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→Creationistic explanation
<math>v^4 = GM\frac{2}{3}a_0\Bigg\{\bigg(\frac{r}{2a}\bigg)^{9/2} 8 \Pi^{3/2}\Bigg\}</math>
<math>v^4 = GM\frac{2}{3}a_0\Bigg\{\bigg(\frac{r}{2a}\bigg)^{9/2} 8 \Pi^{3/2}\Bigg\}</math>
where r = radial position, a<sub>0</sub> is a critical acceleration value, G is the gravitational constant, M is the total luminous mass of the galaxy (or group or cluster or supercluster) involved, and
where r = radial position, a<sub>0</sub> is a critical acceleration value, G is the gravitational constant, M is the total luminous mass of the galaxy (or group or cluster or supercluster) involved, and <math>\Pi</math> depends on the Bessel functions of the ratio r/2a.
<math>\Pi</math> depends on the Bessel functions of the ratio r/2a.
Hartnett tested the above equation against the observed values of circular velocity of tracer gases in object NGC 3198 as a function of radial distance from the center. He found that this equation fit the observations almost exactly, while a traditional Newtonian equation for radial velocity,
Hartnett tested the above equation against the observed values of circular velocity of tracer gases in object NGC 3198 as a function of radial distance from the center. He found that this equation fit the observations almost exactly, while a traditional Newtonian equation for radial velocity,