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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)

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.

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.

In the following plot I have lifted the negative velocity up into the positive number line by summing the sign reversed negative velocities.

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.

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.

Steven

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 :)

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 4296 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 4169 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 4169 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 4169 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 4296 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.

Steven

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*Steven Sesselmann

Only a person mad enough to think he can change the world, can actually do it...

Only a person mad enough to think he can change the world, can actually do it...