Where did the matter for the Genesis Planet come From?
If, repeat if, the Genesis device had a method to attract particles from the nebula, forming the Genesis Planet would be easy. That is a big if, of course.
The average density of Earth is given as 5.514 g/cm3 (0.1992 lb/cu inch). The total mass of Earth is about 5.97237 times ten to the twenty fourth power kilograms. https://en.wikipedia.org/wiki/Earth
Planet Earth has a diameter of about 8,000 miles. A spherical volume of nebula 800,000 miles in diameter would have 1,000,000 times the volume of Earth. If its density is one millionth that of Earth, it would have the same amount of matter as Earth.
Suppose that the Mutara Nebula had a density one billionth (1 over 1,000,000,000) that of Earth. In that case a spherical volume of nebula with a diameter of 8,000,000 miles would have the same amount of matter as Earth.
Suppose that the Mutara Nebula had a density one trillionth (1 over 1,000,000,000,000) that of Earth. In that case a spherical volume of nebula with a diameter of 80,000,000 miles would have the same amount of matter as Earth.
Suppose that the Mutara Nebula had a density one quadrillionth (1 over 1,000,000,000,000,000) that of Earth. In that case a spherical volume of nebula with a diameter of 800,000,000 miles would have the same amount of matter as Earth. That volume would be about as large as the solar system out to Jupiter's orbit.
Suppose that the Mutara Nebula had a density one quintillionth (1 over 1,000,000,000,000,000,000) that of Earth. In that case a spherical volume of nebula with a diameter of 8,000,000,000 miles would have the same amount of matter as Earth. That volume would have about twice the diameter and eight times the volume as the solar system out to Neptune's orbit.
But Nebulae are really, really thin. According to Wikipedia;
most nebulae are far less dense than any vacuum created on Earth – a nebular cloud the size of the Earth would have a total mass of only a few kilograms.https://en.wikipedia.org/wiki/Nebula
So a volume of nebula would have to have about one to six times ten to the twenty fourth power the volume of Earth to have as much matter as the Earth. So it would have to have a diameter of about one to six times ten to the eighth power the diameter of the Earth. That would be a diameter of about 800,000,000,000 to 1,456,000,000,000 miles, much less than a light year of about 5,878,000,000,000 miles.
But possibly the Mutara Nebula was collapsing to form stars and planets. In that case it would be much more dense than an ordinary nebula and the Genesis device might have had to suck matter in from a much smaller volume of space.
A sun was clearly seen coming from behind the Genesis planet during Spock's funeral, indicating that a sun had already formed in the Mutara Nebula, which thus must have been very thick - for a nebula, that is.
(However, an alternate theory is that the Genesis device formed a satellite for the Genesis planet and built giant fusion reactors in it to power giant lights to light and heat the Genesis planet and thus the "sun" was actually an artificial sun satellite made by the Genesis device.)
Dark matter was only believed to be in the outer halos of galaxies. But in 2015 a new study suggested the presence of dark matter in inner regions of our galaxy much nearer to our solar system - possibly even within our solar system.
http://earthsky.org/space/dark-matter-in-the-inner-milky-way
If correct, perhaps there is dark matter in the Mutara Nebula, possibly many times as dense as the ordinary matter. Maybe the Genesis device sucked in dark matter from a much smaller radius than would have been needed for ordinary matter and transformed it into a type of ordinary matter called protomatter.
SAAVIK: It's time for total truth between us. This planet is not what you intended, or hoped for, is it?
DAVID: Not exactly.
SAAVIK: Why?
DAVID: I used protomatter in the Genesis matrix.
SAAVIK: Protomatter. An unstable substance which every ethical scientist in the galaxy has denounced as dangerously unpredictable.
DAVID: But it was the only way to solve certain problems.
http://www.chakoteya.net/movies/movie3.html
And then the protomatter (in this theory dark matter turned into ordinary matter) soon reverted into dark matter, destroying the Genesis Planet.
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