Dynamic Problems of the Planets and Asteroids, and Their Discussion
Affiliation(s)
Institute of the Earth’s Cryosphere, Siberian Branch of Russian Academy of Sciences, Tyumen, Russia. Institute of Thermophysics of Russian Academy of Sciences, Siberian Branch, Novosibirsk, Russia.
Institute of the Earth’s Cryosphere, Siberian Branch of Russian Academy of Sciences, Tyumen, Russia. Institute of Thermophysics of Russian Academy of Sciences, Siberian Branch, Novosibirsk, Russia.
ABSTRACT
The problems of dynamics of celestial bodies are considered which in the literature are explained by instability and randomness of movements. The dynamics of planets orbits on an interval 100 million years was investigated by new numerical method and its stability is established. The same method is used for computing movements of two asteroids Apophis and 1950DA. The evolution of their movement on an interval of 1000 is investigated. The moments of their closest passages at the Earth are defined. The different ways of transformation of asteroids trajectories into orbits of the Earth’s satellites are considered. The problems of interest are discussed from the different points of view.
The problems of dynamics of celestial bodies are considered which in the literature are explained by instability and randomness of movements. The dynamics of planets orbits on an interval 100 million years was investigated by new numerical method and its stability is established. The same method is used for computing movements of two asteroids Apophis and 1950DA. The evolution of their movement on an interval of 1000 is investigated. The moments of their closest passages at the Earth are defined. The different ways of transformation of asteroids trajectories into orbits of the Earth’s satellites are considered. The problems of interest are discussed from the different points of view.
Cite this paper
J. Smulsky and Y. Smulsky, "Dynamic Problems of the Planets and Asteroids, and Their Discussion," International Journal of Astronomy and Astrophysics, Vol. 2 No. 3, 2012, pp. 129-155. doi: 10.4236/ijaa.2012.23018.
J. Smulsky and Y. Smulsky, "Dynamic Problems of the Planets and Asteroids, and Their Discussion," International Journal of Astronomy and Astrophysics, Vol. 2 No. 3, 2012, pp. 129-155. doi: 10.4236/ijaa.2012.23018.
References
[1] J. Laskar, “Large-scale chaos in the solar system,” Astron. and Astrophys, 1994, L9 – L12. [2] J. Laskar, P. Robutel, F. Joutel, M. Gastineau A. C. M. Correia, and B. Levrard, “A Long-term numeriucal solu-tion for the insolation quantities of the Earth,” Astron. Astrophys., Vol. 428, No.1, 2004, pp. 261–285. doi:10.1051/0004-6361:20041335. [3] J. Laskar, A. C. M. Correia, M. Gastineau, F. Joutel, B. Levrard and P. Robutel, “Long term evolution and chaotic diffusion of the insolation quantities of Mars,” Astron. and Astrophys, 2004, Vol. 428. pp. 261-285. doi:10.1051/0004-6361:20041335. [4] J.D. Giorgini, L.A.M. Benner, S.I. Ostro, H.C. Nolan and M.W. Busch, “Predicting the Earth encounters of (99942) Apophis,” Icarus, Vol. 193, 2008, pp. 1-19. doi:10.1016/j.icarus.2007.09.012. [5] R. Tucker, D. Tholen and F. Bernardi, MPS 109613, 2004. [6] G.J. Garradd, MPE Circ., 2004, Y25. [7] L.V. Rykhlova, B.M. Shustov, V.G. Pol and K.G. Suk-hanov,” Nasuschnye problemy asteroidnoj opasnosti (Urgent problems in protecting the Earth against astero-ids)”, Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 