Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
  • Русский
  • Английский

Methods in simulating gravitational field of the small celestial bodies of complex shapes on the 67P/Churyumov—Gerasimenko comet example

Published: 27.11.2023

Authors: Zhojin Li, Klishin A.N., Koryanov V.V., Kolesnikova D.S.

Published in issue: #11(143)/2023

DOI: 10.18698/2308-6033-2023-11-2319

Category: Aviation and Rocket-Space Engineering | Chapter: Aircraft Dynamics, Ballistics, Motion Control

Determining the spacecraft motion parameters in vicinity to surface of a celestial body of the non-spherical shape is being actively studied, and it is a complex task due to a problem in describing the gravitational field of such a body. The paper analyzes various approaches to simulating gravitational field of bodies of the complex shape including the methods of spherical functions, minimum ambient sphere, minimum ambient ellipsoid and the polyhedral method. The models used were comparatively analyzed, and an approach was proposed based on introducing a neural network to optimize calculation by approximating the data obtained by the polyhedron method. Simulation results are presented to describe the gravitational field of the 67P/Churyumov — Gerasimenko short-period comet, they are illustrated with figures and tables. The paper proposes recommendations to using one or another method in simulating the classical two-body problem.

[1] Werner R., Scheeres D. Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of Asteroid 4769 Castalia. Celestial Mechanics and Dynamical Astronomy, 1996, vol. 65, pp. 313–344.
[2] Werner R. The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celestial Mechanics and Dynamical Astronomy, 1994, vol. 59, pp. 253–278.
[3] Subbotin M.F. Vvedenie v teoreticheskuyu astronomiyu [Introduction to theoretical astronomy]. Moscow, Nauka Publ., 1968, 800 p.
[4] Duboshin G.N. Spravochnoe rukovodstvo po nebesnoy mekhanike i astrodinamike [Reference guide in celestial mechanics and astrodynamics]. Moscow, Nauka Publ., 1976, 234 p.
[5] Elyasberg P. E. Vvedenie v teoriyu poleta iskusstvennykh sputnikov Zemli [Introduction to the theory of flight of the artificial Earth satellites]. Moscow, Editorial URSS Publ., 2020, 542 p.
[6] Chebotarev G. A. Analiticheskie i chislennye metody nebesnoy mekhaniki [Analytical and numerical methods of celestial mechanics]. Moscow, Nauka Publ., 1965, 367 p.
[7] Emelyanov N.V. Prakticheskaya nebesnaya mekhanika [Practical celestial mechanics]. Moscow, Fizicheskiy Fakultet MGU Publ., 2018, 270 p.
[8] Rossi A., Marzari F., Farinella, P. Orbital evolution around irregular bodies. Earth, Planets and Space, 1999, vol. 51, pp. 1173–1180.
[9] Geissler P., Petit J., Durda D., Greenberg R., Bottke W., Nolan M., Moore J. Erosion and ejecta recreation on 243 ida and its moon. Icarus, 1996, vol. 120, no. 0042, pp. 140–157.
[10] Zhao Y., Yang H., Li S. On-board modeling of gravity fields of elongated asteroids using Hopfield neural networks. Astrodynamics, 2023, vol. 7, no. 1, pp. 101–114.
[11] Zhang A., Lipton Z., Mu Li, Smola J. Dive into Deep Learning. Amazon Science, 2023, 1181 p.
[12] Chao B.F., Rubincam D.P. The gravitational field of Phobos. Geophysical Research Letters, 1989, vol. 16, no. 8, pp. 859–862.
[13] Scheeres D.J. Dynamics about uniformly rotating triaxial ellipsoids: Applications to Asteroids. Icarus, 1994, vol. 110, no. 2, pp. 225–238.
[14] Shang H., Wei B., Lu J. Recent advances in modeling gravity field of small bodies. Journal of Deep Space Exploration, 2022, vol. 9, no. 4, pp. 359–372.
[15] Rausenberge, O. Lehrbuch der Analytischen Mechanik. Leipzig, Β.G. Teubner, 1888.
[16] Romain G., Jean-Pierre B. Ellipsoidal harmonic expansions of the gravitational potential: Theory and application. Celestial Mechanics and Dynamical Astronomy, 2001, vol. 79, no. 4, pp. 235–275.
[17] Shi J., Ma Y., Liang H. Research of activity of main belt comets 176P/LINEAR, 238P/Read and 288P/(300163) 2006 VW139. Sci Rep, 2019, vol. 9, no. 5492.
[18] Turgut B. Application of back propagation artificial neural networks for gravity field modelling. Acta Montanistica Slovaca, 2016, vol. 21, no. 3, pp. 200–207.
[19] Yang H., Bai X., Baoyin H. Rapid generation of time-optimal trajectories for asteroid landing via convex optimization. Journal of Guidance, Control, and Dynamics, 2017, vol. 40, pp. 628–641.
[20] Hobson E.W. The Theory of Spherical and Ellipsoidal Harmonics. Chelsea Publishing Company, 1965, 514 p.
[21] Cui H., Zhang Z., Yu M. Computing and analysis of gravity field of Eros433 using polyhedron model. Journal of Harbin Institute of Technology, 2012, vol. 44, pp. 17–22.
[22] Jiang Yu, Baoyin H. Orbital Mechanics near a Rotating Asteroid. Journal of Astrophysics and Astronomy, 2014, vol. 35, pp. 17–38.