Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially

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

doi:doi:10.11648/j.ajaa.20200801.12

| Peer-Reviewed

Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially

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

Published in American Journal of Astronomy and Astrophysics (Volume 8, Issue 1)

Received: 18 December 2019 Accepted: 3 January 2020 Published: 12 February 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

With the aim of improving the Jupiter equilibrium liquid model consisting of two distorted spheroids (“spheroidals”) of our last paper, we generalize it here to any number l of layers, demanding that the calculated gravitational moments, J_2n (n=1,.., 4), agree with those surveyed by the Juno mission, which is fulfilled with a much higher accuracy than for l=2. The layers are of constant density and concentric (but otherwise free from any specific constriction between their semi-axes), each rotating with its own distribution of differential angular velocity, in accordance with our law in a past work. We point out that the angular velocity profiles are a consequence of the equilibrium itself, rather than being imposed ad initio. Although planetary structure aspects are not contemplated in our models, we arrange matters so that they can be compared with Gudkova’s and Guillot’s, paying attention on the distributions of mass and pressure. Our procedure is exact, in contrast with the self-consistent CMS (Concentric Maclaurin Spheroids) method developed by Hubbard, whose inexactitude resides in maintaining a single constant angular velocity while the spheroids are deformed. Our model predicts a differential rotation for Jupiter with periods for pole and equator of 9h38m and 10h14m corresponding to a mean period of 9h55m.

Published in	American Journal of Astronomy and Astrophysics (Volume 8, Issue 1)
DOI	10.11648/j.ajaa.20200801.12
Page(s)	8-14
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), 2020. Published by Science Publishing Group

Keywords

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

References

[1]	Cisneros, J. U., F. J. Martínez, & J. D. Montalvo (2019). ApJS, 241, 8.
[2]	Debras, F., G. Chabrier (2019), ApJ 872, 100.
[3]	Miguel, Y. T.\Guillot, L.\Fayon, 2016, A\&A, 596, A114.
[4]	Militzer, B., W. B. Hubbard (2009). Astrophys.\Space Sci., 322, 129.
[5]	Guillot, T. et al. 2018, Nature Let., 555, 227.
[6]	Debras F., G. Chabrier, 2018, A\&A, 609, A97.
[7]	Galanti E., Y. Kaspi, Y. Miguel, et al., 2018, Geophys. Res. Lett., 45, https://doi.org/10.1029/2018GL078087.
[8]	Hubbard W. B., B. Militzer, 2016, ApJ, 820: 80.
[9]	Kaspi Y., T. Guillot, E. Galanti, et al., 2017, Geophys. Res. Lett., 44, 5960.
[10]	Militzer B., S. Wahl, W. B. Hubbard, 2019, ApJ, 879: 78.
[11]	Nettelmann N., 2019, ApJ, 874, 156.
[12]	Wahl, S. M., W. B. Hubbard, B. Militzer, 2016, Icarus, 000, 1.
[13]	Wisdom J., W. B. Hubbard, 2016, Icarus, 267, 315.
[14]	Hubbard, W. B., 2012, ApJL, 756: L15.
[15]	Hubbard, W. B., 2013, ApJ, 768: 43, 1.
[16]	Cisneros, J.\U., F.\J.\Martínez,\& J.\D.\Montalvo, RMxAA, 2016, 52, 375.
[17]	Gudkova, T. V., Zharkov, V. N., 1999, Planetary and Space Science, 47, 1211-1224.
[18]	Guillot, T. 1999, Planetary and Space Science, 47, 1183-1200.
[19]	Cisneros, J. U., F. J. Martínez,\& J. D. Montalvo, 2017, ApJ, 848, 109.
[20]	Serra D., G.\Lari, G.\Tomme, et al., 2019, MNRAS, 490, 766-772.
[21]	Iess L., W.\M: \Folkner, D.\Durante, et al., 2018, Nature, 555, 220.
[22]	Bizyaev, I. A., A. V. Borisov, I. S. Mamaev, 2015, Celest. Mech. Dyn. Astr., Springer.
[23]	Montalvo J.\D., F.\J.\Martínez,\& J.\U.\Cisneros, 1983, RMxAA, 5, 293.
[24]	Esteban, E. P., Vasquez, S., 2001, Celest. Mech. Dyn. Astr.. 81 (4), 299–312.
[25]	Helled, R., G.\Schubert, J.\D.\Anderson, 2009, Planetary and Space Science 57, 1467-1473.
[26]	Wahl, S. M. et al. 2017, Geophys. Res. Lett, 44, 4649-4659. Helled, R., E.\Galanti, Y.\Kaspi, 2015, Nature 520, 202-204.

