A Different Hypothesis in Regard to Dark Matter and Dark Energy

The 1/R dependence is a given, from Vera Rubin's original observations of galactic rotation. It's derivation, however, is something I would expect to be much more difficult to do than the three body problem, since it is already an n-body problem. You've given an answer, which is fine, but have not shown your work.

If this was derived using modified Newtonian dynamics (MOND), that model has already been shown to be in error for explaining the 1/R velocity dependence despite the fact that some treatments come up with the necessary 1/R expected.

Not to name-drop, but several of my local mensa group are still good friends and stay in touch with Vera. If you have a real idea of what you are doing, I could commend it to her for you.

 

Log in or Sign up to hide all adverts.

Hello Danshawan

I truly appreciate you taking the time to discuss this with me.


My derivation of why the variation of the rotational gravitational force with 1/r is actually very simplistic. Probably too simplistic, but it worked for me.


First I converted Newton’s equation so that the important factor involved in it was energy as opposed to mass as the equation would normally be written. As we know from Einstein’s equation that there is an equivalence between mass and energy. I did that as follows:


F = (G/c^2)*(M*c^2)*m/r^2

Where (M*c^2) is the energy contained within the mass.


The next assumption I made was that force is uniform and proceeds from a central point within the mass. Einstein’s way of looking at it would be that space was being distorted by the mass. I believe this would also be such that the central point of the mass was the low point that everything would be trying to fall into. From this I concluded that the gravitational force (force density if you wish) would tend to diminish as the surface area out from this central point becomes larger. Thus F would fall off with the inverse of the surface area.

F being proportional to 1/A or 1/(4πr^2). This is the normal form for Newton’s formula.

However, the force from a rotating cylinder (in my opinion) would not originate from a single point, but equally along the central axis of rotation. Or in other words space would not be distorted uniformly. So the basis for my assumption in regard to rotational gravity is that there is a non-uniformity of spatial deformity.

In fact what I’m suggesting is that space is distorted such that a “trough” forms out from the periphery of the cylinder which appears as an attractive force for other masses and that a bulge forms at the ends of the axis which appears as a repulsive force.



An analogy for this is to imagine a cylinder spinning very rapidly in the air. What happens here is that there would be a vacuum created at its poles and a pressure created at its equator. I realize this is a poor analogy of what actually happens, but then considering a ball thrown onto a sheet to illustrate how mass distorts space is not a very accurate representation either.

In the case of the rotational gravitational force it would also be expected that the force would diminish with expanding surface area as one proceeds out from the axis. But since the force is considered to be emanating more or less equally along the axis, then this surface area is equal to πDr. Where D is the length of the axis and is a constant.

F would then be proportional to 1/(πDr)

I was therefore able to replace 4*πr^2 in Newton’s equation with π*D*r.

Thus the equation for the rotational gravitational force becomes:

Fr = (G*4/(c^2*D)*(M*Vr ^2)/r

I’m sure that you can probably throw lots of rocks at my rationale, but it worked for me.

I believe that the significance of what I am suggesting is that this theory has the potential to not only answer some of the phenomena presently being attributed to “Dark Matter”, but also suggests the possibility of a repulsive force that could help to explain “Dark Energy”.


As far as my interfacing with ‘Vera, I’m not sure that I really have the expertise or background to converse with her at the same level that you would be capable of. What I’m really after is to put forward this theory to those in the physics/astronomy community who are still investigating theories that try to explain these perplexing phenomena without needing to incorporate “Dark Matter” and “Dark Energy”.

I have probably carried this theory as far as I am technically capable.

The true test of any theory, no matter how we try to explain it, lies in its ability to predict outcomes under various diverse conditions. Perhaps you have some thoughts how this might be done in this case.

 

Log in or Sign up to hide all adverts.

I do like part of your idea that mass movement of galactic matter (stars, planets, bass) and energy carries some additional gravitational attraction not pondered by things like General Relativity. GR, like MOND, falls short of explaining the 1/r velocity dependence in simulations. It's a big deal, because without explaining where the extra attraction comes from, the outer 1/3 of spiral galaxies have already achieved escape velocity, and so they should no longer be orbiting the distributed mass of a spiral galaxy.

Both GR and Newton gravitational dynamics suffer from enslavement of their central ideas to geometry based mathematics rooted in the centers of gravitational masses as though the idea that absolute space and absolute time had not died an ignoble death along with the luminiferous aether wind in 1905.

It's like Ptolemy and epicycles never really went away, and it's almost as disgusting an idea as a flat Earth, or turtles all the way down. Oh, for the simplicity of a single time zone! Simpler science for simpler people. Many computer generated stable solutions now exist for the three body problem. But nothing simple seems to work to explain spiral galaxies with 1/r velocities.

