Jupiter and Saturn Multi-layer Models Rotating Differentially

Joel Uriel Cisneros-Parra; Francisco Javier Martinez-Herrera; Daniel Montalvo-Castro

doi:doi:10.11648/j.ajaa.20210903.12

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Jupiter and Saturn Multi-layer Models Rotating Differentially

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro

Published in American Journal of Astronomy and Astrophysics (Volume 9, Issue 3)

Received: 2 July 2021 Accepted: 19 July 2021 Published: 27 July 2021

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Abstract

In a past work, models for Jupiter were constructed in base to a set of concentric distorted spheroids (“spheroidals”) rotating differentially—whose semi-axes are independent of one another—a task that was achieved with a law of rotation deduced from a generalization of Bernoulli’s theorem, and which holds exclusively for axial-symmetric masses. The shape of the mass is that of a spheroid whose surface equation contains an extra term, d/z⁴, where d is a parameter which measures the degree of distortion. Each layer rotates with its own profile of angular velocity. The rotation law has a simple dependence on the derivative of the gravitational potential. No magnetic fields or equations of state were involved. The multi- structures were demanded, firstly, to reproduce the gravitational moments of the planets, as surveyed by space missions; and, secondly, to be equilibrium figures. For the calculation of the gravitational moments, a minimization procedure was employed. Paying attention on the outermost laye—the relevant one in the present context—of the formerly reported models for Jupiter, we became aware that they all share an angular velocity profile that decreases from the pole towards the equator, an event that, so far, has not been verified observationally. Since figures with profiles of the opposite tendency turned out to be also possible, they should be included as candidates for our purpose, as effectively they are herein as a complement of that work. The same procedure is here entailed to Saturn, for which figures to show one or the other tendencies are as well obtained. The dual behavior of the rotation profiles may be explained by arguments involving the centripetal force. According to this standpoint, the double behavior is a consequence of the algebraic sign assigned to d: if positive, so that the surface is more bloated than that of a spheroid, the decreasing tendency results; whereas if negative, so that the surface is more depressed, the increasing tendency shows up. This, in turn, is because for d negative the radial force increases more rapidly from pole to the equator than for d positive. We point out that the rotation profiles of the current figures are determined from their equilibrium, rather than being imposed ad initio.

Published in	American Journal of Astronomy and Astrophysics (Volume 9, Issue 3)
DOI	10.11648/j.ajaa.20210903.12
Page(s)	32-41
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Gravitation, Hydrodynamics, Planets and Satellites: General, Stars: Rotation

References

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[2]	Cisneros, J. U., F. J. Martinez & D. Montalvo, 2020 American Journal of Astronomy and Astrophysics. Vol. 8, No. 1, 2020, pp. 8-14.
[3]	Kitchatinov L. L., 2005, Physics-Uspekhi, 48 (5), 449.
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[5]	Garcia-Melendo E., S. Pérez-Hoyos, A. Sánchez-Lavega \& R. Hueso, Icarus (2011) 215, 62–74.
[6]	Helled, R., E. Galanti & Y. Kaspi, 2015, Nature 520, 202-204.
[7]	Gudkova, T. V. & Zharkov, V. N., 1999, Planetary and Space Science, 47, 1211-1224.
[8]	Cisneros, J. U., F. J. Martinez & D. Montalvo, 2017, ApJ, 848, 109.
[9]	Cisneros, J. U., F. J. Martinez & D. Montalvo, RMxAA, 2016, 52, 375.
[10]	Cisneros, J. U., F. J. Martinez, & D. Montalvo, American Journal of Astronomy and Astrophysics. Vol. 8, No. 2, 2020a, pp. 30-34.
[11]	Bolton et al., 2017, Science 356, 821–825.
[12]	Folkner, W. M. et al (2017), Geophys. Res. Lett, 44, 4694-4700.
[13]	Durante, D., M. Parisi, D. Serra, et. al, (2020) Geophys. Res. Lett., 47 (4), e86572.
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[18]	Howard, R., J., M. Adkins et al 1983, Solar Phys. 83, 321.

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APA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. (2021). Jupiter and Saturn Multi-layer Models Rotating Differentially. American Journal of Astronomy and Astrophysics, 9(3), 32-41. https://doi.org/10.11648/j.ajaa.20210903.12

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ACS Style

Joel Uriel Cisneros-Parra; Francisco Javier Martinez-Herrera; Daniel Montalvo-Castro. Jupiter and Saturn Multi-layer Models Rotating Differentially. Am. J. Astron. Astrophys. 2021, 9(3), 32-41. doi: 10.11648/j.ajaa.20210903.12

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AMA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. Jupiter and Saturn Multi-layer Models Rotating Differentially. Am J Astron Astrophys. 2021;9(3):32-41. doi: 10.11648/j.ajaa.20210903.12

