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For those out there hitchhiking, I’m composing this from Earth, a mainly harmless rock sphere in Galactic ar ZZ9 many Z Alpha. Together my first examination of galactic mapping, I’d like to indulge my curiosity and also see if I can solve what that means. Where exactly is Galactic ar ZZ9 plural Z Alpha?
A fruitless endeavor? Possibly. Am ns gonna try anyway? Definitely.
We only have actually two known specimens – ZZ9 many Z Alpha, and also QQ7 active J Gamma (the just other sector offered in the divine Texts). Can these coordinates actually it is in divined and contorted into a positional mechanism that makes sense?
First that all, likely not. It was a joke on Douglas Adams’ component – it’s a rash letter salad meant to phone call us only one thing – an are is BIG, and all that. But just possibly there’s enough information there to bend it into something the works. LET’S try ANYWAY.Possible Systems
First we have to list what we know about Sol’s real-world galactic position. From our initial short article establishing our coordinate device as Sagittocentric Galactic, we recognize Sol is ~50ly over the galactic aircraft (+Z), and 27,000ly from Galactic center (-Y). We recognize that the X is arbitrarily collection to 0 – we’ve favored to set the X origin straight at Sol, which would be exceptionally unlikely in a true Galactic ar system. However, since we don’t have an alternative, I’m walk to leaving it for now.
So what we have is the complying with constraints on our deductions: 0,-27000,50 somehow is same to ZZ9 many Z Alpha. Because a coordinate device that slices increase the galaxy would most likely be based on common sense things like the basic plane that the galaxy and the galactic facility being the origin, ns will reduced through a most speculation and just assume those things as facts. Come theorize otherwise would be madness. I mean, of food it can be a coordinate system based on Arcturan time the day, or based on the Golgafrinchian axial tilt the -78 degrees, or counting indigenous the outside of the galaxy in, and backwards, through threes. Yet we’re walk to i think it’s not, due to the fact that that means lies madness.
What we recognize of our existing galactic works with is the following:
X=0 – Again, this is arbitrary, due to our place Sol best on the X origin. Sol’s position relative to Galactic facility could it is in anything native 0-360 levels in a circle, for this reason it method nothing yet.
Y=27,000 – this is a medium-large value, approximately equal to 1/4 the diameter that the galaxy. Every little thing coordinate ingredient covers this needs to be robust and also will ar Sol ideal in the center of that range.
Z=50. This is a very little amount. If we’re utilizing the basic plane the the galaxy (we are), this is likely at the start of a variety that will go to plenty of tens of times this value.
Sol’s place in the galaxy.
So what any type of coordinate mechanism needs is 3 components – x, y, and also z: position horizontal, position vertical, and position depth from everything reference allude you’re dealing with.
Note: indigenous Hitchhiker’s guide to the Galaxy, we understand that the plural relates to probability and its impacts on space travel – people from Plural area shouldn’t travel in hyperspace, for fear of winking the end of presence (or, more accurately, popping right into a cosmos where they never ever existed in the first place and promptly self-correcting). That pipeline use through ZZ9 Z Alpha and also QQ7 J Gamma to recognize 3 variables.Coordinate Components
What deserve to we magnificent from ZZ9 Z Alpha? there three methods to rest it up:
ZZ, 9, Z AlphaZ, Z9, Z AlphaZZ9, Z, Alpha
What can we glean indigenous the really units?
Z – part of a system of at least 26 (there room 26 letters in the English alphabet).
9 – component of a device of at least 9 (obviously)
ZZ – component of a mechanism of one of two people 26 (if every letters are in duplicate pairs, native AA to ZZ, exactly once), 26*2=52 (if the mechanism starts with solitary letters, A, B, C etc and then doubles come AA, BB, CC), or 26*2+26=702 (if the mechanism starts v A, B, C and runs through every two letter combination of letters, native A come AA to ab to ZA to ZZ).
