Perturbations of planetary orbit parameters due to decreasing in stellar mass and the expansion of the universe from a classical approach
DOI:
https://doi.org/10.31349/RevMexFisE.21.020202Keywords:
Universe expansion, stellar mass, orbital period, semi-major axis, eccentricity, central forcesAbstract
In this analysis we found the disturbances caused by the decrease in stellar mass and the expansion of the universe, to three fundamental parameters that represented the stability of a planetary orbit: the period, the semi-major axis and the eccentricity. First, by assuming much greater the mass of the star than the planetary, the star-planet interaction is reduced to a single-body problem with origin of reference system lying in the greater mass; and, through the mathematical formalism of the central forces, the variations of the three orbital parameters to be considered were obtained. As a result, the variations corresponding to the period and semi-major axis have been characterized in their mathematical structure by the terms that describe each phenomenon; namely, ξ ∼ 2.16 × 10−21 for the case of Sun, and ̈α/α ∼ 3 × 10−36 concerning the decrease in stellar mass and the expansion of the universe, respectively. In the case of eccentricity, it is shown that this parameter is an invariant quantity under the disturbances produced by these two cosmological phenomena.
References
S. Hawking, A hombros de gigantes (Crítica, España, 2010).
J. Laskar, M. Gastineau, Existence of collisional trajectories of Mercury, Mars and Venus with the Earth, Nature Letters 459 (2009) 817, https://doi.org/10.1038/nature08096
R. A. Mardling, Resonance, Chaos and Stability: The Three-Body Problem in Astrophysics, In S. J. Aarseth, C. A. Tout, and R. A. Mardling, eds., The Cambridge N-Body Lectures, vol. 760, pp. 59-96 (Springer Netherlands, Dordrecht, 2008), https://doi.org/10.1007/978-1-4020-8431-7 3
A. N. Kolmogorov, On the conservation of conditionally periodic motions under small perturbation of the Hamiltonian, Dokl. Akad. Nauk. SSR 98 (1954) 527
V. I. Arnol, Proof of a Theorem by A. N. Kolmogorov on the invariance of quasi-periodic motions under small perturbations of the Hamiltonian, Russian Math. Survey 18 (1963) 9, https://dx.doi.org/10.1070/RM1963v018n05ABEH004130
J. Laskar, Large-scale chaos in the solar system., Astron. Astrophysics 287 (1994) L9, https://ui.adsabs.harvard.edu/abs/1994A&A...287L...9L J. Laskar, Large-Scale chaos in the solar system, Astron. Astrophysics L9-L12 (1994) 287, https://ui.adsabs.harvard.edu/abs/1994A%26A...287L...9L/abstract
E. Chávez Nambo and O. Sarbach, Static spherical perfect fluid stars with finite radius in general relativity: a review, Rev. Mex. Fis. 18 (2021) 020208 1, https://10.31349/RevMexFisE.18.020208
J. Chacón, J. A. Vázquez, and R. Gabbasov, Dark matter with n-body numerical simulations, Rev. Mex. Fis. E 17 (2020) 241, https://doi.org/10.31349/RevMexFisE.17.241
J. A. Vázquez González, L. E. Padilla, and T. Matos, Inflationary cosmology: from theory to observations, Rev. Mex. Fis. E 17 (2020) 73, https//doi.org/10.31349/RevMexFisE.17.73
M. Carrera and D. Giulini, Influence of global cosmological expansion on local dynamics and kinematics, Rev. Mod. Phys. 82 (2010) 169, https://doi.org/10.1103/RevModPhys.82.169
J. J. Arenas, ¿Es estable el Sistema Solar?, Lat. Am. J. Phys. Educ. 8 (2014) 328, https://www.lajpe.org/jun14/13LAJPE915JoseArenas.pdf
H. Goldstein C. P. Poole, and J. L. Safko, Classical mechanics, 3rd ed. (Pearson, 2002)
J. H. Jeans, Cosmogonic problems associated with a Secular Decrease of Mass, Monthly Notices of the Royal Astronomical Society 85 (1924) 2, https://doi.org/10.1093/mnras/85.1.2
E. Hubble and M. L. Humason, The Velocity-Distance Relation among Extra-Galactic Nebulae, Astrophys. J. 74 (1931) 43, https://doi.org/10.1086/143323
A. G. Riess, et al, Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant, Astrophys. J. 116 (1998) 1009, https://doi.org/10.1086/300499
G. C. Rodr´ıguez, J. Reyes, and I. A. Monroy, Analysis of the K-Factor in the Cobb-Douglas habitability function for exoplanets from the Buckingham theorem, RMxAC 55 (2023) 95, https://doi.org/10.22201/ia.14052059p.2023.55.31
F. I. Cooperstock, V. Faraoni, and D. N. Vollick, The Influence of the Cosmological Expansion on Local Systems, Astrophys. J. 503 (1998) 61, https://doi.org/10.1086/305956
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Juan D. Fonseca, Ignacio Alberto Monroy, G. Cardona Rodríguez
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física E right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
