It should be noted that the references at the end should be explored first to understand some dynamics and essentials of the investigation of the following work. When reading Newtons Principia, I was surprised to learn that he had objectively denied gravity as a drag phenomenon and in recent light of evidence discovered in which a star was found to drag space and time around with it, I felt the need to revisit his laws and implement the drag coefficient for the new physics. It has been an essential argument of mine for a while now that the supermassive black holes at the centers of most typical spiral galaxies will play the role of a spacetime polarization in which dark matter effects results from the same binding energy they harbour with trillions of solar masses.

To start off, Newtons law is:

[math]F = \frac{Gm^2}{R^2} = \frac{mv^2}{R}[/math]

He went off to find a unification to prove that Keplers law for planetary motion around the sun was justified. To do this he took the rotation velocity

[math]v_{rot} = \frac{2 \pi R}{t}[/math]

And he plugged it in giving

[math]G(\frac{m}{R})^2 = \frac{m(2 \pi R/t)^2}{R}[/math]

By rearranging he found that Keplers third law was obtained as

[math]\frac{R^3}{t^2} = \frac{Gm_{sun}}{4 \pi^2} = \frac{\mu_{sun}}{4 \pi^2}[/math]

It is interesting that he wholeheartedly objected to the drag interpretation of gravity since all the planets part from one, rotates in the direction of the spin of the sun. That rule even extended to spiral galaxies in which there is no typical spiral galaxy that rotated in a direction opposite to the black hole they harbour. This was no coincidence in my eyes and strongly suggested to me that the thing we call dark matter was in fact produced from a more local effect inside of the galaxies themselves as opposed to some fundamental field rendering it superfluous and excessive. I will continue from the drag formula I created to predict a heuristic approach to explaining the drag dynamics of the supermassive black hole, from it the binding energy is found as

[math]E_{binding} = F_{drag} \cdot \int dR = \frac{1}{2}f(\rho + 3P)\ \int dV_{smbh}[/math]

The drag in this case changes linearly to the volume of the supermassive black hole and I also invited to relativistic correction of [math]3P[/math] where [math]f[/math] is the gravitational drag coefficient. We can rewrite the last equation as

[math]E_{binding} = m_{drag}g \cdot \int dR[/math]

In which we define

[math]g \equiv \frac{m_1}{m_2}\frac{v^2}{R} = \frac{Gm}{R^2}[/math]

Where [math]Gm[/math] is the gravitational parameter denoted as [math]\mu[/math] and has dimensions of [math]Rv^2 = Gm[/math].

where [math]g[/math] is the usual gravitational acceleration, by solving for the drag coefficient I get

[math]f \equiv 2g(\frac{R}{v^2}\frac{V_2}{V_1}) = \frac{4 \pi^2 R^2}{v2t^2} = \frac{4 \pi^2 R}{t^2}\frac{R}{v^2} = \frac{4 \pi^2 R}{t^2}g^{-1}[/math]

Distributing the factor of acceleration, we get

[math]f(\frac{Gm}{R^2}) = \frac{4 \pi^2R}{t^2}[/math]

and by distributing the radius squared we obtain Keplers third law under the drag coefficient interpretation of gravity:

[math]f \cdot Gm = \frac{4 \pi^2R^3}{t^2}[/math]

From here I wanted to get a little bit more creative, and found that by plugging in the rotational velocity into the gravitational acceleration defined near the beginning of the work I could obtain:

[math]g \equiv (\frac{m_1}{m_2})\frac{4 \pi^2 R^2}{t^2 R}[/math]

Multiplying through by a mass term yields Newtons force equation with a twist, mind the pun, because we obtain a quantity known as the rotational inertia [math]mR^2[/math]

[math]F_{drag} \equiv mg = (\frac{m_1}{m_2})\frac{4 \pi^2 mR^2}{t^2 R}[/math]

and can be rearranged for the rotational energy associated to the moment of inertia with a double time derivative

[math]F_{drag} \cdot \int dR = 4 \pi^2 (\frac{m_1}{m_2}) \ddot{I_{rot}}[/math]

This subtle unification of gravity drag into Newtons formula will provide a toy model, or starting point towards a revised Newtonian law that satisfies the new experimental evidence.

**References**

https://en.wikipedia...zeau_experiment

https://en.wikipedia...Reynolds_number

https://en.wikipedia...rag_coefficient

**Edited by Dubbelosix, 27 March 2020 - 07:16 AM.**