Alpha – part of a mechanism of any kind of number from 2 come 24, utilizing the Greek alphabet. The Star Trek galaxy only uses the first four, Alpha/Beta/Gamma/Delta, because that its quadrants. This system might use that, or it can use the whole alphabet native Alpha come Omega. (Don’t worry about why the system uses English and also Greek – consult her Babelfish user guide).Coordinate system 1: XYZ
26 radial slices, with Sol in ZZ.
Since our street from facility is 27,000ly (approximately), and we room in Ring 9, that means that every ring would certainly cover at least 2700ly radially (if us are best on the cusp of Ring 10), and no an ext than 3000ly (if we are best at the beginning of Ring 9). That means that the approximate ‘edge’ of the galaxy at 120,000ly in diameter ends at between Ring 41 and also Ring 45.
26 radial slices, and also showing the first 26 (A-Z) depth bands. We are in tape Z (outer bands no shown)
So i was emotion pretty an excellent about this, having made sense out of ZZ9 and also gotten angle and radial distance from galactic center, which got rid of ZZ9 indigenous the problem and also got me X and Y. Climate it all dropped apart.
This left me v Z Alpha because that my Z (depth) coordinate, or distance over and below the galactic plane.
I began with other simple. Z would be the depth, and also Alpha would be a sublevel that Z. (Alpha that Z, meaning there was a Z Beta, a Z Gamma, etc, complied with by a Y Alpha, Y Beta…). The trouble with this is that would put Sol’s +50ly Z depth over the galactic aircraft in the Z slice of the galaxy’s depth layer. This is no good. Allow me define why.
Z come at the finish of the alphabet, and here we are at +50ly hovering right above the galactic equator. Any great numbering system should start at 0 and count up, no at 26 and also count down, an interpretation we need to really be in ~ A Alpha instead of Z Alpha, hovering right above the galactic plane. Being at Z Alpha way it deserve to only count down to A (A Alpha, if girlfriend like, due to the fact that if one range counts under the other must too). Since we would recognize that Z Alpha = +50ly (or, the finish of the Z depth slice which starts in ~ Z=0), we can assume the the complete system indigenous Z Omega (or some other finishing Greek letter) come A Alpha cannot extend much past 26*50ly over the galactic plane, put A Alpha at a mere +1300ly (plus a tiny more, assuming we room not in ~ the very finish of the Alpha block that Z) above the galactic plane. That’s no good, as a coordinate device must have the ability to extend to infinity in all directions.
This would also mean the the numbering device would one of two people go an unfavorable below the galactic equator (ZZ9 -Z Alpha), or it would certainly use twin letters to denote negatives (ZZ9 ZZ Alpha).
In the end, this system had actually to be thrown out, and I began fresh.Coordinate mechanism 2: ideal Ascension/Declination
After trying multiple attempts at an XYZ system and also hitting repetitive roadblocks, it arisen to me that any great spherical coordinate system would use the galactic facility as the origin, as I originally assumed, yet would it is in in state of appropriate ascension, declination, and depth indigenous the galactic equator.
In this way, the galaxy would certainly be sliced up not into sections of a cylinder, however in peeled great of a sphere like onion layers.
So, I collection about to convert our works with of 0,-27000,50 right into RA/Dec relative to galactic center.
We begin by rearranging. Here, X=0 is a function of ideal Ascension (rotational level from part arbitrary galactic longitude), Z=50 is a duty of Declination (rotational level from galactic equator), and Y=-27000 is a duty of street (from galactic center). It’s basically exactly how we measure stars now, other than relative come galactic center instead that Sol, and also with the added detail that slicing the street levels right into discreet area (which we don’t at this time do).
So as discussed above, we will be discarding the 0 (Right Ascension), because an arbitrarily 0 is as good as any type of other number. We will certainly assume the Galactic Meridian lines increase perfectly v Earth. Why not? It’s largely harmless.