25-33. [8] V.A. Emel’yanov, Yu.K. Merkushev and S.I. Barabanov, “Periodichnost' seansov nabljudenija asteroida Apofis kosmicheskimi i nazemnymi teleskopami (Cyclicity of Apophis observation sessions with space and ground-based telescopes),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 38 -43. [9] V.A. Emel’yanov, V.I. Luk’yashchenko, Yu.K. Merku-shev and G.R. Uspenskii “Tochnost' opredelenie parame-trov orbity asteroida Apofis, obespechivaemaja kosmi-cheskimi teleskopami (Determination accuracy of asteroid Apophis’ orbit parameters ensured by space telescopes),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 59-64. [10] L.L. Sokolov, A.A. Bashakov, N.P. Pit’ev, “O vozmozh-nyh sblizhenijah ACZ 99942 Apofis s Zemlej (On possible encounters of asteroid 99942 Apophis with the Earth),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 33 – 38. [11] E. Everhart, “Implicit single-sequence methods for inte-grating orbits,” Celest. Mech. Vol. 10, 1974, pp. 35-55. [12] L.E. Bykova and T.Yu. Galushina, “Jevoljucija verojatnoj oblasti dvizhenija asteroida 99942 Apofis (Evolution of the probable travel path of asteroid 99942 Apophis),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 48 – 54. [13] L.E. Bykova and T.Yu. Galushina, “Opasnye dlja Zemli traektorii v oblasti vozmozhnyh dvizhenij asteroida 99942 Apophis (Trajectories in the region of possible travel paths of asteroid 99942 Apophis. Fundamental and Applied Problems in Modern Mechanics. Proceedings of the VI All-Russia Scientific Conference September 30 – October 2, 2008, Tomsk, 2008, pp. 419-420. [14] E.A. Smirnov, “Sovremennye chislennye metody integri-rovanija uravnenij dvizhenija asteroidov, sblizhajuschihsja s Zemlej (Advanced numerical methods for integrating motion equations of asteroids approaching the Earth),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 54-59. [15] V.V. Ivashkin, K.A. Stikhno, “Analiz problemy korrekcii orbity asteroida Apofis (An analysis of the problem on correcting asteroid Apophis’ orbit),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 44 – 48. [16] J. J. Smulsky, “The Theory of Interaction,” Publishing house of Novosibirsk University, Novosibirsk, 1999. (In Russian: http://www.ikz.ru/~smulski/TVfulA5_2.pdf). [17] J. J. Smulsky, “The Theory of Interaction,” Publishing house "Cultural Information Bank", Ekaterinburg, Russia 2004 (In English: http://www.ikz.ru/~smulski/TVEnA5_2.pdf). [18] E.A. Grebenikov and J.J.Smulsky, “Evoljucija orbity Marsa na intervale vremeni v sto millionov let (Numerical investigation of the Mars orbit evolution in the time interval of hundred million),” A.A. Dorodnitsyn Computing Center of RAS, Moscow, 2007. (In Russian, http://www.ikz.ru/~smulski/Papers/EvMa100m4t2.pdf). [19] V. P. Melnikov and J.J. Smulsky, “Astronomical theory of ice ages: New approximations. Solutions and challenges,” Academic Publishing House, Novosibirsk, 2009. (Information see http://www.ikz.ru/~smulski/Papers/AsThAnE.pdf). [20] V.P. Mel’nikov, I.I. Smul’skii and Ya.I. Smul’skii, “Compound modeling of Earth rotation and possible im-plications for interaction of continents,” Russian Geology and Geophysics, 2008, Vol. 49, 851–858. doi:10.1016/j.rgg.2008.04.003. http://www.ikz.ru/~smulski/Papers/RGG190.pdf. [21] J.J. Smulsky, “Optimization of Passive Orbit with the Use of Gravity Maneuver,” Cosmic Research, 46, No. 55, 