Email this article Comparison of the orbital elements of major planets, the Moon and the Sun using various mathematical models on the time interval with 1600 to 2200
- Authors: Zausaev A.F.1, Romanyuk M.A.1
-
Affiliations:
- Samara State Technical University
- Issue: Vol 26, No 4 (2022)
- Pages: 738-763
- Section: Mathematical Modeling, Numerical Methods and Software Complexes
- URL: https://journals.eco-vector.com/1991-8615/article/view/89040
- DOI: https://doi.org/10.14498/vsgtu1888
- ID: 89040
Cite item
Full Text
Abstract
An analysis of the accuracy of the orbital elements obtained according to the coordinates and components of the velocities, found using the coefficients of the Chebyshev polynomials of the DE405 planetary catalog, is carried out. We compared the elements of orbital elements in the time interval from 1600 to 2200 years found using the DE405 catalog and obtained by numerical integration of the equations of motion based on the interaction of moving material bodies with the surrounding space. On the example of the numerical integration of the Moon motion equations, the advantage of using the equations of motion based on the interaction of moving material bodies with the surrounding space is shown in comparison with relativistic equations. Based on a comparison of the elements of Mercury's orbits, found by coordinates obtained by solving equations based on the interaction of moving material bodies with the surrounding space, and obtained using the DE405 catalog, it is shown that the orbital elements practically coincide on a given interval time. The maximum discrepancy in the mean anomaly at the end of the integration interval is less than 1′′ (second). The discrepancies of the secular displacements of perihelions for Mercury, Venus, Earth + Moon and Mars were determined, the values of which for DE405 are respectively: 43.08′′, 8.4′′, 3.83′′ and 1.14′′. It is shown that the errors of the secular displacements of the perihelions of the planets Mercury, Venus, the barycenter of the Earth + Moon and Mars obtained using the DE405 catalog take the following values: 0′′, 6.06′′, 3.83′′ and 1.08′′. For the outer planets: Jupiter, Saturn, Uranus, Neptune and the dwarf planet Pluto, on the basis of the considered comparisons of various equations of motion, no discrepancies in the orbital elements were found. Based on the studies carried out, it is shown that the use of harmonic coordinates in relativistic equations when creating the DE405 catalog is justified only for Mercury and the outer planets: Jupiter, Saturn, Uranus, Neptune and the dwarf planet Pluto.
About the authors
Anatoliy F. Zausaev
Samara State Technical University
Email: zausaev_af@mail.ru
ORCID iD: 0000-0002-5035-9615
SPIN-code: 5114-8373
Scopus Author ID: 57210957428
http://www.mathnet.ru/person38377
Dr. Phys. & Math. Sci.; Professor; Dept. of Applied Mathematics & Computer Science
Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244Mariya A. Romanyuk
Samara State Technical University
Author for correspondence.
Email: zausmasha@mail.ru
ORCID iD: 0000-0003-1352-6725
SPIN-code: 2220-5490
Scopus Author ID: 57210961558
http://www.mathnet.ru/person70435
Cand. Tech. Sci.; Associate Professor; Dept. of Applied Mathematics & Computer Science
Russian Federation, 443100, Samara, Molodogvardeyskaya st., 244References
- Maxwell J. C. Izbrannye sochineniia po teorii elektromagnitnogo polia [Selected Papers on Electromagnetic Field Theory]. Moscow, Gostekhizdat, 1952, 687 pp. (In Russian)
- Chebotarev G. A. Analytical and Numerical Methods of Celestial Mechanics, Modern Analytic and Computational Methods in Science and Mathematics, vol. 9. New York, American Elsevier Publishing Co., Inc., 1967, xviii+331 pp.
- Subbotin M. F. Vvedenie v teoreticheskuiu astronomiiu [Introduction to Theoretical Astronomy]. Moscow, Nauka, 1968, 800 pp. (In Russian)
- Bogorodsky A. F. Vsemirnoe tiagotenie [Universal Gravitation]. Kiev, Nauk. Dumka, 1971, 352 pp. (In Russian)
- Brumberg V. A. Reliativistskaia nebesnaia mekhanika [Relativistic Celestial Mechanics]. Moscow, Nauka, 1972, 384 pp. (In Russian)
- Vizgin V. P. On the discovery of the gravitational field equations by Einstein and Hilbert: new materials, Phys. Usp., 2001, vol. 44, no. 12, pp. 1283–1298. EDN: LGQDQR. DOI: https://doi.org/10.1070/PU2001v044n12ABEH001014.
