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Could dark matter or dark energy be explained by a massive amount of 'mass' creating far reaching gravity far beyond our galaxy? Pulling things away from us at an accelerated rate? Or maybe a 'sucking' effect of nothingness pulling space/mass?


marked as duplicate by Kyle Kanos, user108787, Rob Jeffries, Jon Custer, Qmechanic Nov 29 '16 at 14:28

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Dark matter can be best understood according to Newtonian mechanics and Gauss' law. We start with the Newtonian force law $$ \vec F~=~-\frac{GMm\vec r}{r^3}. $$ This is equated to $ma$ by Newton's second law and we then consider the field $\vec f~=~\vec F/m$.Consider the mass $M$ in a region of space with radius R and bounded by an sphere with an area $A~=~4\pi R^2$. We then integrate the above force over this sphere with normal vector outwards at every place so that $d\vec a$ at a radial direction means $$ \int\vec f\cdot d\vec a~=~-4\pi GM. $$ This Gauss' law result defines gravity according to the source of the field in a region or volume of space bounded by a surface. In a crude sense the force law can be “reconstructed” as $|f||A|~=~4\pi GM$ and then divide by the area $A~=~4\pi R^2$.

Let us modify this slightly by considering the mass in this volume as due to the distribution of matter with density $\rho~=~M/(4\pi R^3/3)$ so that $$ f 4\pi R^2~=~-4G\pi\rho R^3/3. $$ Then the force law, or force per mass (acceleration) inside this region with mass density $\rho$ is $$ f~=~-G\rho R/3. $$ This force is the same as the spring force $F~=~-kx$ and the motion of a test mass in this region will obey the equations of motion of the two dimensional harmonic oscillator, here assuming motion in the plane of the galaxy. The angular frequency of the oscillator is $\omega~=~\sqrt{k/m}$, which is independent of the magnitude of the orbit.

The motion of a test mass in this region has a periodicity around the region that is independent of the radius of the orbit. This orbit is not the same as what is derived from Newton's laws or equivalently Kepler's third law $T^2~\propto~R^3$. What the astronomer Zwicky realized is that the orbits of stars in a galaxy are mixture of Kepler's law and the motion of a 2-d harmonic oscillator. The diagram below illustrates the predicted motion of stars in the Milky Way in red and the observed in blue, with the yellow dot representing the sun. This leads to the conclusion there is likely some galactic halo of mass surrounding the galaxy. This matter so far appears to not be directly observable, but only observable from its gravitational effects. The diagram here is taken from the wikipedia page on the galactic halo. enter image description here


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