The exterior gravitational potential of toroids

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The exterior gravitational potential of toroids

Popis výsledku v původním jazyce

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 &apos;similarity&apos; 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.

Název v anglickém jazyce

The exterior gravitational potential of toroids

Popis výsledku anglicky

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 &apos;similarity&apos; 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10300 - Physical sciences

Projekt

<a href="/cs/project/GA17-13525S" target="_blank" >GA17-13525S: Zdroje silné gravitace a jejich astrofyzikální význam</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Monthly Notices of the Royal Astronomical Society

ISSN

0035-8711

e-ISSN

—

Svazek periodika

494

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

14

Strana od-do

5825-5838

Kód UT WoS článku

000539097800092

EID výsledku v databázi Scopus

2-s2.0-85096998209