The galaxy is nearly a thousand light years thick; that is not a practical limit worth considering.
Space is far more vast than that. As a rule of thumb, assuming that stars are, on average, 3 or 4 light years apart, then for any volume of space the number of stars in that volume will double. So if you have one star (1) and 5 light years from it there are two other stars (3) and then double the number of stars every five light years...
If that spacing is consistent, a volume of space 100 light years across could have more than one million stars, all of them still (on average) 5 light years apart.
To put that in perspective: on the whole of the planet Earth, counting all incorporated cities, towns and villages with a population of more than, say, 50 people, there is somewhere upwards of 380,000 cities and towns. We don't know the exact number, because no one has ever bothered to count them all, and not all of them are even mapped. Think about that: 380,000 cities and towns, all on a single planet, and we don't even know for sure where all of them are. TRIPPLE that number, and then imagine that every single one of those towns is on a completely different planet, and THEN imagine that you have only been charting those planets for the last, say, 75 years. Then project this onto a three dimensional volume of space that is not 100, but actually closer to, say, 400 light years thick AND there are huge unexplored regions in between them.
There you begin to see the problem. Space is BIG, planets are small, and governments, countries and nations are smaller still.
Maurice said:
Actually, stellar density out here in the unfashionable end of the western spiral arm is about one star per cubic parsec, so in 100 cubic lightyears you'd have about 26,362 stars, about 1/38th of a million.
Sgt_G said:
I remember reading some place, perhaps in a Trek novel, that when such developing civilizations are discovered, the Federation places their planet and all planets within 10-15 light-years off-limits to provide said civilization room and resources to grow.
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Actually, stellar density out here in the unfashionable end of the western spiral arm is about one star per cubic parsec, so in 100 cubic light-years you'd have about 26,362 stars, about 1/38th of a million.
Interesting. In the game "Federation & Empire" (F&E), the map hexes are 500 parsecs across by 500 parsecs thick. I suggested that is there is an average of one stellar body every five parsecs cubes, there are one-million systems per hex. Further, using conservative estimates, if one were to assume that 10% of these are stars with planetary systems, and then 1% of those have planets worth visiting, that's about a thousand planets that one could "safely" put a mining base or military outpost on. Let's further estimate that 1% of these planets are Class-M and can support life without too much terraforming required. Therefore, by this math, there are approximately ten potential colony worlds in each F&E hex.
What you're telling me is my math is off by 125 to 1 ....... there's over a thousand Class-M planets per hex on the F&E map.
According to Wikipedia "Stellar Density":
Stellar density is the average number of stars within a unit volume. It is similar to the stellar mass density, which is the total
solar masses (MSun) found within a unit volume. Typically, the volume used by astronomers to describe the stellar density is a cubic
parsec (pc3). If compared in the entire universe the closest thing to the density of a star is 3 watermelons under the sun.
In the solar neighborhood, this value can be determined from surveys of nearby stars, combined with estimates of the number of faint stars that may have been missed. The true stellar density near the Sun is estimated as 0.004 stars per cubic
light year, or 0.14 stars pc−3. When combined with estimates of the stellar masses, this yields a mass density estimate of 4 × 10−24 g/cm3. The density estimate varies across space, with the density decreasing rapidly in the direction out of the galactic plane.
[1]
The locations within the Milky Way that have the highest stellar density are the central core and the interior of
globular clusters. A typical mass density for a globular cluster is 70 MSun pc−3, which is 500 times the mass density near the Sun.
[2] In the solar neighborhood, the stellar density of a star cluster must be greater than 0.08 MSun pc−3 in order to avoid tidal disruption.
[3]
If there are 0.004 stars per cubic light year, and there are about 34.64 cubic light years in a cubic parsec, there are about 0.1385 stars per cubic parsec. Thus there would be one million stars in a volume of about 250,000,000 cubic light years or about 7,220,216.6 cubic parsecs.
According to my calculations a space 100 light years in one dimension could contain a million stars if the other two dimensions were both 1,581.1388 light years.