Next, we have the +50 Z depth. To find how that relates come declination, we require to transform it to angular diameter to uncover out just how far over the galactic equator the lies, indigenous the perspective of galactic center (the beginning of our system, and also the point of view of one “observer” deciding galactic name: coordinates systems). Angular diameter is the obvious size of an item at a details distance, usually offered in degrees (1/360th the a circle), arcminutes (1/60th of a degree), and arcseconds (1/60th of one arcminute). Because that example, the Moon with a radius the 1,079.4 mile at a street of 225.6 thousands miles, subtends an angular diameter of approximately 31 arcminutes, or 0.5 degrees, from a approach on Earth.
The formula for angular diameter (a) for little angles wherein object street (D) > thing diameter (d), is:
If we plugin our number to the formula above, we gain a(arcseconds)=206,265*(50/27000) = 381.9722222222222 arcseconds. This way that from galactic center, 0 to 50ly of Z depth consist of an arc of 381.972 arcseconds, or 6.366203 arcminutes, or 0.106 levels (1/10th the a degree).
Note: Angular diameter is not really the correct an approach for act this, yet is a good shortcut since the resulting angle will certainly be therefore small. I should really be making use of arctangents, i beg your pardon I do in the testing phase below. Thankfully, the answer ns got above is specific to within less than a thousandth the a degree: the result from angular diameter is 0.106 degrees, and the answer utilizing trigonometry is 0.1061031741 degrees.
The an initial guess is that, since we space trying to resolve for the 9 in ZZ9, we are in tape 9 above the galactic equator. You can say our Declination somehow equates to “Band 9,” which method 0.106 levels = “Band 9.”
If between 9 and 10 Bands (again, depending on if we’re at the beginning or finish of band 9) covers 1/10th (0.1) of a degree, climate each Band would certainly cover approximately 0.01 degrees. A full variety of Declination, or 90 degrees (from “level” to “straight up”) would certainly cover 90/0.01 = approximately 9000 Bands of Declination. Let’s look in ~ the math a little an ext closely.
If we take a nice center number, prefer 8000 Galactic Declination Bands i m sorry cover ours 90 degrees of Declination, climate each tape covers 90/8000=0.01125 degrees. Our position at Declination 0.106 levels puts us in 0.106/0.01125=9.422222222222222, or in Galactic Declination band 9.42, or roughly halfway into Band 9.
So this works, but it’s extremely ugly. Allow me explain why.
We room hovering right over the galactic equator, putting us in ~ ZZ9 (Right Ascension ZZ, Declination 9). However, a star hovering directly over the top of galactic facility would it is in at collaborates ZZ8000. That’s right at the ZZ Top. 8000 is a LOT that Declination Bands to deal with.
Elevation watch of the galaxy v 8000 declination bands… too many!
Note the in the key view, our +50ly Z position doesn’t even register together a pixel.
Good thing for us, there’s another option!
Currently, ours Declination device starts at 0 at the horizon, and also counts approximately 90 right up, and also down to -90 right down. What if the Galactic Declination System, instead of covering horizon to pole, spanned pole come pole? This would mean that the system would sheathe -180 come 180 together one range of numbers. As it transforms out, this works reaaaally nicely.
Let’s set Band 0 to directly down (-180 degrees), and let’s location us in band 9 right above the galactic equator. This method that the southerly Declination hemisphere consists Bands 0-9, which would divide the 90 level arc right into 9 Bands of 10 degrees each. Perfect! That means that Galactic Declination in ~ -180 degrees is band 0, right at the horizon is band 9, and also 180 degrees is band 18. If 90/9=10 levels per band, and also we space 0.106 degrees above the horizon, climate we space in tape 9.0106, or best at the beginning of band 9, which would certainly cover Declinations indigenous 0 degrees to 10 degrees, then band 10 is 10 degrees to 20 degrees.