 

Log in or Sign up to hide all adverts.

Well, you could take what the galactic dynamics were telling you and infer that there was extra, non-luminous mass in the galaxy.

Then you could measure the galaxy with gravitational lensing to see if the amount of mass measured that was agreed with the rotation evidence.

Then you could look to cosmological measurements independent of galactic dynamics that suggest that there is quite a lot of non-luminous mass in the universe.

But to do this would be to build up a web of scientific evidence, mutually agreeing and supporting each piece of evidence. And that wouldn't be fun.

 

Thanks for the input:

One thing I did to check the efficacy of my equation was to back calculate what I would expect the solar system velocity around the Milky Way would be based only on my equation for rotational gravity.

The following is what I found.

Predicting the velocity of the solar system based on the preceding theory:

One way to test this hypothesis is to see how well it would predict the velocity of the solar system around the Milky Way.


Assuming that the bulk of the gravitational force on the solar system is due to the rotational gravitational force we can express it as follows:

G/(c^2 *4*D))*(M V^2)*m /R = m*v^2 /R


m = mass of solar system

v = velocity of solar system around the galaxy

V = rotational velocity of central mass

We can see that m and R will cancel out and transposing we get:


v =( G/(c^2 *4*D))*(M V^2))^.5


I’ve assumed M to = 1 million solar masses and

V = .5% of the speed of light
D = 22,000,000,000 meters


Therefore:

v = 137964 m/s
The actual v has been determined to be approximately 222,000 m/s

I think that this is remarkably good accuracy considering that the mass, velocity and diameter of the central (black hole) is not accurately known.

 

One additional calculation that I did was to determine how far a mass might be thrown from the axial ends of this rotating mass assuming that there was a repulsive force and that this force followed the same equation I have espoused for the attractive rotational force. How far would this mass travel during the life of the universe (i.e. 14 billion years)?

The calculations are as follows:

Another calculation we can do is to determine how far a mass would travel if it was subjected to the repulsive forces presumed to be emanating from the axial ends of the mass rotating at the center of our galaxy.


Let us assume that a mass equal to that of our solar system is sitting at a distance just beyond where the rotational forces of the rotating center are greater than the Newtonian gravitational forces.

We know that F = ma where F is the force, m is the mass the force is acting on and a is the acceleration being experienced by this mass.


a = F/m

a = dvs/dt

If we integrate we get

vs =( F/m)*t + vo

Where vs = velocity of above mass

vo = initial velocity

Knowing that vs = dx/dt and F = Ci*M*V2 *m/x

x = distance travelled


Then

x dx/dt = Ci*M*V2 *t + vo


Let us assume that vo = 0

Integrating and transposing we get:

x2/2 = G/(c2 *4*D )*M*V2 *t2 /2 + xo

x = (G/(c2 *4*D )*M*V2 *t2 + 2*xo ) 0.5

t = time traveled

Assuming vo = 0 is most certainly a bad assumption as it would be expected that at a time not to long after the big bang that vo would in all likelihood be close to that of the speed of light. However, in light of not knowing what it was we’ll assume it to be zero.

xo is essentially 0.

During the early age of the universe and the scale of distances we are looking at today, this is probably not a bad assumption.

If the age of the universe is 14 billion years and we insert this as t than we would calculate the distance travelled from the start of the universe to be 17 billion light years. This seems surprisingly close to what is observed.

I don’t think too much should be read into this at this point in time since the assumptions for the rotational velocity and mass at the center of the galaxy are still very uncertain and need to be verified.

Admittedly there is not enough evidence provided here to prove this hypothesis, but there is enough evidence to warrant more study.

 

Hello Danshawen

I have one additional question that I wonder if you could help me out with. It came about as I was contemplating the possibility of rotational gravity.

What I discovered was that I could predict the orbits and rotational velocities of the sun and the planets quite accurately while only knowing something about their geometric data and did
not need to take into account gravitational forces or mass.

The equation is as follows:

C* Vs^2*Rs^2=Vp^2*Rp

where C = 6.5E-5
Vs = suns surface rotational velocity
Rs = radius of the sun
Vp = velocity of planet
Rp = radius of the planet

This works just as well when applying it to the moons of the various planets. In particular it was very accurate in predicting the orbits of the moons of mercury.

It was not as accurate for the earths moon, but I suspect that this is due to the fact that the moon is approaching the same diameter as the earth.

This is obviously not an equation that is good for all occasions, but does seem to predict what eventually become stable orbits.

I'm sure this fact has already been derived by someone. I 'm curious to know what the derivation is.

 

Sorry Darshawen

Rp is the distance of the planet from the sun.