Cite This Article

Plain Text BibTeX RIS

APA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. (2020). Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially. American Journal of Astronomy and Astrophysics, 8(1), 8-14. https://doi.org/10.11648/j.ajaa.20200801.12

Copy | Download

ACS Style

Joel Uriel Cisneros-Parra; Francisco Javier Martinez-Herrera; Daniel Montalvo-Castro. Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially. Am. J. Astron. Astrophys. 2020, 8(1), 8-14. doi: 10.11648/j.ajaa.20200801.12

Copy | Download

AMA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially. Am J Astron Astrophys. 2020;8(1):8-14. doi: 10.11648/j.ajaa.20200801.12

Copy | Download

@article{10.11648/j.ajaa.20200801.12,
  author = {Joel Uriel Cisneros-Parra and Francisco Javier Martinez-Herrera and Daniel Montalvo-Castro},
  title = {Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {8},
  number = {1},
  pages = {8-14},
  doi = {10.11648/j.ajaa.20200801.12},
  url = {https://doi.org/10.11648/j.ajaa.20200801.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20200801.12},
  abstract = {With the aim of improving the Jupiter equilibrium liquid model consisting of two distorted spheroids (“spheroidals”) of our last paper, we generalize it here to any number l of layers, demanding that the calculated gravitational moments, J2n (n=1,.., 4), agree with those surveyed by the Juno mission, which is fulfilled with a much higher accuracy than for l=2. The layers are of constant density and concentric (but otherwise free from any specific constriction between their semi-axes), each rotating with its own distribution of differential angular velocity, in accordance with our law in a past work. We point out that the angular velocity profiles are a consequence of the equilibrium itself, rather than being imposed ad initio. Although planetary structure aspects are not contemplated in our models, we arrange matters so that they can be compared with Gudkova’s and Guillot’s, paying attention on the distributions of mass and pressure. Our procedure is exact, in contrast with the self-consistent CMS (Concentric Maclaurin Spheroids) method developed by Hubbard, whose inexactitude resides in maintaining a single constant angular velocity while the spheroids are deformed. Our model predicts a differential rotation for Jupiter with periods for pole and equator of 9h38m and 10h14m corresponding to a mean period of 9h55m.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially
AU  - Joel Uriel Cisneros-Parra
AU  - Francisco Javier Martinez-Herrera
AU  - Daniel Montalvo-Castro
Y1  - 2020/02/12
PY  - 2020
N1  - https://doi.org/10.11648/j.ajaa.20200801.12
DO  - 10.11648/j.ajaa.20200801.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 8
EP  - 14
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20200801.12
AB  - With the aim of improving the Jupiter equilibrium liquid model consisting of two distorted spheroids (“spheroidals”) of our last paper, we generalize it here to any number l of layers, demanding that the calculated gravitational moments, J2n (n=1,.., 4), agree with those surveyed by the Juno mission, which is fulfilled with a much higher accuracy than for l=2. The layers are of constant density and concentric (but otherwise free from any specific constriction between their semi-axes), each rotating with its own distribution of differential angular velocity, in accordance with our law in a past work. We point out that the angular velocity profiles are a consequence of the equilibrium itself, rather than being imposed ad initio. Although planetary structure aspects are not contemplated in our models, we arrange matters so that they can be compared with Gudkova’s and Guillot’s, paying attention on the distributions of mass and pressure. Our procedure is exact, in contrast with the self-consistent CMS (Concentric Maclaurin Spheroids) method developed by Hubbard, whose inexactitude resides in maintaining a single constant angular velocity while the spheroids are deformed. Our model predicts a differential rotation for Jupiter with periods for pole and equator of 9h38m and 10h14m corresponding to a mean period of 9h55m.
VL  - 8
IS  - 1
ER  -

Copy | Download

Author Information

Joel Uriel Cisneros-Parra

Facultad de Ciencias, Universidad Autonoma de San Luis Potosi, San Luis Potosi, Mexico
Francisco Javier Martinez-Herrera

