How Large is the Union?
In a recent episode of The Orville, probably "All the World is Birthday cake" the Orville detected a signal from a distant star and traveled beyond the Union borders to make first contact with the inhabitants.
The star was Gamma Velorum.
Gamma Velorum is about 342 parsecs or about 1,115 light years from Earth.
https://scifi.stackexchange.com/questions/204077/has-the-gamma-velorum-star-system-been-mentioned-in-a-show-or-movie/204100#204100
So if the Union is a compact spherical region of space centered on Earth, Earth and other members of the Union should have explored to a distance of less than about 1,000 light years from Earth, to chose an arbitrary figure. That would be sphere with a radius of 1,000 light years and a diameter of 2,000 light years.
In the region of space near our solar system the average stellar density is 0.004 stars per cubic light year.
So a sphere of space with a radius of 250 light years and a diameter of 500 light years would have a volume of 65,400,000 cubic light years and thus contain about 261,600 stars. If 10 percent to ninety percent of those stars have planets, that would make 26,160 to 235,440 to stars with planets.
So a sphere of space with a radius of 500 light years and a diameter of 1,000 light years would have a volume of 524,000,000 cubic light years and thus contain about 2,092,800 stars. If 10 percent to ninety percent of those stars have planets, that would make 209,280 to 1,883,520 stars with planets.
So a sphere of space with a radius of 750 light years and a diameter of 1,500 light years would have a volume of 1,770,000,000 cubic light years and thus contain about 7,080,000 stars. If 10 percent to ninety percent of those stars have planets, that would make 708,000 to 6,372,00 stars with planets.
So a sphere of space with a radius of 1,000 light years and a diameter of 2,000 light years would have a volume of 4,190,000,000 cubic light years and thus contain about 16,760,000 stars. If 10 percent to ninety percent of those stars have planets, that would make 1,676,000 to 15,084,000 stars with planets.
It seems likely that even the sphere with a radius of only 250 light years would be large enough to contain the entire Union.
By comparison, the disc of our Milky Way Galaxy is about 50,000 light years in radius (100,000 light years in diameter) and about 1,000 to 2,000 light years thick. Thus there could easily be room for 10,000 space governments the size of the Union in the galaxy.
So which real stars have been mentioned in The Orville?
I read somewhere that Deneb was mentioned in one episode of The Orville. Deneb is believed to be about 2,615 light years, plus or minus 215 light years, from Earth, which may be a problem for the consistency of The Orville.
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