The exterior gravitational potential of toroids

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10422796" target="_blank" >RIV/00216208:11320/20:10422796 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lvaY7dguss" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=lvaY7dguss</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/mnras/staa980" target="_blank" >10.1093/mnras/staa980</a>

Result language
angličtina
Original language name
The exterior gravitational potential of toroids
Original language description
We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed at the centre of the section, consists in an infinite series in the powers of the minor-to-major radius ratio e of the shell. It is appropriate for a solid, homogeneous torus, as well as for inhomogeneous bodies (the case of a core stratification is considered). We show that the leading term is identical to the potential of a loop having the same main radius and the same mass - this 'similarity' is shown to hold in the O(e(2)) order. The series converges very well, especially close to the surface of the toroid where the average relative precision is similar to 10(-3) for e = 0.1 at order zero, and as low as a few 10(-6) at second order. The Laplace equation is satisfied exactly in every order, so no extra density is induced by truncation. The gravitational acceleration, important in dynamical studies, is reproduced with the same accuracy. The technique also applies to the magnetic potential and field generated by azimuthal currents as met in terrestrial and astrophysical plasmas.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10300 - Physical sciences

Project
<a href="/en/project/GA17-13525S" target="_blank" >GA17-13525S: Sources of strong gravity and their astrophysical meaning</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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