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@article{10.11648/j.ajaa.20210903.12,
  author = {Joel Uriel Cisneros-Parra and Francisco Javier Martinez-Herrera and Daniel Montalvo-Castro},
  title = {Jupiter and Saturn Multi-layer Models Rotating Differentially},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {3},
  pages = {32-41},
  doi = {10.11648/j.ajaa.20210903.12},
  url = {https://doi.org/10.11648/j.ajaa.20210903.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210903.12},
  abstract = {In a past work, models for Jupiter were constructed in base to a set of concentric distorted spheroids (“spheroidals”) rotating differentially—whose semi-axes are independent of one another—a task that was achieved with a law of rotation deduced from a generalization of Bernoulli’s theorem, and which holds exclusively for axial-symmetric masses. The shape of the mass is that of a spheroid whose surface equation contains an extra term, d/z4, where d is a parameter which measures the degree of distortion. Each layer rotates with its own profile of angular velocity. The rotation law has a simple dependence on the derivative of the gravitational potential. No magnetic fields or equations of state were involved. The multi- structures were demanded, firstly, to reproduce the gravitational moments of the planets, as surveyed by space missions; and, secondly, to be equilibrium figures. For the calculation of the gravitational moments, a minimization procedure was employed. Paying attention on the outermost laye—the relevant one in the present context—of the formerly reported models for Jupiter, we became aware that they all share an angular velocity profile that decreases from the pole towards the equator, an event that, so far, has not been verified observationally. Since figures with profiles of the opposite tendency turned out to be also possible, they should be included as candidates for our purpose, as effectively they are herein as a complement of that work. The same procedure is here entailed to Saturn, for which figures to show one or the other tendencies are as well obtained. The dual behavior of the rotation profiles may be explained by arguments involving the centripetal force. According to this standpoint, the double behavior is a consequence of the algebraic sign assigned to d: if positive, so that the surface is more bloated than that of a spheroid, the decreasing tendency results; whereas if negative, so that the surface is more depressed, the increasing tendency shows up. This, in turn, is because for d negative the radial force increases more rapidly from pole to the equator than for d positive. We point out that the rotation profiles of the current figures are determined from their equilibrium, rather than being imposed ad initio.},
 year = {2021}
}

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TY  - JOUR
T1  - Jupiter and Saturn Multi-layer Models Rotating Differentially
AU  - Joel Uriel Cisneros-Parra
AU  - Francisco Javier Martinez-Herrera
AU  - Daniel Montalvo-Castro
Y1  - 2021/07/27
PY  - 2021
N1  - https://doi.org/10.11648/j.ajaa.20210903.12
DO  - 10.11648/j.ajaa.20210903.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 32
EP  - 41
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210903.12
AB  - In a past work, models for Jupiter were constructed in base to a set of concentric distorted spheroids (“spheroidals”) rotating differentially—whose semi-axes are independent of one another—a task that was achieved with a law of rotation deduced from a generalization of Bernoulli’s theorem, and which holds exclusively for axial-symmetric masses. The shape of the mass is that of a spheroid whose surface equation contains an extra term, d/z4, where d is a parameter which measures the degree of distortion. Each layer rotates with its own profile of angular velocity. The rotation law has a simple dependence on the derivative of the gravitational potential. No magnetic fields or equations of state were involved. The multi- structures were demanded, firstly, to reproduce the gravitational moments of the planets, as surveyed by space missions; and, secondly, to be equilibrium figures. For the calculation of the gravitational moments, a minimization procedure was employed. Paying attention on the outermost laye—the relevant one in the present context—of the formerly reported models for Jupiter, we became aware that they all share an angular velocity profile that decreases from the pole towards the equator, an event that, so far, has not been verified observationally. Since figures with profiles of the opposite tendency turned out to be also possible, they should be included as candidates for our purpose, as effectively they are herein as a complement of that work. The same procedure is here entailed to Saturn, for which figures to show one or the other tendencies are as well obtained. The dual behavior of the rotation profiles may be explained by arguments involving the centripetal force. According to this standpoint, the double behavior is a consequence of the algebraic sign assigned to d: if positive, so that the surface is more bloated than that of a spheroid, the decreasing tendency results; whereas if negative, so that the surface is more depressed, the increasing tendency shows up. This, in turn, is because for d negative the radial force increases more rapidly from pole to the equator than for d positive. We point out that the rotation profiles of the current figures are determined from their equilibrium, rather than being imposed ad initio.
VL  - 9
IS  - 3
ER  -

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Author Information

Joel Uriel Cisneros-Parra

Sciences Faculty, Autonomous University of San Luis Potosí, San Luis Potosí, Mexico
Francisco Javier Martinez-Herrera

Physics Institute, Autonomous University of San Luis Potosí, San Luis Potosí, Mexico
Daniel Montalvo-Castro

Physics Institute, Autonomous University of San Luis Potosí, San Luis Potosí, Mexico

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APA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. (2021). Jupiter and Saturn Multi-layer Models Rotating Differentially. American Journal of Astronomy and Astrophysics, 9(3), 32-41. https://doi.org/10.11648/j.ajaa.20210903.12