Elevation check out of the galaxy with only 18 bands (0 come 17), 9 bands per 90 degree arc, and us in tape 9
If we return to our ahead radial part solution used above:
Even despite the XY coordinate mechanism didn’t work out, I believe this part is tho sound.
Still valid: 26 radial slices, v us in the 26th depth band (Z).
That way we only require our depth! If ZZ is the radial slice and 9 is our Declination Band, then Z Alpha is our distance function.
Let’s assume that Alpha means that we are at the beginning (or close to the beginning) the the Z depth band, which method we can place the start of Z at no much more than 27,000ly indigenous center. That way 27000/25 letters=up to 1080ly every letter tape (the Z tape would end at no much more than 28080ly indigenous galactic center).
If us assume we are using the whole Greek alphabet the 24 letters, then each Z depth tape of 1080ly is split into 24 letter sub-bands, or 1080/24=45ly every letter. If we accept this, then the Z depth tape extends from 27000ly come 28080ly indigenous center, and the Z Alpha sub-band extends indigenous 27000ly come 27044ly, and also Z Beta begins at 27045ly from center. If we go towards galactic center by 1ly, that would placed us in ~ 26999ly from center in Y Omega.
So what happens after we go beyond Z Omega, which end at 28080? We deserve to roll right right into AA Alpha and continue outward from galactic center.
To solve this, we have to look in ~ it differently. Since there room 25 Depth Bands behind united state (we room in the Z, or 26th Band), and each Band has 24 sub-bands, there room 25*24=600 sub-bands behind united state (we room in the 601st sub-band). In ~ 27000ly, we room either at the start or the end of the 601st sub-band (sub-band 600.000 come 600.9999 – remember that the 1st sub-band, A Alpha, is native sub-band 000.000 come 000.999) . That way that each sub-band is in between 27000/600=45ly in depth (if we space at the start of Z Alpha, or in ~ the beginning of the 601st sub-band in ~ 600.000), and also 27000/601=44.92512479201331ly (if we room at the end of Z Alpha, the 601st sub-band at 600.999). If we choose a nice straightforward number of, say, 44.95ly per sub-band, then at 27000ly we space at sub-band 27000/44.95=600.6674082313682, or 66.7% (about 2/3) into Z Alpha.
That areas the start of the Z band (and Z Alpha) at 600*44.95=26970 ly from galactic center, and the start of Z Beta in ~ 601*44.95=27014.95ly native center. Ns am entirely fine v this.
As mentioned above, as soon as we go beyond Z Omega (which end at 26*24*44.95ly=28048.8ly from galactic center, we simply roll right into AA Alpha, and then on to AAA Alpha and AAAA Alpha, onwards come infinity. However, for our useful “end that the galaxy” which typically ends at -60000ly from center, the puts it in ~ 60000/28048.8=2.139128946692907 runs of 26 letters, or top top the 3.617352614015573th letter of the 3rd set, definition the BBB Depth band, or the 14.81646273637372th sub-band (the 14th Greek letter is Xi). 60000ly lands at 80% (0.816) v BBB Xi. Through this system, a star us were occluding at the same best ascension and declination from galactic center, but at 60000ly native origin, would have actually the works with ZZ9 BBB Xi.
A keep in mind above: We room basing this turn off of our approximate street to galactic facility of 27000ly, i m sorry we recognize to be subject to a big margin that error. Luckily, we deserve to just scale up or down our Z depth set if we somehow find out through more accurate measurement the the real figure is closer to, say, 25000 or 28000. However for now, this is fine.Testing
To test this, we’ll must do some simple (inverse) trigonometry using our Sagittocentric collaborates to map some stars to their H2G2 Galactic Coordinates, because that the reason that to gain from XYZ to RA/Dec from galactic center, we require rotation indigenous Galactic Meridian (the suggest between slices AA and also ZZ, i beg your pardon we room assuming we space on in ~ X=0), and also distance to center.