2008, pp. 456–464. doi:10.1134/S0010952508050122. http://www.ikz.ru/~smulski/Papers/COSR456.PDF. [22] K.F. Steffensen, “On the Problem of Three Bodies in the Plane,” Kong. Danske Videnskab. Seskab., Mat. Fys. Medd., 13 (3), 1957. [23] M.S. Yarov-Yarovoi,. “O primenenii utochnennyh meto-dov chislennogo integrirovanija v nebesnoj mehanike (The use of refined methods of numerical integration in celestial mechanics,)” GAISh Transactions, Vol. 45, 1974, pp. 179-200. [24] J. J. Smulsky, “Osesimmetrichnaya zadacha vzaimideist-viya N-tel (The axisymmetrical problem of gravitational interaction of N bodies),” Matematicheskoe Modelirovanie, Vol. 15, No. 5, 2003 pp. 27-36. (In Russian http://www.smul1.newmail.ru/Russian1/IntSunSyst/Osvnb4.doc). [25] T. R. Quinn, S. Tremaine and M. Duncan, “A three million year integration of the Earth's orbit,” Astronomical Journal, Vol. 101, 1991, pp. 2287-2305. [26] J.J. Smulsky, “New Components of the Mercury’s Peri-helion Precession,” Natural Science, Vol. 3, No. 4, 2011, pp. 268-274. doi:10.4236/ns.2011.34034.http://www.scirp.org/journal/ns. [27] S. Newcomb, “The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy,” Washington: Government printing office. 1895. [28] J. L.Simon, P. Bretagnon, J. Chapront, G. Francou and J. Laskar, “Numerical Expression for Precession Formulae and Mean Elements for the Moon and the Planets,” Astron. and Astrophys., Vol. 282, pp. 663-683, 1994. [29] Bowell, E. 2008. The Asteroid Orbital Elements Database, Lowell Observatory, ftp://ftp.lowell.edu/pub/elgb/. [30] JPL Small-Body Database 2008. Jet Propulsion Labora-tory. California Institute of Technology. 99942 Apophis (2004 MN4). http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Apophis;orb=1. [31] G. N. Duboshin (Editor), “Nebesnaya Mekhanica I As-trodinamica (Celestial Mechanics and Astrodynamics),” Nauka, Moskva, 1976. [32] J.J. Smulsky, “Matematicheskaya model solnechnoi sis-temy (A Mathematical model of the Solar System)” In: V. A. Bereznev, (Ed.), “Teoreticheskie i pricladnye zadachi nelineinogo analiza”. Vychislitelny centr imeni Dorod-nitsyna, Moskva, 2007, pp. 119-139. (In Russian http://www.ikz.ru/~smulski/Papers/MatMdSS5.pdf). [33] Ephemerides of the Jet Propulsion Laboratory. USA. 2008. http://ssd.jpl.nasa.gov/?ephemerides. [34] E.M. Standish, “JPL Planetary and Lunar Ephemerides,” DE405/LE405. Interoffice memorandum: JPL IOM 312. F – 98-048, 1998, August 26. (ftp://ssd.jpl.nasa.gov/pub/eph/planets/ioms/de405.iom.pdf.). [35] J.D. Giorgini and 13 colleagues, “Asteroid 1950 DA En-counter with Earth in 2880: Physical Limits of Collision Probability Prediction,” Science Vol. 296, No. 5565, 2002, pp.132 – 136. [36] U. Corliss, “Mystery of the Universe,” Mir, Moscow, 1970 [in Russian]. [37] B. D.V. Cole, and D.W. Cox, “Islands in Space,” Chilton Books, Philadelphia, 1964. [38] J.J. Smulsky, “Gravitation, Field and Rotation of Mercury Perihelion,” Proceedings of the Natural Philosophy Al-liance. 15th Annual Conference 7-11 April 2008 at the University of New Mexico, Albuquuerque, USA. Vol. 5, No. 2. Published by Space Time Analyses, Ltd. Arlington, MA, USA, 2009, pp. 254-260. http://www.ikz.ru/~smulski/Papers/08Smulsky2c.pdf. [39] I. I. Smul'skii, “Multilayer Ring Structures,” Physics of Particles and Nuclei Letters, Vol. 8, No. 5, 2011, pp. 436-440. doi:10.1134/S1547477111050189. http://www.ikz.ru/~smulski/Papers/PHPL436.pdf.
