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Astronomy Question

quixote100104

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Greetings :),

If someone wanted to plot a globular area around our star system that would include 10,000 other star systems, what would it's radius be?

Also, how far out do we have named stars classified?

Thanks :),
 
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efkelley

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Well..... Hmm...

Do you need 10,000 stars to tell your story? I mean, that's a helluvan infodump. The radius can really be anything you want it to be. Comes to it, you could say 'every star within 10,000 light years' and you're only covering a portion of the Milky Way. I suppose this is the 'cheaters way' of answering with 'I have no idea', but what's your ultimate objective in getting a radius that includes 10,000 stars?

The 'how far out' is mildly misleading. Stars have been classified by brightness since the beginning of formal observations. Here's a list of nearby stars: http://en.wikipedia.org/wiki/List_of_nearest_stars . You can see that some are bright simply because they're close. Send them out another 100 light years, and we wouldn't see them. Conversely, we have http://en.wikipedia.org/wiki/Eta_Canis_Majoris which is 3200 light years away, yet has an apparent magnitude of 2.45. Which means nothing until you load up http://en.wikipedia.org/wiki/List_of_brightest_stars and sort them by distance and/or apparent magnitude and see that it ranks as number 8 on apparent magnitude in a list of 90 stars, half of which are within 200 light years.

Again, I'm wondering about the context here. How does either answer/question apply to what you're writing?
 

quixote100104

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Again, I'm wondering about the context here. How does either answer/question apply to what you're writing?
My most successful writing venue to date has been in collaborative Star Trek simms (see my sig). Sad, but true ;-). In the group I write in, the best map-maker has issues with scaling his maps and I'm trying to convince him that a reasonable scale could be established. Not nessesarily accurate, but reasonable enough for a sci-fi setting utillizing 2D maps to represent space.

Trek canon suggests that the Federation has roughly 10,000 member systems. It's political center is Earth. So I was looking for a general notion of how far across it might be and for resources that would tell me, with no experiance and little interest in astronomy in general, to locate RW locations within that area to help establish map scales.
 

Misa Buckley

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It would really depend on how far out the other star systems are from Earth. However, it should be possible to create a map to scale, but I would have thought that the Federation would use computer-generated maps that were 3D.
 

Sarpedon

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And I doubt that every single star in an area would have an inhabitable system. Just pick a radius and call it a day.

Trekkie geekness begins:

If I were you, I'd decide how long of a trip is reasonable for your story, calculate what your average cruising warp speed is, and arrive at your number from there. So if warp 6 is your cruising speed, and you decide that the farthest system from earth is a whole year away, then its 216 light years from earth (assuming they haven't changed how the warp numbers work while I wasn't looking, again)
 

benbradley

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According to this article there are 50 stars within 16.3 (rounding to three digits, close enough for fiction and anyone who would actually check your work) light years of the Solar System.
The volume of a sphere with 16.3 light years radius is
v = 4/3 pi r^3, or 18140 cubic light years.
Dividing by 50 stars gives a density of 363 stars per cubic light year.

Presuming the density of the nearest 10,000 stars are in the same density as the nearest 50 stars (perhaps a rough approximation but good enough for this), they would be in an area of 10,000 * 363 or 3630000 cubic light years. Reversing the formula for the volume of a sphere,
r = (3v/4pi)^(1/3) = 95.3 light years.

Or (perhaps a simpler method, using fewer calculations) one can take the ratio of these numbers of stars:
10,000/50=200
and take the cube root of that to get the ratio of radii for volumes with the same star density:
5.85
and multiply by the original 16.3 light years:
5.85 * 16.3 = 95.3 light years radius of a sphere with the nearest 10,000 stars

If you want "only inhabitable star systems," decide on the ratio of all stars to such star systems and multiply the radius by the cube root of that ratio.
 

Lhun

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Trek canon suggests that the Federation has roughly 10,000 member systems. It's political center is Earth. So I was looking for a general notion of how far across it might be and for resources that would tell me, with no experiance and little interest in astronomy in general, to locate RW locations within that area to help establish map scales.
Well, you're looking for 10k habitable, inhabited, member systems, not just stars. So probably a lot more.
That aside, aren't there some astrographical facts established by Trek Canon? I.e. all that stuff about quadrants? (Although using quadrant in that context makes no sense) Or are you trying to correct some glaring mistakes?

On another note keep in mind that globular area only works up to around 1k lys. Which is the average thickness of the milky way. After that, you'd have to calculate for a disc shaped section of the milky way, instead of a sphere. Possibly some different shaped if your starting point is close to the edge. Also, if you want to be very accurate, the density of stars is obviously higher in the arms and the center, than in the spaces between. (Though the center would be uninhabitable anyway)
 

quixote100104

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I would have thought that the Federation would use computer-generated maps that were 3D.
I'm sure they would. But while our imaginations soar into the 24th century, our bodies are still stuck here in the 21st and I am scientifically and mathamatically challenged even for the 20th ;-)

Well, you're looking for 10k habitable, inhabited, member systems, not just stars. So probably a lot more.
That aside, aren't there some astrographical facts established by Trek Canon? I.e. all that stuff about quadrants? (Although using quadrant in that context makes no sense) Or are you trying to correct some glaring mistakes?
Always, but there's only so much you can do with Trek without making it not-Trek ;-). What I generallly try to do is create internal consistancy in the simms. Hence the desire to scale the map. The problem is, not being designed to pay any attention to scale, the map Bravo Fleet uses (which is a beautiful piece of art) doesn't even allow realistic scaling. I once tried to resolve the issue by selecting three RW systems shown on the map and comparing thier map distance to Sol, but each yielded a different scale!

