Rant - The Scale of the Federation

"Space," it says, "is big. Really big. You just won't believe how vastly hugely mindboggingly big it is. I mean you may think it's a long way down the road to the chemist, but that's just peanuts to space. Listen ..." and so on.

[...]

To be fair though, when confronted by the sheer enormity of distances between the stars, better minds than the one responsible for the Guide's introduction have faltered. Some invite you to consider for a moment a peanut in reading and a small walnut in Johannesburg, and other such dizzying concepts.

The simple truth is that interstellar distances will not fit into the human imagination.

Even light, which travels so fast that it takes most races thousands of years to realize that it travels at all, takes time to journey between the stars. It takes eight minutes from the star Sol to the place where the Earth used to be, and four years more to arrive at Sol's nearest stellar neighbour, Alpha Proxima.

For light to reach the other side of the Galaxy, for it to reach Damogran for instance, takes rather longer: a hundred thousand years.

The record for hitch hiking this distance is just under five years, but you don't get to see much on the way.

- Douglas Adams

The Scale of the Federation

This is an older article, brushed up and reposted by request.

Many times when I am talking with people about one of my favorite subjects, I.E. starships, the matter arises as to how crowded space in a given region would be. It has been claimed that my 40,000 ship Starfleet is too large by far.

I shall scatter one hundred grains of black sand on a mile of white beach. Thousands of ships can be in Earth orbit, and never see each other. The volume of space involved is beyond easy comprehension. I will try and bring this down to a size the human brain can grasp.

I have nice series of images that helps put it in perspective. 100 pixels = 1 meter then 10 pixels = 1 meter and so forth. We start with a tie fighter and an man for comparison. We go to the Millennium Falcon, and a runabout compared to the space shuttle. Then the Defiant and such ships compared with with the Titanic. We move out to Enterprise sized ships, then the borg cube dwarfed by the Deathstar which is a pebble next to the Moon. the Moon is only 2,160 miles across, the Earth 7960. as we move up the scales.

If the sun is the size of a basketball, the Earth is a city block away and the size of a bullet point in 12 point type. Pluto is 2.5 miles away. The Deathstar is microscopic, the Enterprise nanoscopic. The Kingdom of the Sun reaches out about twice the distance from Pluto in terms of the Oort cloud and the orbits of comets. So with the sun the size of a basketball, the solar system is a globe 10 miles across, and the average ship is the size of a water molecule.

Now, how crowded are those "several thousand ships"?

Now that these images have sunk in, lets talk interstellar distance.

The distance from the Sun to the Earth is 93 million miles, or 1 AU Pluto is 39 AU from the sun. 3 billion 627 million miles. Four times that number, the size of the "Kingdom of the Sun", is 14 billion, 80 million miles. A light year is 5 trillion, 886 billion, 938 million, 432 thousand miles, or 406 diameters of the Kingdom of the Sun. 10 x 406, that is 4060 miles for one light year. That is slightly larger that half the diameter of the real Earth for our basketball light year. Proxima Centauri, the nearest other basketball lies 17,133 miles away. The numbers are getting big again, no way to avoid it. I am assuming a rough globe of 300 light years diameter for the Federation, or a globe with a diameter of 1,200,000 miles for the Basketball Federation. (wait, I only have 40,000 water molecules to oversee this area. I am feeling a little stretched.)

I can't keep the numbers small. Even shrinking the Sun to a basketball, I am soon talking millions of miles.

Now, how crowded are those space lanes again? As I see it, a grizzled old freighter Captain can serve 60 years, man and boy in the major space lanes and never visual another ship in deep space. These are objective hard numbers that no one can tell you are made up. Space is huge beyond an easy grasp, or even a medium grasp.

Based on the old FASA maps I use to place things in the Epiphany Trek universe the Federation looks something like this. There are 160 Federation members spread over a rough area some 400 by 200 light years. The fastest ships take over two months to cross that space (warp 9.5 cruise, 6 lys/day), most take four months or more (warp 8 cruise, 3 lys/day). You are never close enough to the nearest person that needs help. If you turn the Federation into a sphere 300 light years across that means it contains (gulp) 7,951,924 cubic light years.

Based on that figure I estimate a Starfleet of 40,000 patrol capable ships. This does not count the ships that are required to support those 40,000 ships. That elispoid of 400x200 light years will take 40,000 ships and swallow them all while moaning for more. To support those 40,000 ships you need 80,000,000 people. It sounds like a lot but that is a staffing level of 2000 beings for every ship patroling. If the US had armed forces of equal size on a per capa basis it would number 24,000. Eighty would come from my home town of Detroit.