Instituto de Fisica, Universidad Autonoma de San Luis Potosi, San Luis Potosi, Mexico
Daniel Montalvo-Castro

Instituto de Fisica, Universidad Autonoma de San Luis Potosi, San Luis Potosi, Mexico

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. (2020). Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially. American Journal of Astronomy and Astrophysics, 8(1), 8-14. https://doi.org/10.11648/j.ajaa.20200801.12

Copy | Download

ACS Style

Joel Uriel Cisneros-Parra; Francisco Javier Martinez-Herrera; Daniel Montalvo-Castro. Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially. Am. J. Astron. Astrophys. 2020, 8(1), 8-14. doi: 10.11648/j.ajaa.20200801.12

Copy | Download

AMA Style

Joel Uriel Cisneros-Parra, Francisco Javier Martinez-Herrera, Daniel Montalvo-Castro. Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially. Am J Astron Astrophys. 2020;8(1):8-14. doi: 10.11648/j.ajaa.20200801.12

Copy | Download

@article{10.11648/j.ajaa.20200801.12,
  author = {Joel Uriel Cisneros-Parra and Francisco Javier Martinez-Herrera and Daniel Montalvo-Castro},
  title = {Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {8},
  number = {1},
  pages = {8-14},
  doi = {10.11648/j.ajaa.20200801.12},
  url = {https://doi.org/10.11648/j.ajaa.20200801.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20200801.12},
  abstract = {With the aim of improving the Jupiter equilibrium liquid model consisting of two distorted spheroids (“spheroidals”) of our last paper, we generalize it here to any number l of layers, demanding that the calculated gravitational moments, J2n (n=1,.., 4), agree with those surveyed by the Juno mission, which is fulfilled with a much higher accuracy than for l=2. The layers are of constant density and concentric (but otherwise free from any specific constriction between their semi-axes), each rotating with its own distribution of differential angular velocity, in accordance with our law in a past work. We point out that the angular velocity profiles are a consequence of the equilibrium itself, rather than being imposed ad initio. Although planetary structure aspects are not contemplated in our models, we arrange matters so that they can be compared with Gudkova’s and Guillot’s, paying attention on the distributions of mass and pressure. Our procedure is exact, in contrast with the self-consistent CMS (Concentric Maclaurin Spheroids) method developed by Hubbard, whose inexactitude resides in maintaining a single constant angular velocity while the spheroids are deformed. Our model predicts a differential rotation for Jupiter with periods for pole and equator of 9h38m and 10h14m corresponding to a mean period of 9h55m.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Modeling Jupiter with a Multi-layer Spheroidal Liquid Mass Rotating Differentially
AU  - Joel Uriel Cisneros-Parra
AU  - Francisco Javier Martinez-Herrera
AU  - Daniel Montalvo-Castro
Y1  - 2020/02/12
PY  - 2020
N1  - https://doi.org/10.11648/j.ajaa.20200801.12
DO  - 10.11648/j.ajaa.20200801.12
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 8
EP  - 14
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20200801.12
AB  - With the aim of improving the Jupiter equilibrium liquid model consisting of two distorted spheroids (“spheroidals”) of our last paper, we generalize it here to any number l of layers, demanding that the calculated gravitational moments, J2n (n=1,.., 4), agree with those surveyed by the Juno mission, which is fulfilled with a much higher accuracy than for l=2. The layers are of constant density and concentric (but otherwise free from any specific constriction between their semi-axes), each rotating with its own distribution of differential angular velocity, in accordance with our law in a past work. We point out that the angular velocity profiles are a consequence of the equilibrium itself, rather than being imposed ad initio. Although planetary structure aspects are not contemplated in our models, we arrange matters so that they can be compared with Gudkova’s and Guillot’s, paying attention on the distributions of mass and pressure. Our procedure is exact, in contrast with the self-consistent CMS (Concentric Maclaurin Spheroids) method developed by Hubbard, whose inexactitude resides in maintaining a single constant angular velocity while the spheroids are deformed. Our model predicts a differential rotation for Jupiter with periods for pole and equator of 9h38m and 10h14m corresponding to a mean period of 9h55m.
VL  - 8
IS  - 1
ER  -

Copy | Download