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Galaxy Rotation Curves

Tue Mar 31, 2015 8:05 pm

Everyone is now familiar with the problem of galaxy rotation curves, and how it has given rise to speculations about galaxies containing dark matter. The problem was first announced by American astronomers Vera Rubin and Kent Ford in 1975, who collaborated to show that galaxies displayed a flat rotation curve and did not exhibit the expected Keplerian motion.

Unable to explain such flat rotation curves, theoreticians proposed that there had to be additional invisible matter in the galaxy in order to account for the flat rotation curve, and it was coined "dark matter".

Keplerian orbital velocity follows the function;

\[v = \sqrt{\frac{GM}{r}}\]

We see when plotting the keplerian function for increasing radius, we get a velocity curve with exponential decay as in the yellow scetch below. (Google "galaxy rotation curves" to see excamples of real plots)

galaxy rotation curve
Blackboard_rot_curve.png (42.86 KiB) Viewed 5576 times

Keplers law describes planetary motions with great accuracy, but somehow fails to describe orbital velocities of stars in galaxies, why is this?

Confident that Ground Potential would solve this problem, I started thinking about this and soon realised how a flat rotation curve was perfectly normal, it was instead Keplers law which was an anomaly.

According to GPT, velocity of orbiting bodies ought to increase as radius increases, because \( \Delta v \) is proportional to \( \Delta \phi \) so if GPT is correct, then was Kepler wrong?

It appears Kepler made a rather naive assumption, namely that planets move forward in time which turns out to be wrong, at least when looking up from a lower potential to a higher potential.

If we take the sun to be the reference point, the arrow of time points towards the centre of gravity i.e. the past is radially outwards, therefore an observer on the Sun is temporally ahead of the planets which indeed move backwards relative to the sun, so the velocities are subsequently negative. Therefore the sum of the negative velocities from consecutive Kepler orbits will result in a real velocity increase.

Planet Orbital Velocity
data-table.png (119.79 KiB) Viewed 5449 times

In the table above we can see how the forward velocity assumption differs from the retro temporal motion clearly changing the velocity curve as seen in the chart below.

Decreasing negative values resulting in increasing velocity overall.

Planet Rotation Curve
planet-plot.png (67.33 KiB) Viewed 5449 times

In the following plot I have lifted the negative velocity up into the positive number line by summing the sign reversed negative velocities.
Combined Rotation Curve
combined.png (36.99 KiB) Viewed 5449 times

So I have deliberately plotted the rotation curve in the positive quadrant to show the similarity between my plot and those measured by astronomers, like this one below. It should however appear in the bottom quadrant of the graph.

M33 Galaxy
M33_rotation_curve_HI.png (245.15 KiB) Viewed 5576 times

My conclusion is, that the temporal direction of an orbiting body depends on the potential of the observer, so for an observer looking down into a gravitational well with orbiting bodies, these bodies will appear to move according to Keplers law, ie faster the further down the well they orbit, but for an observer standing at the bottom of a potential well, looking up, the orbiting bodies move backwards at increasing velocities as the radius increases (non Keplerian motion).

When we observe a galaxy from Earth, we are looking into the past, GPT states that potential falls over time, so we should expect to se galaxies follow non Keplerian velocity curves, which indeed we do.

According to GPT there is no need to postulate any additional dark matter to explain galaxy rotation curves, they appear more or less excactly as they should.


PS: If you agree with my conclusion above, help me like, share & tweet the good news, so all the scientists trying to find dark matter can do something more useful :)
Last edited by Steven Sesselmann on Sat Apr 11, 2015 4:12 pm, edited 8 times in total.
Reason: Sorry, had to amend the velocity function to reflect the sum of differences rather than the sum of velocities - SS

Re: Galaxy Rotation Curves

Mon Apr 06, 2015 9:35 pm

In this sketch I show how the backwards moving planets give the appearance of forward motion. The apparent forward motion is an optical illusion and would have been less obvious if there were more planets in orbits. the fact that we only have a few planets means that their relative forward motion appears more obvious than their backwards motions.

Planetary Orbits
revolution.png (59.7 KiB) Viewed 5485 times

Keplers law describe the forward motion of planets, which gives us the incorrect sum for the velocity.

This discovery is a direct prediction of GPT, as Keplers law of diminishing velocity with increasing potential was simply incompatible with GPT.

In GPT the relative velocity between two bodies follows \( \Delta V = c*(\frac{\Delta \phi}{\Phi})\) therefore velocities in consecutive orbits should/must increase with increasing radii.

Pretty revolutionary isn't it ?


Re: Galaxy Rotation Curves

Mon Jun 15, 2015 1:36 pm

Here is a nice animation on Wikipedia showing prograde and retrograde motion of the planets.

https://en.wikipedia.org/wiki/Retrograd ... deBaan.gif

The problem here is I don't think the interpretation is correct, because the planets currently believed to be rotating in a prograde fashion are retrograde and vise versa.

Re: Galaxy Rotation Curves

Tue Jun 16, 2015 11:31 am

As an ultimate test to see weather relative motion is positive or negative we can imagine having a very long string on a spool, then tying one end of the string to the ground and place the spool on the moving object.

spool.jpg (20.71 KiB) Viewed 5338 times

If the spool is unwinding, then the relative motion is negative, ie. it is receeding, which confirms it has higher potential than ground potential,on the other hand if the string is winding up on the spool, the velocity is positive, confirming that the object is approaching, and therefore of lower potential than ground.

This may seem like an obvious argument, but when it comes to planetary motion, Kepler's law contradicts the obvious and should therefore be wrong. If one were to tie one end of a string to the ground on earth and place the spool on the moon, it is obvious that the spool would be unwinding, therefore the moon is receding in its orbit, and not approaching.

Now take this concept one step further, hammer a peg into Mercury, and tie a string to Venus, then continue the string to Earth, Mars, Jupiter and Saturn, and it will immediately become obvious that these planets are moving in a retrograde fashion with increasing velocity, and not with prograde motion as currently believed to be the case.

Solar System
solarsys_poster.jpg (153.58 KiB) Viewed 5338 times

Why does it matter which way the planets rotate?

It does because, retrograde motion produces the same flat rotation curve as we see in Galaxies, which means there is no need to postulate additional dark matter in order to explain galaxy rotation rates.

Read this thread from the beginning to reveal why and how.
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