinity of asteroids with solar Perturbation. In: 65th International Astronautical Congress, pp. 4610-4620 (2014)
[33] Ni, Y., Jiang, Y., Baoyin, H.: Multiple bifurcations in the periodic orbit around Eros. Astrophys. Space Sci. 361(5) (2016)
[34] Pedros-Faura, A., McMahon, J.W.: Effects of primary shadowing on asteroid ejecta captured into periodic orbits. In: 73rd International Astronautical Congress (2022)
[35] Romanov, V.A., Doedel, E.J.: Periodic orbits associated with the libration points of the homogeneous rotating gravitating triaxial ellipsoid. Int. J. Bifurc. Chaos 22(10) (2012) · Zbl 1258.70025
[36] Romanov, V.A., Doedel, E.J.: Periodic orbits associated with the libration points of the massive rotating straight segment. Int. J. Bifurc. Chaos 24(4) (2014) · Zbl 1296.70018
[37] Scheeres, DJ, Orbital Motion in Strongly Perturbed Environments (2012), Berlin: Springer, Berlin · doi:10.1007/978-3-642-03256-1
[38] Scheeres, DJ; Ostro, SJ; Hudson, RS, Orbits close to asteroid 4769 castalia, Icarus, 121, 1, 67-87 (1996) · doi:10.1006/icar.1996.0072
[39] Scheeres, DJ; Williams, BG; Miller, JK, Evaluation of the dynamic environment of an asteroid: applications to 433 eros, J. Guid. Control. Dyn., 23, 3, 466-475 (2000) · doi:10.2514/2.4552
[40] Scheeres, D.J., Britt, D., Carry, B., et al.: Asteroid interiors and morphology. In: Michel, P., DeMeo, F.E., Bottke, W.F. (eds) Asteroids IV. University of Arizona Press, pp. 777-798 (2015)
[41] Scheeres, DJ; Hesar, SG; Tardivel, S., The geophysical environment of Bennu, Icarus, 276, 116-140 (2016) · doi:10.1016/j.icarus.2016.04.013
[42] Scheeres, D.J., French, A.S., Tricarico, P., et al.: Heterogeneous mass distribution of the rubble-pile asteroid (101955) Bennu. Sci. Adv. 6(41):eabc3350 (2020)
[43] Scheeres, D.J., Brown, G.M., Takahashi, S., et al.: The Dynamics about Asteroid (101955) Bennu. In: AIAA SCITECH 2022 Forum (2022)
[44] Seydel, R., Practical Bifurcation and Stability Analysis (2010), Berlin: Springer, Berlin · Zbl 1195.34004 · doi:10.1007/978-1-4419-1740-9
[45] Tardivel, S.C.V.: The Deployment of Scientific Packages to Asteroid Surfaces. PhD thesis, University of Colorado Boulder (2014)
[46] Werner, RA; Scheeres, DJ, Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia, Celest. Mech. Dyn. Astron., 65, 3, 313-344 (1996) · Zbl 0881.70008
[47] Yu, Y.; Baoyin, H., Generating families of 3D periodic orbits about asteroids, Mon. Not. R. Astron. Soc., 427, 1, 872-881 (2012) · doi:10.1111/j.1365-2966.2012.21963.x
[48] Yu, Y., Baoyin, H.: Orbital dynamics in the vicinity of asteroid 216 Kleopatra. Astrono. J. 143(3) (2012b)
[49] Yu, Y.; Baoyin, H.; Jiang, Y., Constructing the natural families of periodic orbits near irregular bodies, Mon. Not. R. Astron. Soc., 453, 3, 3269-3277 (2015) · doi:10.1093/mnras/stv1784
[50] Zimovan-Spreen, E.M., Howell, K.C., Davis, D.C.: Near rectilinear halo orbits and nearby higher-period dynamical structures: orbital stability and resonance properties. Celestial Mech. Dyn. Astron. 132(5) (2020) · Zbl 1448.70085
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