Difference between revisions of "User:Tohline/Appendix/Ramblings/Bordeaux"
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==Exterior Gravitational Potential of Toroids== | ==Exterior Gravitational Potential of Toroids== | ||
[https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.5825H/abstract J. -M. Huré, B. Basillais, V. Karas, A. Trova, & O. Semerák (2020), MNRAS, 494, 5825-5838] have published a paper titled, ''The Exterior Gravitational Potential of Toroids.'' Here we examine how their work relates to the published work by [http://adsabs.harvard.edu/abs/1973AnPhy..77..279W C.-Y. Wong (1973, Annals of Physics, 77, 279)], which we have separately [[User:Tohline/Apps/Wong1973Potential#Wong.27s_.281973.29_Analytic_Potential|discussed in detail]]. | [https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.5825H/abstract J. -M. Huré, B. Basillais, V. Karas, A. Trova, & O. Semerák (2020), MNRAS, 494, 5825-5838] have published a paper titled, ''The Exterior Gravitational Potential of Toroids.'' Here we examine how their work relates to the published work by [http://adsabs.harvard.edu/abs/1973AnPhy..77..279W C.-Y. Wong (1973, Annals of Physics, 77, 279)], which we have separately [[User:Tohline/Apps/Wong1973Potential#Wong.27s_.281973.29_Analytic_Potential|discussed in detail]]. | ||
On an initial reading, it appears as though the most relevant section of the [https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.5825H/abstract Huré, et al. (2020)] paper is §8 titled, ''The Solid Torus.'' They state that the gravitational potential outside of an homogeneous (circular cross-section) torus is, | |||
<div align="center"> | |||
<table border="0" cellpadding="5" align="center"> | |||
<tr> | |||
<td align="right"> | |||
<math>~\Psi_\mathrm{grav}(\vec{r})</math> | |||
</td> | |||
<td align="center"> | |||
<math>~=</math> | |||
</td> | |||
<td align="left"> | |||
<math>~ | |||
-4G\rho_0 \int_0^b \int_0^{2\pi} a\kappa b' d\theta db' | |||
</math> | |||
</td> | |||
</tr> | |||
</table> | |||
</div> | |||
{{LSU_HBook_footer}} | {{LSU_HBook_footer}} | ||
Revision as of 22:57, 16 June 2020
Université de Bordeaux
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Spheroid-Ring Systems
Through a research collaboration at the Université de Bordeaux, B. Basillais & J. -M. Huré (2019), MNRAS, 487, 4504-4509 have published a paper titled, Rigidly Rotating, Incompressible Spheroid-Ring Systems: New Bifurcations, Critical Rotations, and Degenerate States.
Exterior Gravitational Potential of Toroids
J. -M. Huré, B. Basillais, V. Karas, A. Trova, & O. Semerák (2020), MNRAS, 494, 5825-5838 have published a paper titled, The Exterior Gravitational Potential of Toroids. Here we examine how their work relates to the published work by C.-Y. Wong (1973, Annals of Physics, 77, 279), which we have separately discussed in detail.
On an initial reading, it appears as though the most relevant section of the Huré, et al. (2020) paper is §8 titled, The Solid Torus. They state that the gravitational potential outside of an homogeneous (circular cross-section) torus is,
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<math>~\Psi_\mathrm{grav}(\vec{r})</math> |
<math>~=</math> |
<math>~ -4G\rho_0 \int_0^b \int_0^{2\pi} a\kappa b' d\theta db' </math> |
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© 2014 - 2021 by Joel E. Tohline |