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In this paper we derive a novel circular velocity relation for a testparticle in a 3D gravitational potential applicable to every system ofcurvilinear coordinates, suitable to be reduced to orthogonal form. As anillustration of the potentiality of the determined circular velocity expressionwe perform the rotation curves analysis of UGC 8490 and UGC 9753 and weestimate the total and dark matter mass of these two galaxies under theassumption that their respective dark matter halos have spherical, prolate andoblate spheroidal mass distributions. We employ stellar population synthesismodels and the total HI density map to obtain the stellar and HI+He+metalsrotation curves of both galaxies. The subtraction of the stellar plus gasrotation curves from the observed rotation curves of UGC 8490 and UGC 9753generates the dark matter circular velocity curves of both galaxies. We fit thedark matter rotation curves of UGC 8490 and UGC 9753 through the newlyestablished circular velocity formula specialised to the spherical, prolate andoblate spheroidal mass distributions, considering the Navarro, Frenk and White,Burkert, Di Cintio, Einasto and Stadel dark matter halos. Our principalfindings are the following: globally, cored dark matter profiles Burkert andEinasto prevail over cuspy Navarro, Frenk and White and Di Cintio. Also,spherical/oblate dark matter models fit better the dark matter rotation curvesof both galaxies than prolate dark matter halos.

monthly notices of the royal astronomical society

General circular velocity relation of a test particle in a 3D  gravitational potential: application to the rotation curves analysis and  total mass determination of UGC 8490 and UGC 9753