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On the spherical geopotential approximation for Saturn
Department of Mathematics, Brown University, Box 1917, Providence, RI 02912, USA |
In this paper, we show by means of a diffeomorphism that when approximating the planet Saturn by a sphere, the errors associated with the spherical geopotential approximation are so significant that this approach is rendered unsuitable for any rigorous mathematical analysis.
References:
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A. Affholder, F. Guyot, B. Sauterey, R. Ferrière and S. Mazevet,
Bayesian analysis of Enceladus's plume data to assess methanogenesis, Nat. Astron., 8 (2021), 805-814.
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P. Benard,
An oblate-spheroid geopotential approximation for global meteorology, Quart. J. Roy. Meterol. Soc., 140 (2014), 170-184.
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Krümmungseigenschaften konvexer Flächen, Acta Math., 66 (1936), 1-47.
doi: 10.1007/BF02546515. |
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A. Constantin and R. S. Johnson,
On the modelling of large-scale atmospheric flow, J. Differ. Equ., 285 (2021), 751-798.
doi: 10.1016/j.jde.2021.03.019. |
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A. Constantin and R. S. Johnson, On the propagation of waves in the atmosphere, Proc. A, 477 (2021), 25 pp. |
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A. Constantin, D. G. Crowdy, V. S. Krishnamurthy and M. H. Wheeler,
Stuart-type polar vortices on a rotating sphere, Discrete Cont. Dyn. Syst., 41 (2021), 201-215.
doi: 10.3934/dcds.2020263. |
[7] |
G. Faure and T. M. Mensing, Introduction to Planetary Science: The Geological Perspective, Springer, Dordrecht, The Netherlands, 2007. |
[8] |
R. A. Freedman and W. J. Kaufmann III, Universe: The Solar System, Freeman, New York, NY, 2002. |
[9] |
B. Galperin and P.L. Read, Zonal Jets: Phenomenology, Genesis and Physics, Cambridge University Press, Cambridge, 2019.
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E. Gregersen, The Outer Solar System, Britannica Educational Publishing, New York, NY, 2009.
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[11] |
P. Gruber, Convex and Discrete Geometry, Springer-Verlag, Berlin-Heidelberg, 2007.
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[12] |
W. K. Hartmann, Moons and Planets, Brooks/Cole, Belmont, CA, 2005. |
[13] |
A. P. Ingersoll, et al., Atmospheres of the giant planets in The New Solar System, Sky Publishing, Cambridge, MA, 1999. |
[14] |
J. E. Klepeis,
Hydrogen-helium mixtures at megabars pressure: Implications for Jupiter and Saturn, Science, 254 (1991), 986-989.
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[15] |
J. Lunine,
Saturn's Titan: A Strict Test for Life's Cosmic Ubiquity, Proceed. Amer. Phil. Soc., 153 (2009), 403-418.
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[16] |
NASA/Jet Propulsion Laboratory, Life on Titan? New clues to what's consuming hydrogen, acetylene on Saturn's moon, Sci. Daily, 2010. |
[17] |
A. Staniforth,
Spherical and spheroidal geopotential approximations, Quart. J. Roy. Meterol. Soc., 140 (2014), 2685-2692.
|
show all references
References:
[1] |
A. Affholder, F. Guyot, B. Sauterey, R. Ferrière and S. Mazevet,
Bayesian analysis of Enceladus's plume data to assess methanogenesis, Nat. Astron., 8 (2021), 805-814.
|
[2] |
P. Benard,
An oblate-spheroid geopotential approximation for global meteorology, Quart. J. Roy. Meterol. Soc., 140 (2014), 170-184.
|
[3] |
H. Busemann and W. Feller,
Krümmungseigenschaften konvexer Flächen, Acta Math., 66 (1936), 1-47.
doi: 10.1007/BF02546515. |
[4] |
A. Constantin and R. S. Johnson,
On the modelling of large-scale atmospheric flow, J. Differ. Equ., 285 (2021), 751-798.
doi: 10.1016/j.jde.2021.03.019. |
[5] |
A. Constantin and R. S. Johnson, On the propagation of waves in the atmosphere, Proc. A, 477 (2021), 25 pp. |
[6] |
A. Constantin, D. G. Crowdy, V. S. Krishnamurthy and M. H. Wheeler,
Stuart-type polar vortices on a rotating sphere, Discrete Cont. Dyn. Syst., 41 (2021), 201-215.
doi: 10.3934/dcds.2020263. |
[7] |
G. Faure and T. M. Mensing, Introduction to Planetary Science: The Geological Perspective, Springer, Dordrecht, The Netherlands, 2007. |
[8] |
R. A. Freedman and W. J. Kaufmann III, Universe: The Solar System, Freeman, New York, NY, 2002. |
[9] |
B. Galperin and P.L. Read, Zonal Jets: Phenomenology, Genesis and Physics, Cambridge University Press, Cambridge, 2019.
![]() |
[10] |
E. Gregersen, The Outer Solar System, Britannica Educational Publishing, New York, NY, 2009.
![]() |
[11] |
P. Gruber, Convex and Discrete Geometry, Springer-Verlag, Berlin-Heidelberg, 2007.
![]() |
[12] |
W. K. Hartmann, Moons and Planets, Brooks/Cole, Belmont, CA, 2005. |
[13] |
A. P. Ingersoll, et al., Atmospheres of the giant planets in The New Solar System, Sky Publishing, Cambridge, MA, 1999. |
[14] |
J. E. Klepeis,
Hydrogen-helium mixtures at megabars pressure: Implications for Jupiter and Saturn, Science, 254 (1991), 986-989.
|
[15] |
J. Lunine,
Saturn's Titan: A Strict Test for Life's Cosmic Ubiquity, Proceed. Amer. Phil. Soc., 153 (2009), 403-418.
|
[16] |
NASA/Jet Propulsion Laboratory, Life on Titan? New clues to what's consuming hydrogen, acetylene on Saturn's moon, Sci. Daily, 2010. |
[17] |
A. Staniforth,
Spherical and spheroidal geopotential approximations, Quart. J. Roy. Meterol. Soc., 140 (2014), 2685-2692.
|





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