Corrected Newtonian potentials in the two-body problem with applications

Abstract

The paper deals with an analytical study of various corrected Newtonian potentials. We offer a complete description of the corrected potentials, for the entire range of the parameters involved. These parameters can be fixed for different models in order to obtain a good concordance with known data. Some of the potentials are generated by continued fractions, and another one is derived from the Newtonian potential by adding a logarithmic correction. The zonal potential, which models the motion of a satellite moving in the equatorial plane of the Earth, is also considered. The range of the parameters for which the potentials behave or not similarly to the Newtonian one is pointed out. The shape of the potentials is displayed for all the significant cases, as well as the orbit of Raduga-1M 2 satellite in the field generated by the continued fractional potential U3, and then by the zonal one. For the continued fractional potential U2 we study the basic problem of the existence and linear stability of circular orbits. We prove that such orbits exist and are linearly stable. This qualitative study offers the possibility to choose the adequate potential, either for modeling the motion of planets or satellites, or to explain some phenomena at galactic scale

Authors

Mira Cristiana Anisiu
Romanian Academy, Tiberiu Popoviciu Institute of Numerical Analysis, Cluj-Napoca

Iharka Szucs-Csillik
Romanian Academy, Institute of Astronomy, Astronomical Observatory Cluj-Napoca

Keywords

Celestial mechanics; Newtonian potential; Two-body problem; Circular orbits

Paper coordinates

M.-C. Anisiu, I. Szucs-Csillik, Corrected Newtonian potentials in the two-body problem with applications, Astrophys. Space Sci., 361 (2016) 382, 8 pp., https://doi.org/10.1007/s10509-016-2967-x

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About this paper

Journal

Astrophysics and  Space Science

Publisher Name

Springer

Print ISSN

0004-640X

Online ISSN

1572-946X

google scholar link

[1] Abd El-Salam, F.A., Abd El-Bar, S.E., Rasem, M., Alamri, S.Z.: Astrophys. Space Sci. 350, 507 (2014) Article ADS Google Scholar
[2] Anisiu, M.-C.: In: Dumitrache, C., Popescu, N.A., Suran, D.M., Mioc, V. (eds.) AIP Conference Proceedings, vol. 895, p. 308 (2007) Chapter Google Scholar
[3] Battin, R.H.: An Introduction to the Mathematics and Methods of Astrodynamics. AIAA, Reston (1999) Book MATH Google Scholar
[4]  Blaga, C.: Rom. Astron. J. 25, 233 (2015) Google Scholar
[5] Bozis, G., Anisiu, M.-C., Blaga, C.: Astron. Nachr. 318, 313 (1997) Article ADS Google Scholar
[6] Diacu, F., Mioc, V., Stoica, C.: Nonlinear Anal. 41, 1029 (2000) Article MathSciNet Google Scholar
[7] Fabris, J.C., Pereira Campos, J.: Gen. Relativ. Gravit. 41, 93 (2009) Article ADS Google Scholar
[8] King-Hele, D.G., Cook, G.E., Rees, J.M.: Geophys. J. Int. 8, 119 (1963) Article ADS Google Scholar
[9] Kinney, W.H., Brisudova, M.: Ann. N.Y. Acad. Sci. 927, 127 (2001) Article ADS Google Scholar
[10] Korn, G.A., Korn, T.M.: Mathematical Handbook for Scientists and Engineers: Definitions, Theorems, and Formulas for Reference and Review. Courier Corporation, North Chelmsford (2000) MATH Google Scholar
[11] Maneff, G.: C. R. Acad. Sci. Paris 178, 2159 (1924) Google Scholar
[12] Mücket, J.P., Treder, H.-J.: Astron. Nachr. 298, 65 (1977) Article ADS Google Scholar
[13] Ragos, O., Haranas, I., Gkigkitzis, I.: Astrophys. Space Sci. 345, 67 (2013) Article ADS Google Scholar
[14]  Roman, R., Szücs-Csillik, I.: Astrophys. Space Sci. 349, 117 (2014) Article ADS Google Scholar
[15] Roy, A.E.: Orbital Motion. CRC, Bristol (2004) Book MATH Google Scholar
[16] Seeliger, H.: Astron. Nachr. 137, 129 (1895) Article ADS Google Scholar
[18] Szücs-Csillik, I., Roman, R.: In: Workshop on Cosmical Phenomena that Affect Earth and Their Effects, October 18, 2013, Bucharest (2013) Google Scholar
[19] Whittaker, E.T.: A Treatise on the Analytical Dynamics of Particles and Rigid Bodies. Cambridge University Press, Cambridge (1917)

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