A cube about 630 light years on each side would contain about 250,000,000 cubic light years and about 1,000,000 stars, A sphere with a radius of about 390 light years and a diameter of about 780 light years will have a volume of about 250,000,000 cubic light years and about 1,000,000 stars.
Shawnster said:
Instead of thinking of a civilization's territory as being contiguous, like most nations on earth, each star system should be viewed as an island, like the example above.
So, in reality, Federation, Romulan, Klingon etc... Territories could all be intermingled. Or a 3d map might look like a DNA helix with each species territory wrapping around the others.
With plenty of unclaimed stars mixed in.
Official and fan maps disagree, but it makes a lot of sense to think of a space realm as a set of dots instead of a solid area of space.
Interstellar treaties may allow each space realm to claim a spherical volume of space with a specific radius around each star system that it claims to rule.
And possibly each space realm is allowed to claim for its exclusive use narrow cylinders of space connecting each of its stars with about one to three of the neighboring stars also claimed by that space realm.
Thus a small space realm might look like a model of a simple molecule. And a large space realm might look like a model of a very complex molecule with hundreds and thousands of atoms.
And probably a 3-D space map would show different space realms partially overlapping or interpenetrating.
The official warp factors for TOS were too slow for many desirable plot elements. Since starships tended to travel at the speed of plot, sometimes they traveled at approximately the speed of the official warp scale, and sometimes they traveled tens, or hundreds of times as fast.
In the extreme case, "That Which Survives" the
Enterprise was thrown a vast distance away from a planet, stranding the landing party:
RAHDA: It doesn't make any sense. But somehow I'd say that in a flash we've been knocked one thousand light years away from where we were.
SPOCK: Nine hundred and ninety point seven light years to be exact, Lieutenant.
A light year is defined as the distance traveled by light in one Julian year, or 365.25 days. It thus contains 8,766 light hours, a light hour being the distance traveled by light in one hour. 990.7 light years contain 8,684,476.2 light hours.
RAHDA: We're holding warp eight point four, sir. If we can maintain it, our estimated time of arrival is eleven and one half solar hours.
SPOCK: Eleven point three three seven hours, Lieutenant. I wish you would be more precise.
Assuming that the entire trip at warp 8.4 takes 11.337 hours, the
Enterprise travels 8,684,476.2 light hours in 11.337 hours, at a speed of 766,029.47 times the speed of light. Warp 8.4 would be 8.4 cubed, or 592.704 times the speed of light. Thus the
Enterprise travels 1,292.4317 times as fast as it should at warp factor 8.4.
So I think that creators of new
Star Trek productions should acknowledge that and make 1,292.4317 the new magic number that constantly appears in various episodes, instead of 47.
One theory to explain how starships sometimes reach their destinations in less time than the warp factor formula allows is a theory that each solar system contains one or more space warps leading to other solar systems that may be tens, hundreds, or thousands of light years away.
Thus when the
Enterprise was thrown 990.7 light years, the computers calculated the fasted route through the space warps from its position to the planet where Kirk was stranded. At warp factor 8.4 they could travel 6,719.4852 light hours, or about 0.766 light years, in 11.337 hours.
So the
Enterprise would have traveled at warp 8.4 to the mouth of the nearest wormhole or space warp, appeared in a distant solar system, traveled at warp 8.4 to the mouth of another space warp, appeared in another distant solar system, and so on, for a total of 11.337 hours until reaching the planet Kirk was stranded on.
According to this theory a space realm would consist of many star system connected by space warps, each one being tens, or hundreds, or thousands of light years from the next one, as well as all the star systems the space realm might reach and annex by traveling though space outwards from the various star systems they reach through the space warps.
So when the Federation, or the Romulans, or the Klingons, reach a star system through the system of space warps, and make that system part of their realm, they might decide not to bother with colonizing or annexing any of its neighbors reached by travelling a few light years using warp drive. Or they might decide to colonize or annex some of the neighboring star systems reached by warp drive, and a claim a sphere of space with a radius of 5, or 10, or 20 light years, or some other radius, around that system.
Thus a 3-D map of space might include many dots or spheres of space claimed by various pace realms, each space realm using a different color, as well as showing many non claimed star systems.
