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→Creationistic explanation
More to the point, Carmeli and Hartnett showed that space itself expands in any [[galaxy]] or larger-sized object, and this expansion predicts a significantly increased rotational speed for any particle in that object. Specifically,
More to the point, Carmeli and Hartnett showed that space itself expands in any [[galaxy]] or larger-sized object, and this expansion predicts a significantly increased rotational speed for any particle in that object. Specifically,
<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 <math>\Pi</math> depends on the Bessel functions of the ratio r/2a.
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.
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,
<math>v^2 = \frac{GM}{r}</math>
<math>v^2 = \frac{GM}{R}</math>
predicted circular velocities much lower than observed. Hence Hartnett's conclusion that ''luminous masses are correct, but the physical model that predicts radial velocity is incorrect.'' Hence, as Einstein obviated the planet [[Vulcan]], Hartnett now claims to obviate dark matter.
predicted circular velocities much lower than observed. Hence Hartnett's conclusion that ''luminous masses are correct, but the physical model that predicts radial velocity is incorrect.'' Hence, as Einstein obviated the planet [[Vulcan]], Hartnett now claims to obviate dark matter.