- Dirak P. Printsipy kvantovoi mekhaniki [The Principles of Quantum Mechanics]. Moscow, Nauka, 1979, 440 pp. (In Russian)
- Feynman R. P. The Development of the Space-Time View of Quantum Electrodynamics, Nobel Lecture, December 11, 1965. Preprint les Prix Nobel en 1965. Stockholm, The Nobel Foundation, 1966.
- Casimir H. B. G., Polder D. The influence of retardation on the London-van der Waals forces, Phys. Rev., 1948, vol. 73, no. 4, pp. 360–372. DOI: https://doi.org/10.1103/PhysRev.73.360.
- Zel’dovich Ya. B. Vacuum theory: a possible solution to the singularity problem of cosmology, Sov. Phys. Usp., 1981, vol. 24, no. 3, pp. 216–230. DOI: https://doi.org/10.1070/PU1981v024n03ABEH004772.
- Zausaev A. F. Theory of motion of n material bodies, based on a new interaction principle, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2006, no. 43, pp. 132–139. EDN: HUYDOB. DOI: https://doi.org/10.14498/vsgtu463.
- Zausaev A. F., Zausaev A. A. Matematicheskoe modelirovanie orbital’noi evoliutsii malykh tel Solnechnoi sistemy [Mathematical Modelling of Orbital Evolution of Small Bodies of the Solar System]. Moscow, Mashinostroenie-1, 2008, 250 pp. (In Russian). EDN: QJUWVV.
- Zausaev A. F. The investigation of the motion of planets, the Moon, and the Sun based on a new principle of interaction, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2014, no. 3(36), pp. 118–131 (In Russian). EDN: TLEURX. DOI: https://doi.org/10.14498/vsgtu1304.
- Zausaev A. F. Comparison of the coordinates of the major planets, Moon, and Sun obtained based on a new principle of interaction and of the data bank DE405, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2016, vol. 20, no. 1, pp. 121–148. EDN: WQPYBB. DOI: https://doi.org/10.14498/vsgtu1458.
- Zausaev A. F., Romanyuk M. A. Chislennye metody v zadachakh matematicheskogo modelirovaniia dvizheniia nebesnykh tel v Solnechnoi sisteme [Numerical Methods in the Problems of Mathematical Modeling of the Motion of Celestial Bodies in the Solar System]. Samara, Samara State Technical Univ., 2017, 265 pp. (In Russian)
- Newhall X. X., Standish E M., Williams J. G. DE 102: A numerically integrated ephemeris of the Moon and planets spanning forty-four centuries, Astron. Astrophys., 1983, vol. 125, no. 1, pp. 150–167.
- Poincaré J. H. O nauke [About Science]. Moscow, Nauka, 1983, 560 pp. (In Russian)
- Zausaev A. F., Romanyuk M. A. Comparison of various mathematical models on the example of solving the equations of the movement of large planets and the Moon, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2019, vol. 23, no. 1, pp. 152–185. EDN: BGRYUJ. DOI: https://doi.org/10.14498/vsgtu1663.
- Standish E. M. JPL Planetary and Lunar Ephemerides, DE405/LE405. Interoffice memorandum: JPL IOM 312. F–98-048, 1998, August 26, 18 pp. ftp://ssd.jpl.nasa.gov/pub/eph/planets/ioms/de405.iom.pdf.
- Gribkova V. P. Effektivnye metody ravnomernykh priblizhenii, osnovannye na polinomakh Chebysheva [Efficient Methods of Uniform Approximations Based on Chebyshev Polynomials]. Moscow, Sputnik, 2017, 194 pp. (In Russian)
- Montenbruck O., Pfleger T. Astronomy on the Personal Computer. Berlin, Heidelberg, Springer, 2000, xv+300 pp. DOI: https://doi.org/10.1007/978-3-642-03436-7.
- Khemming R. V. Chislennye metody dlia nauchnykh rabotnikov i inzhenerov [Numerical Methods for Scientists and Engineers]. Moscow, Nauka, 1972, 400 pp. (In Russian)
- Park R. S. JPL Planetary and Lunar Ephemerides, 2020. https://ssd.jpl.nasa.gov/planets/eph_export.html.
- Le Verrier U. J. Theorie du movement de Mercure, Annales de l’Observatoire imperial de Paris, vol. 5, Annales de l’Observatoire de Paris. Memoires. Paris, Mallet-Bachelier, 1859, 195 pp.
Supplementary files
