Jet53man: Created page with "The gravitational potential (both inside and outside) of any axisymmetric mass distribution may be determined from the following integral expression that we will refer to as t..."

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Created page with "The gravitational potential (both inside and outside) of any axisymmetric mass distribution may be determined from the following integral expression that we will refer to as t..."

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The gravitational potential (both inside and outside) of any axisymmetric mass distribution may be determined from the following integral expression that we will refer to as the,
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<font color="#770000">'''Gravitational Potential of an Axisymmetric Mass Distribution (Version 1)'''</font>
{{ Math/EQ_CT99Axisymmetric }}
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and, <math>~K(\mu)</math> is the complete elliptic integral of the first kind. This Key Equation<sup>&dagger;</sup> may be straightforwardly obtained, for example, by combining Eqs. (31), (32b), and (24) from [http://adsabs.harvard.edu/abs/1999ApJ...527...86C Cohl & Tohline (1999)]; see also, [http://adsabs.harvard.edu/abs/2011MNRAS.411..557B Bannikova et al. (2011)], [http://adsabs.harvard.edu/abs/2012MNRAS.424.2635T Trova, Huré & Hersant (2012)], and [http://adsabs.harvard.edu/abs/2016AJ....152...35F Fukushima (2016)].

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<sup>&dagger;</sup>Building upon a previously little-known ''[[Appendix/Ramblings/CCGF#Compact_Cylindrical_Green_Function_.28CCGF.29|Compact Cylindrical Green's Function]]'' expansion, [http://adsabs.harvard.edu/abs/1999ApJ...527...86C Cohl & Tohline (1999)] derived an integral expression for the gravitational potential that is applicable to all mass distributions, irrespective of geometric symmetries. The Key Equation highlighted here — that is relevant to axisymmetric mass distributions — is a special case of this more general expression.

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Jet53man: Created page with "The gravitational potential (both inside and outside) of any axisymmetric mass distribution may be determined from the following integral expression that we will refer to as t..."