[1] J. Laskar, “Large-scale chaos in the solar system,” Astron. and Astrophys, 1994, L9 – L12. [2] J. Laskar, P. Robutel, F. Joutel, M. Gastineau A. C. M. Correia, and B. Levrard, “A Long-term numeriucal solu-tion for the insolation quantities of the Earth,” Astron. Astrophys., Vol. 428, No.1, 2004, pp. 261–285. doi:10.1051/0004-6361:20041335. [3] J. Laskar, A. C. M. Correia, M. Gastineau, F. Joutel, B. Levrard and P. Robutel, “Long term evolution and chaotic diffusion of the insolation quantities of Mars,” Astron. and Astrophys, 2004, Vol. 428. pp. 261-285. doi:10.1051/0004-6361:20041335. [4] J.D. Giorgini, L.A.M. Benner, S.I. Ostro, H.C. Nolan and M.W. Busch, “Predicting the Earth encounters of (99942) Apophis,” Icarus, Vol. 193, 2008, pp. 1-19. doi:10.1016/j.icarus.2007.09.012. [5] R. Tucker, D. Tholen and F. Bernardi, MPS 109613, 2004. [6] G.J. Garradd, MPE Circ., 2004, Y25. [7] L.V. Rykhlova, B.M. Shustov, V.G. Pol and K.G. Suk-hanov,” Nasuschnye problemy asteroidnoj opasnosti (Urgent problems in protecting the Earth against astero-ids)”, Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 25-33. [8] V.A. Emel’yanov, Yu.K. Merkushev and S.I. Barabanov, “Periodichnost' seansov nabljudenija asteroida Apofis kosmicheskimi i nazemnymi teleskopami (Cyclicity of Apophis observation sessions with space and ground-based telescopes),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 38 -43. [9] V.A. Emel’yanov, V.I. Luk’yashchenko, Yu.K. Merku-shev and G.R. Uspenskii “Tochnost' opredelenie parame-trov orbity asteroida Apofis, obespechivaemaja kosmi-cheskimi teleskopami (Determination accuracy of asteroid Apophis’ orbit parameters ensured by space telescopes),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 59-64. [10] L.L. Sokolov, A.A. Bashakov, N.P. Pit’ev, “O vozmozh-nyh sblizhenijah ACZ 99942 Apofis s Zemlej (On possible encounters of asteroid 99942 Apophis with the Earth),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 33 – 38. [11] E. Everhart, “Implicit single-sequence methods for inte-grating orbits,” Celest. Mech. Vol. 10, 1974, pp. 35-55. [12] L.E. Bykova and T.Yu. Galushina, “Jevoljucija verojatnoj oblasti dvizhenija asteroida 99942 Apofis (Evolution of the probable travel path of asteroid 99942 Apophis),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 48 – 54. [13] L.E. Bykova and T.Yu. Galushina, “Opasnye dlja Zemli traektorii v oblasti vozmozhnyh dvizhenij asteroida 99942 Apophis (Trajectories in the region of possible travel paths of asteroid 99942 Apophis. Fundamental and Applied Problems in Modern Mechanics. Proceedings of the VI All-Russia Scientific Conference September 30 – October 2, 2008, Tomsk, 2008, pp. 419-420. [14] E.A. Smirnov, “Sovremennye chislennye metody integri-rovanija uravnenij dvizhenija asteroidov, sblizhajuschihsja s Zemlej (Advanced numerical methods for integrating motion equations of asteroids approaching the Earth),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 54-59. [15] V.V. Ivashkin, K.A. Stikhno, “Analiz problemy korrekcii orbity asteroida Apofis (An analysis of the problem on correcting asteroid Apophis’ orbit),” Proceedings of Intern. Conf. Near-Earth Astronomy 2007, September 3-7, Terskol, Nal’chik, Russia, 2008, pp. 44 – 48. [16] J. J. Smulsky, “The Theory of Interaction,” Publishing house of Novosibirsk University, Novosibirsk, 1999. (In Russian: http://www.ikz.ru/~smulski/TVfulA5_2.pdf). [17] J. J. Smulsky, “The Theory of Interaction,” Publishing house "Cultural Information Bank", Ekaterinburg, Russia 2004 (In English: http://www.ikz.ru/~smulski/TVEnA5_2.pdf). [18] E.A. Grebenikov and J.J.Smulsky, “Evoljucija orbity Marsa na intervale vremeni v sto millionov let (Numerical investigation of the Mars orbit evolution in the time interval of hundred million),” A.A. Dorodnitsyn Computing Center of RAS, Moscow, 2007. (In Russian, http://www.ikz.ru/~smulski/Papers/EvMa100m4t2.pdf). [19] V. P. Melnikov and J.J. Smulsky, “Astronomical theory of