As to canon, astrographical terms are used in Trek, but there are few facts. 'Quadrant' is meaningless in astrographic terms. The Alpha and Beta quadrants are side by side, Gamma and Delta hell and gone away. Supposedly, they are quarters of the galaxy but in practice, they just give you a general idea of what's in your neighborhood. 'Sector' is not defined at all in canon, and I've only seen a definition once (in the Star Trek Encyclopedia, I think (most fans seem to regard 'canon' as only what apeared on screen; even manuals and other supplements published by Paramount are, at best, 'semi-canon'). Sectors are numbered randomly, at the whim of the writers. And pre-Next Generation, most of the canon is designed to obscure rather than enlighten.

It's understandable, from the perspective of the studios. Those people were employed to get out an interesting show/movie in a limited timeframe. They mostly didn't have time to worry about the limitations imposed by what other people wrote before them and the people in the fan base who did worry about such things were always a vocal but tiny minority, who were also mostly rabid fans who would watch the show/movie regardless ;-).

Fan-generated material is just the opposite. It's created by people in thier spare time, who aren't staking thier livelihoods on thier writing being done in a certian timeframe. They think a lot about the process and, as a result, often produce better material. Another problem specific to my personality is that I work best inside a defined setting, learning it and then building stories based on that knowlege. Most people, near as I can tell, map out thier story and then build the setting around it. So while others can move thier ship "at the speed of plot", I'm just not comfortable with that.

I have this idea about using a website to create a layered 2d map to give a sense of the three dimensionality of space. It would be 20 layers deep (a Federation sector is a 20 ly cube) and consist of a large scale map subdivided into sectors, which you could click on the get smaller scale, more detailed maps of the sectors. In either, you could view either a composite image of the layers or a single layer. Locations would be indicated by thier horizonal position on thier layer (like D4) and thier layer's position relative to the center plane of the map (like -4 or +7). Some website people I know (again...clueless; why do you think I play a CO ;-) ) say the framework shouldn't be too hard to create.

To make it worthwhile though, you need maps. To get maps, you need a graphic artist inclined to do the work and the only good one one I've found even willing to talk to me about it needs to be convinced that scaling the map would be less difficult and more useful than he has previously believed.

On another note keep in mind that globular area only works up to around 1k lys. Which is the average thickness of the milky way. After that, you'd have to calculate for a disc shaped section of the milky way, instead of a sphere. Possibly some different shaped if your starting point is close to the edge. Also, if you want to be very accurate, the density of stars is obviously higher in the arms and the center, than in the spaces between. (Though the center would be uninhabitable anyway)
The logical starting point is Sol, since we're all pretty sure where that is ;-). As for the thickness of the galaxy, I don't think that would be too much of an issue. 1,000 ly would be a little over 6 months at warp 9 (approx. 5 ly/day) and roughly 2.75 years at warp 6 (approx. 1ly/day) according to the warp scale I use (from the "Star Trek Encyclopedia").

Maybe that would be the best way to define the mapping perimeter: a 1,000 ly across. 1,000 pixels square is a nice image size and that would allow a large map scale of 1 ly/pixel. It would cover 50 sectors and could probably fully enclose any reasonable size for the Federation and it's immediate neighbors. For really far away stuff, like the Gamma and Delta Quadrants, you make different maps.

Just in case anyone's interested, I've been thinking lately about a new setting: The First Class. It would be set at the birth of the Federation, in 2168 when the first class of Starfleet Academy graduates hit the Fleet. All thier superiors are members of the founding world's independant star navies, some rather reluctanly merged into the newly formed Starfleet.

The original series is 98 years in the future. The ships are slower, the galaxy less explored and developed and there is very little defined canon. It's before phasers, before photon torps, before holodecks, before the Prime Directive. Shipboard transporters are not yet rated for transport of living beings. Though ground-based units are, transporter psychosis has not yet been diagnosed, much less cured. The Federation is far from unified and it's survival is threatened more by internal dissent than external foes. No Earthling has ever seen a Romulan, despite fighting an interstellar war with them less than a decade ago.

This would be original material; I don't really acknowledge Enterprise. If any of you are familiar with Trek RPG material, the setting would mostly be FASA's Triangle region, at this point a mostly wide open, unclaimed
frontier between Federation, Romulan and Klingon space. There's a lot of developed material for it, but in play, most of it awaits discovery.
 

blacbird

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According to this article there are 50 stars within 16.3 (rounding to three digits, close enough for fiction and anyone who would actually check your work) light years of the Solar System.
The volume of a sphere with 16.3 light years radius is
v = 4/3 pi r^3, or 18140 cubic light years.
Dividing by 50 stars gives a density of 363 stars per cubic light year.

Presuming the density of the nearest 10,000 stars are in the same density as the nearest 50 stars (perhaps a rough approximation but good enough for this), they would be in an area of 10,000 * 363 or 3630000 cubic light years. Reversing the formula for the volume of a sphere,
r = (3v/4pi)^(1/3) = 95.3 light years.

Or (perhaps a simpler method, using fewer calculations) one can take the ratio of these numbers of stars:
10,000/50=200
and take the cube root of that to get the ratio of radii for volumes with the same star density:
5.85
and multiply by the original 16.3 light years:
5.85 * 16.3 = 95.3 light years radius of a sphere with the nearest 10,000 stars

If you want "only inhabitable star systems," decide on the ratio of all stars to such star systems and multiply the radius by the cube root of that ratio.

You probably don't have any idea how much I detest you mathematical sumbitches, do you?

caw
 

K Ackermann

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@benbradley - nice work.

And the surface area (4 • π • r²) would be 95 * 3.14 * 4 = 113,000 sq light years... call it 110,000 sq light years.

This means that even if all 10,000 stars resided at the surface of the sphere, there would be 11 light years mean between each star.