Why is 96% of the Universe " Dark"? Part V

-1598 - The previous Review #1597 calculated that 73% of the Universe was composed of Dark Energy, leaving the 27% composed of matter. How did we learn that 85% of that matter was “ Dark Matter” and not ordinary matter?

----------------------- # 1598 - Why is 96% of the Universe “ Dark“? ( Part V of VI )

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- How did we learn that 85% of the Matter in the Universe was Dark Matter?

---------------- ( 23% / 27% is 85% ).

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- In this calculation use Redshift calculations to get orbital velocities. From orbital velocities we can calculate the mass needed to create their stable orbits. Also called radial velocity, when the velocity is coming towards us it is Blueshifted. When the radial velocity is going away from us it is Redshifted.

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- Kepler’s 3^rd law of motion tells us that the period of orbits squared is proportional to the radius of orbits cubed.

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---------------- periods ^2 = k * radius^3

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------------------ p^2 = k * r^3

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- I am using “r” for radius but if the orbit is elliptical , not a circle, the semi major axis of the ellipse is used in this calculation. Later in history Isaac Newton made this proportion an equality by defining the constant of proportionality. The constant includes the Gravitational Constant, “G”, and the masses , “M” , involved in the orbit.

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------------------ p^2 = 4* pi^2 * r^2 / G * M

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- We can substitute the period with the radial velocity using the relationship that the circumference, 2 * pi * r, divided by the period equals the velocity.

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------------------ p = 2 * pi * r / v

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- Substituting this into Newton’s equation:

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----------------- 4 * pi^2 * r^2 / v^2 = 4 * pi^2 r^3 / G * M

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---------------- M = r * v^2 / G

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- The gravitational constant , G = 6.67 * 10^-11

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- Using the Redshift method the velocity was measured to be: v = 13.7*10^3 meters / second for a planet orbiting a star in another galaxy. The planet is an exoplanet that is transiting a star in another galaxy.

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- We estimate the star to be 1/4^th the size of our Sun ( 25% Solar Mass).

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- We estimate the radius of orbit to be 1.5 * 10^11 meters, about the same radius as our Earth, 93 million miles.

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- We assume the Gravitational Constant to be the same every where in the Universe.

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----------------------- M = 1.5*10^11 * (13/7 *10^3 )^2 / 6.67* 10^-11

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---------------------- M = 42.2* 10^ 28 kilograms.

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---------------------- 1 Solar Mass = 2 * 10^30 kilograms

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---------------------- Mass = 0.21 Solar Mass

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- The mass of the star is 21% Solar Mass, very close to the 25% that we estimated.

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- Therefore we think that the calculations are the same every where, not just in our galaxy, but, in every other galaxy. When we do these same calculations for stars orbiting the center of their galaxies we get a calculation for mass that is 5 times greater than all the mass we can see in counting all the stars in the galaxy.

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- The same happens when we do the calculation for a cluster of galaxies orbiting a cluster center of gravity. Stars and galaxies would be flying out of their orbits if it were not for some unseen mass existing around the galaxies. We call this Dark Matter because we can not see it and we do not know what it is.

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