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ACS Style

Joel Uriel Cisneros-Parra; Francisco Javier Martinez-Herrera; Daniel Montalvo-Castro. Jupiter and Saturn Multi-layer Models Rotating Differentially. Am. J. Astron. Astrophys. 2021, 9(3), 32-41. doi: 10.11648/j.ajaa.20210903.12

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AMA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. Jupiter and Saturn Multi-layer Models Rotating Differentially. Am J Astron Astrophys. 2021;9(3):32-41. doi: 10.11648/j.ajaa.20210903.12

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@article{10.11648/j.ajaa.20210903.12,
  author = {Joel Uriel Cisneros-Parra and Francisco Javier Martinez-Herrera and Daniel Montalvo-Castro},
  title = {Jupiter and Saturn Multi-layer Models Rotating Differentially},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {3},
  pages = {32-41},
  doi = {10.11648/j.ajaa.20210903.12},
  url = {https://doi.org/10.11648/j.ajaa.20210903.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210903.12},
  abstract = {In a past work, models for Jupiter were constructed in base to a set of concentric distorted spheroids (“spheroidals”) rotating differentially—whose semi-axes are independent of one another—a task that was achieved with a law of rotation deduced from a generalization of Bernoulli’s theorem, and which holds exclusively for axial-symmetric masses. The shape of the mass is that of a spheroid whose surface equation contains an extra term, d/z4, where d is a parameter which measures the degree of distortion. Each layer rotates with its own profile of angular velocity. The rotation law has a simple dependence on the derivative of the gravitational potential. No magnetic fields or equations of state were involved. The multi- structures were demanded, firstly, to reproduce the gravitational moments of the planets, as surveyed by space missions; and, secondly, to be equilibrium figures. For the calculation of the gravitational moments, a minimization procedure was employed. Paying attention on the outermost laye—the relevant one in the present context—of the formerly reported models for Jupiter, we became aware that they all share an angular velocity profile that decreases from the pole towards the equator, an event that, so far, has not been verified observationally. Since figures with profiles of the opposite tendency turned out to be also possible, they should be included as candidates for our purpose, as effectively they are herein as a complement of that work. The same procedure is here entailed to Saturn, for which figures to show one or the other tendencies are as well obtained. The dual behavior of the rotation profiles may be explained by arguments involving the centripetal force. According to this standpoint, the double behavior is a consequence of the algebraic sign assigned to d: if positive, so that the surface is more bloated than that of a spheroid, the decreasing tendency results; whereas if negative, so that the surface is more depressed, the increasing tendency shows up. This, in turn, is because for d negative the radial force increases more rapidly from pole to the equator than for d positive. We point out that the rotation profiles of the current figures are determined from their equilibrium, rather than being imposed ad initio.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Jupiter and Saturn Multi-layer Models Rotating Differentially
AU  - Joel Uriel Cisneros-Parra
AU  - Francisco Javier Martinez-Herrera
AU  - Daniel Montalvo-Castro
Y1  - 2021/07/27
PY  - 2021
N1  - https://doi.org/10.11648/j.ajaa.20210903.12
DO  - 10.11648/j.ajaa.20210903.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 32
EP  - 41
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210903.12
AB  - In a past work, models for Jupiter were constructed in base to a set of concentric distorted spheroids (“spheroidals”) rotating differentially—whose semi-axes are independent of one another—a task that was achieved with a law of rotation deduced from a generalization of Bernoulli’s theorem, and which holds exclusively for axial-symmetric masses. The shape of the mass is that of a spheroid whose surface equation contains an extra term, d/z4, where d is a parameter which measures the degree of distortion. Each layer rotates with its own profile of angular velocity. The rotation law has a simple dependence on the derivative of the gravitational potential. No magnetic fields or equations of state were involved. The multi- structures were demanded, firstly, to reproduce the gravitational moments of the planets, as surveyed by space missions; and, secondly, to be equilibrium figures. For the calculation of the gravitational moments, a minimization procedure was employed. Paying attention on the outermost laye—the relevant one in the present context—of the formerly reported models for Jupiter, we became aware that they all share an angular velocity profile that decreases from the pole towards the equator, an event that, so far, has not been verified observationally. Since figures with profiles of the opposite tendency turned out to be also possible, they should be included as candidates for our purpose, as effectively they are herein as a complement of that work. The same procedure is here entailed to Saturn, for which figures to show one or the other tendencies are as well obtained. The dual behavior of the rotation profiles may be explained by arguments involving the centripetal force. According to this standpoint, the double behavior is a consequence of the algebraic sign assigned to d: if positive, so that the surface is more bloated than that of a spheroid, the decreasing tendency results; whereas if negative, so that the surface is more depressed, the increasing tendency shows up. This, in turn, is because for d negative the radial force increases more rapidly from pole to the equator than for d positive. We point out that the rotation profiles of the current figures are determined from their equilibrium, rather than being imposed ad initio.
VL  - 9
IS  - 3
ER  -

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