If we map, let’s say, 3 locations: Sol, Barnard’s Star (which is likewise supposed to it is in in ZZ9 many Z Alpha, and also the Horsehead Nebula (Hitchhiker’s pan will understand why; if not, a future write-up will covering this).
We take your RA/Dec/Distance below:
Sol: RA 0h0m0s, Dec 0°, Dist 0ly
Barnard’s Star: RA 17h 57m 48.49803s, Dec 04° 41′ 36.2072, Dist 5.978ly
Horsehead Nebula: RA 05h 40m 59.0s, Dec −02° 27′ 30.0″, Dist 1500ly
When we convert these come Sagittocentric Galactic Coordinates, we acquire the following:
|Star||Xs ly||Ys ly||Zs ly|
We will usage arctangents (specifically, the atan2 function) to transform these from Galactic XYZ to XY radial degrees and distance, which i won’t cover in information here (but if you’re interested, I have actually a lengthy spreadsheet). Then, we have the right to use a an easy lookup table to convert XY radial levels to part letter, from AA come ZZ.
Similarly, the newly-calculated street from galactic facility can be offered with a basic lookup table to find the Depth tape (Z for Sol) and also Depth Sub-Band (Alpha for Sol).
We now have Radial Slice and Depth! We just need Declination.
We have to go earlier to our Galactic XYZ and also now through our new Distance (or Radius), we deserve to again use arctangents to transform Radius and Z to degrees. This we have the right to use with another lookup table to convert from real-world declination (180 to -180) come the Declination Band us will require (Sol is tape 9).
When we put all this together, the works! The Sagittocentric Coordinates detailed above convert into the following:
Sol: ZZ9 Z Alpha
Barnard’s Star: ZZ9 Z Alpha
Horsehead Nebula: AA8 AA ZetaPlural Zones and You
Now for the critical part. “Plural.” This is wherein I start acquiring creative, due to the fact that there’s literally no data to traction from various other than that we have Plural and Active, and that they relate to probability.
That being said, ns still needed a way to get some variable that would end up being what we’ll call the “Probability Rating” the a star. The only info I have actually is the RA/Dec, XYZ, and also the brand-new Galactic sector information. Ns opted to use that critical part, because it’s what we operated so difficult to get.
WARNING: MATH(S) NONSENSE and also POSSIBLY A DEBASEMENT of SCIENCE!
For each location, I added up every the factors in its calculation to obtain a single, unique number. Specifically, ns added slice levels + declination levels + depth tape scalar + depth sub-band scalar. The numbers that came out were the following:
Barnard’s Star: 116.4794721
Horsehead Nebula: 481.9917798
I then necessary some way to make the number a little more uniform, therefore I divided them by…
The an outcome was this:
Barnard’s Star: 2.773320765
Horsehead Nebula: 11.47599476
Then, to tighten the range and create a unique, uniform identifier, ns discarded anything beyond 1.00, and also multiplied by 10. This provided me a number between 0 and 10 to use for the Probability Rating.
Barnard’s Star: 7.733207653
Horsehead Nebula: 4.759947562
Using a lookup table, ns assigned 0-10 to part words the sound choose they’d be amazing to check out on a Probability Rating scale:
And as soon as we put it all together? We obtain this:
Sol: ZZ9 plural Z Alpha
Barnard’s Star: ZZ9 plural Z Alpha
Horsehead Nebula: AA8 Planar AA ZetaConclusion:
All that this is nonsense. However, amazingly, it’s nonsense us were able to make feeling of with some creativity, a dash that trigonometry, and also a many of an innovative problem solving. It simply goes to show what type of difficulties you have the right to solve as soon as you placed your mind (and a significant chunk of totally free time) to it!
…And because that those of girlfriend that space upset through this rotate of events or disagree with my calculations (or the truth that this was also undertaken in the very first place), feel cost-free to leave a comment or call me.
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Otherwise you have the right to lodge a complaint with your local planning room on Alpha Centauri.