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Could the requirement of a dark matter for the missing mass in the universe simply be explained by objects having high relativistic mass change with respect to other objects?

If this is not the case, how is it explained mathematically?

m_power
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  • @KyleKanos my question has some similarities, but I want a mathematical explanation. – m_power Apr 07 '17 at 16:42
  • what objects? do you mean explain the galaxy rotation curves https://en.wikipedia.org/wiki/Dark_matter#Galaxy_rotation_curves ? – anna v Apr 07 '17 at 16:53
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    the speeds in the rotational curves are at most 200 km/sec page 2 here http://www2.astro.psu.edu/~caryl/a480/Lecture10.pdf . the velocity of light is 300.000 km/sec so these are not relativistic velocities. – anna v Apr 07 '17 at 16:59
  • @anna that's the speed of observable objects? – m_power Apr 07 '17 at 17:16
  • of luminous masses in the galaxy – anna v Apr 07 '17 at 17:19
  • @anna so we actually have no idea of what the average speed of non- luminous masses in the galaxy is? – m_power Apr 07 '17 at 17:22
  • that is why it is called dark matter. – anna v Apr 07 '17 at 17:23
  • But in the theory of dark matter, is it assumed that the average speed of non-luminous objects is similar to the average speed of luminous objects? – m_power Apr 07 '17 at 17:30
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    It is assumed they have masses so they get affected by gravity the same way. But they interact very little with each other or luminous particles, so they don't collide as much or clump non gravitationally, so they can be affected by different forces and have different velocities and average separations. In the Bullet Cluster you can see the dark matter and luminous matter separate because of collisions of luminous matter, and little of that for dark matter. – Bob Bee Apr 08 '17 at 08:10

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This is the typical rotational curve of a galaxy:

rotcurvegal

Rotation curve of a typical spiral galaxy: predicted (A) and observed (B). Dark matter can explain the 'flat' appearance of the velocity curve out to a large radius.

The red curve is what the luminous mass shows, the blue is what is expected if the luminous mass were the only mass in the system. To make the two curves agree one has to assume a lot of non luminous(dark) matter .

The arms of spiral galaxies rotate around the galactic centre. The luminous mass density of a spiral galaxy decreases as one goes from the centre to the outskirts. If luminous mass were all the matter, then we can model the galaxy as a point mass in the centre and test masses orbiting around it (similar to the solar system). From Kepler's Second Law, we expect that the rotation velocities will decrease with distance from the centre. This is not observed. Instead, the galaxy rotation curve remains flat as distant from the centre as the data is available.

In this link(page2) one gets an estimate of the scale of speeds, the maximum is around 150 km/sec. The velocity of light is 300.000km/second so the motions are non relativistic, newtonian mechanics should be adequate in explaining orbits. Thus the need for dark matter arose.

anna v
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No. First of all, relativistic mass is an outdated concept that is no longer used in modern physics. In modern usage, the mass of an object is invariant, that is, it is the same in every reference frame regardless of how fast it is moving with respect to that frame. It is just the energy of the object that changes as the object increases in speed. General Relativity describes how gravity behaves given the energy of an object. However, unless the object is moving very close to the speed of light, the energy of the object is approximately equivalent to just the mass of the object (times the speed of light squared). This is the case for stars moving around the center of a galaxy, which is what first allowed us to know that dark matter is present. Accounting for the additional energy of the stars due to their motion would change the equations only very slightly.

Travis
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  • Are you telling that the equation E = $\gamma$mc² is an outdated concept? – m_power Apr 07 '17 at 17:26
  • m_power: No, that equation is correct and gives the energy of the object. – Travis Apr 07 '17 at 18:15
  • So what relativistic mass concept are you referring to? Because for me, the relativistic mass is $\gamma m$. – m_power Apr 07 '17 at 19:03
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    $\gamma m$ is outdated as something you can call relativistic mass. It gets confusing because it's easy a to see and need to analyze particles and collisions in different frames of reference, and then better to label things by invariants if you can. – Bob Bee Apr 08 '17 at 08:13