That is one patrol ship per 198.7 cubic light years, if every ship patrols. I don't assume that is the case. I use 20 light year sectors. The Federation has one thousand sectors. That gives each sector 40 ships to patrol its 8000 cubic light years. If you spread them right you can get everywhere within one day of a starship, provided they are least the warp 8 cruise ships.

Space is frigging HUGE. You could scatter the entire 40,000 ship patrol fleet, and the 80,000 support ships, plus a 500,000 estimated civilian ships into the Sol system, toss a planet though and never hit ANYTHING. If the whole model was a 10 mile diameter globe and the 620,000 ships were water molecules the globe would contain a vacuum harder than the interstellar medium.

--
Garry AKA --Phoenix-- Rising above the Flames.

Then you get back into the question of scale and distance - how big is the Federation?

In Jay-Trek I re-drew the maps to be consistent with the Travel speeds specified - Warp factor = c*WF^3

for TOS that means a cruising Speed of about 2 light years per 3 days. (TOS warp 6, about 216c) That means 20 light years is going to take 30 days to cross.

For TMP onward It's about 1 light year per day. A 20 Light Year sector takes 20 days to cross.

From historical records about the longest people are really willing to spend on a Ship going from here to there is about a year - 365 days (Look at the Voyage from Liverpool to Sydney, or from New York to San Fransisco during the 1850s Gold rush.)

So the extreme border of the Federation is about 300 light years in any direction from Earth.

Sounds tiny, right?
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Now we have a Sphere and we know the radius

R=300

Pi = 3.14159265

And we have a formula to plug these into

Volume of a Sphere = (4/3)(pi R^3)

4/3 = 1.3333333

R^3 = 300 Light years cubed = 27,000,000 27 million cubic light years

27,000,000 * 3.14159265 = 84,823,001.55

1.3333333 * 84,823,001.55 = 113,097,332.572566615

or about 113,097,332.57 cubic light years in a sphere 300 light years radius. 113,097,332.57/40,000 Now -

Expand that sphere by 25 light years radius

325^3 = 34,328,125

34,328,125 * 3.14159265 = 107,844,985.18828125

107,844,985.19 * 1.3333333 = 143,793,309.991833827

143,793,310 - 113,097,332.57 - 30,695,977.43

By expanding that radius 25 light years (In all directions, to keep my head from exploding)

You just added 30 MILLION cubic light years to the Federation!

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So when you aim for so many Starfleet units per N-Cubic Light years - a little expansion means a hell of a lot more space

http://zebu.uoregon.edu/~imamura/123/lecture-2/lecture-2.html

This website has the average galactic Stellar density (How many Stars per cubic Light year) at 1 star per 125 cublic light years

Okay

so in a sphere with 300 Light years radius from Earth we could have 904,778 Stars

In a sphere with a radius of 325 light years we might see 1,150,346 stars

Adding 25 light years to the sphere (in all directions) adds 245,568 stars

The Classifications for stars within a loud shout of the sun's mass (and therefore heat and radiation output) are K- Orange, G- Yellow and F - Yellow-white

http://en.wikipedia.org/wiki/Stellar_classification

assuming 904,778 Stars in our globe

F- 3.1% of stars = 904,778 * 0.031 = 28,048

G- 8% of stars = 904,778 * 0.08 = 72,382

K- 13% of stars (The less massive, the more numerous) 904,778 * 0.13 = 117,621

28,048 + 72,382 + 117,621 = 218,051

So assuming 218,051 stars of Interest

Assume 1/3 have stellar systems we'd find useful (All of the Exo-Planets we're discovering now are super large and super close to their star. I'd imagine that precludes a class M world)

72,684 planetary systems

Assume 1 in 100 has an earth like world (For Trekness. - there may well be NONE)

7,268 earthlike worlds.

I have been making up stuff for a long time but I haven't made it to 7,000 new worlds yet.

Okay, one in one hundred is a friendly world and signs a treaty of alliance with the Federation

That leaves 700 new planets that need equipment, resources, ships and people.

How many of each does it take to defend a world?

A 40,000 ship Starfleet gives us one ship per 675 cubic light years.

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I have said it before and now I have backed it up - the numbers get crazy quickly.

Disclaimer: Paramount owns all things Trek. I claim original characters and situations in this material for me.

Jay P. Hailey

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