ice ages: New approximations. Solutions and challenges,” Academic Publishing House, Novosibirsk, 2009. (Information see http://www.ikz.ru/~smulski/Papers/AsThAnE.pdf). [20] V.P. Mel’nikov, I.I. Smul’skii and Ya.I. Smul’skii, “Compound modeling of Earth rotation and possible im-plications for interaction of continents,” Russian Geology and Geophysics, 2008, Vol. 49, 851–858. doi:10.1016/j.rgg.2008.04.003. http://www.ikz.ru/~smulski/Papers/RGG190.pdf. [21] J.J. Smulsky, “Optimization of Passive Orbit with the Use of Gravity Maneuver,” Cosmic Research, 46, No. 55, 2008, pp. 456–464. doi:10.1134/S0010952508050122. http://www.ikz.ru/~smulski/Papers/COSR456.PDF. [22] K.F. Steffensen, “On the Problem of Three Bodies in the Plane,” Kong. Danske Videnskab. Seskab., Mat. Fys. Medd., 13 (3), 1957. [23] M.S. Yarov-Yarovoi,. “O primenenii utochnennyh meto-dov chislennogo integrirovanija v nebesnoj mehanike (The use of refined methods of numerical integration in celestial mechanics,)” GAISh Transactions, Vol. 45, 1974, pp. 179-200. [24] J. J. Smulsky, “Osesimmetrichnaya zadacha vzaimideist-viya N-tel (The axisymmetrical problem of gravitational interaction of N bodies),” Matematicheskoe Modelirovanie, Vol. 15, No. 5, 2003 pp. 27-36. (In Russian http://www.smul1.newmail.ru/Russian1/IntSunSyst/Osvnb4.doc). [25] T. R. Quinn, S. Tremaine and M. Duncan, “A three million year integration of the Earth's orbit,” Astronomical Journal, Vol. 101, 1991, pp. 2287-2305. [26] J.J. Smulsky, “New Components of the Mercury’s Peri-helion Precession,” Natural Science, Vol. 3, No. 4, 2011, pp. 268-274. doi:10.4236/ns.2011.34034.http://www.scirp.org/journal/ns. [27] S. Newcomb, “The Elements of the Four Inner Planets and the Fundamental Constants of Astronomy,” Washington: Government printing office. 1895. [28] J. L.Simon, P. Bretagnon, J. Chapront, G. Francou and J. Laskar, “Numerical Expression for Precession Formulae and Mean Elements for the Moon and the Planets,” Astron. and Astrophys., Vol. 282, pp. 663-683, 1994. [29] Bowell, E. 2008. The Asteroid Orbital Elements Database, Lowell Observatory, ftp://ftp.lowell.edu/pub/elgb/. [30] JPL Small-Body Database 2008. Jet Propulsion Labora-tory. California Institute of Technology. 99942 Apophis (2004 MN4). http://ssd.jpl.nasa.gov/sbdb.cgi?sstr=Apophis;orb=1. [31] G. N. Duboshin (Editor), “Nebesnaya Mekhanica I As-trodinamica (Celestial Mechanics and Astrodynamics),” Nauka, Moskva, 1976. [32] J.J. Smulsky, “Matematicheskaya model solnechnoi sis-temy (A Mathematical model of the Solar System)” In: V. A. Bereznev, (Ed.), “Teoreticheskie i pricladnye zadachi nelineinogo analiza”. Vychislitelny centr imeni Dorod-nitsyna, Moskva, 2007, pp. 119-139. (In Russian http://www.ikz.ru/~smulski/Papers/MatMdSS5.pdf). [33] Ephemerides of the Jet Propulsion Laboratory. USA. 2008. http://ssd.jpl.nasa.gov/?ephemerides. [34] E.M. Standish, “JPL Planetary and Lunar Ephemerides,” DE405/LE405. Interoffice memorandum: JPL IOM 312. F – 98-048, 1998, August 26. (ftp://ssd.jpl.nasa.gov/pub/eph/planets/ioms/de405.iom.pdf.). [35] J.D. Giorgini and 13 colleagues, “Asteroid 1950 DA En-counter with Earth in 2880: Physical Limits of Collision Probability Prediction,” Science Vol. 296, No. 5565, 2002, pp.132 – 136. [36] U. Corliss, “Mystery of the Universe,” Mir, Moscow, 1970 [in Russian]. [37] B. D.V. Cole, and D.W. Cox, “Islands in Space,” Chilton Books, Philadelphia, 1964. [38] J.J. Smulsky, “Gravitation, Field and Rotation of Mercury Perihelion,” Proceedings of the Natural Philosophy Al-liance. 15th Annual Conference 7-11 April 2008 at the University of New Mexico, Albuquuerque, USA. Vol. 5, No. 2. Published by Space Time Analyses, Ltd. Arlington, MA, USA, 2009, pp. 254-260. http://www.ikz.ru/~smulski/Papers/08Smulsky2c.pdf. [39] I. I. Smul'skii, “Multilayer Ring Structures,” Physics of Particles and Nuclei Letters, Vol. 8, No. 5, 2011, pp. 436-440. doi:10.1134/S1547477111050189. http://www.ikz.ru/~smulski/Papers/PHPL436.pdf.