The theory
As indicated in the articleTheparadoxofgravitynotrespectingtheenergyconservationprinciple/ satellites are subject to a double different force, the gravitational one and the centrifugal one. This implies that the nearer a satellite is orbiting around the earth, the faster it has to move to win the bigger gravitational force and the other way round. To better describe this idea we have to introduce the concept of angular moment. This is the product of the impulse of the satellite ( I=mxv where I is the impulse, m is the mass of the satellite and v its speed) and the distance of the satellite from the Earth, R.
As a consequence, M*v*R is the angular moment of the satellite. In harmony with the energy conservation principle and as a consequence of Newton’s Laws of mechanics , the angular moment of a body orbiting around a planet or around a mass center keeps constant.
So, as the angular moment is L=M*v*R and R increases (the satellite moves further away from the Earth) v decreases. When, on the other hand, the satellite moves nearer to the Earth (R decreases) the speed will increase.
The same idea can also be applied to stars that rotate around the galaxy mass center in which they are set. This has been the subject of an interesting study made by Rubin and Ford, two scientists who have observed the speed of the stars that are moving in galaxies. When we consider the stars from the Earth, they appear as fixed in their relative position, that seems to be immutable in the years. Many constellations, for instance the Big Dipper, have been described thousands of years ago and still keep staying in the same position.
The scientific establishment however claims that stars have a big relative speed even when they always appear to be, night by night, in the same position while rotating from east to west.
Since to the average observer It could seem impossible to calculate the speed of stars that are so far from us and that appear immovable, Vera Rubin and Kent Ford, to overcome this problem, used the Doppler effect to give us an idea of the speed of the stars.
Doppler effect gives unexpected results
Doppler Effect
Doppler effect is the change in frequency of a wave when its source is in motion in respect of the observer. In the picture below the jet is departing from observer B and is approaching to observer A. Observer A will perceive the noise as more deep while B as more acute. The reason is that the wave, when the object that emits the light with a certain frequency is approaching, will produce a frequency that, when measured, will be higher (the light will be moved toward light blue) while, when it is departing, the frequency will be lower (the light color will shift toward red). In that way, by measuring the shift of the frequency of light waves from stars toward red or blue, you can deduce their speed in relation to the Earth.

Rubin and Ford applied the Doppler effect to evaluate the speed of the stars. Galaxies are made almost exclusively of stars and calculations should have given, as a result, that stars far from the center of the galaxy have a lower speed than stars nearer to the center of it. The results found by Rubin and Ford however didn’t match the expectations. The stars far from the centers were moving just as fast as those closer in. Rubin and Ford went on to examine about sixty spiral galaxies and always found the same situation.They discovered that the light of the stars is the same no matter of the distance.
This result is highlighted in the picture below. The dot line represents the theoretic expectations when considering the gravitational formulas. The continuous line represents the speeds actually measured with the Doppler effect.
Considering these sort of results maybe scientists feared they would finish to prove that gravitation theory was wrong. To get out of the impasse Rubin and Ford in 1974 introduced, beside the visible matter, a new concept, the obscure matter, an entity extending much further than the apparent boundaries of the galaxy and presenting much more mass than the normal matter. “What you see in a spiral galaxy is not what you get”, Robin concluded. The obscure matter was allowing scientists to say that even when the distance from the center of the mass greatly increases (r in the relation grows up), since M also grows due to the obscure matter, so the speed keeps constant.
The speed of the stars should follow this relation according to the gravitational theory:
Interesting enough is the fact that, up to now, there are no direct evidences for the existence of the dark matter because “it can’t be seen”. Scientists only point to “gravitational proofs”. They are convinced, in fact, that the obscure matter exists because stars move at a speed that is different from that they could expect on the basis of abstract calculations. They assume thus that gravitational theory is an undisputable basis from which to start.
But what to say about this question if the trouble originates from the same foundation? Could it be that the original trickery stays in the possibility that the basic gravitational formulas are not correct? In the opposite case we should really have direct proofs of the existence of the dark matter, but we have not: these proofs are missing.
But when, on the other hand, we consider stars as moving all together from east to west – from the point of view of an Earth observer , fixed on a dome that rotates over a stationary Earth, we will probably find an easier explanation of what has been measured with the Doppler effect.
Gracias guys, enlightening