OCTANTS

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CONTENT
8 OCTANTS
OCTANTS: UP & DOWN
COMPUTE DISTANCES
DISTANCES TO NEIGHBORS
3-D COORDINATES
SUMMARY

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DIVIDE THE HEAVENS
INTO EIGHT OCTANTS.

I	II	III	IV	V	VI	VII	VIII	Overview

OCTANTS Example Stellar System RA Dec Dist 3-D Coord. Time α δ d x y z t Origin Sol n/a n/a 0 0 0 0 0 OCT-I Groombridge34 4.6° 44° 11.62 8.3 0.7 8.1 18.9 OCT-II Wolf 359 164° 7° 7.78 -7.4 2.1 0.9 12.9 OCT-III Barnard's Star 270° 5° 5.96 -0.1 -5.9 0.5 10.1 OCT-IV Ross 248 356° 44° 10.32 7.34 -0.6 7.2 16.9 OCT-V Luyten 726-8  25° -18° 8.79 7.5 3.5 -2.7 14.4 OCT-VI Sirius 101° -17° 8.58 -1.6 8.2 -2.6 14.4 OCT-VII α Centauri 217° -63° 4.37 -1.6 -1.4 -3.8 7.6 OCT-VIII Ross 154 283° -23° 9.7 1.9 -8.7 -3.8 15.9 OBSERVED:  α;  δ;  d dCEP  = d × cos(δ) x = dCEP×cos(α) y = dCEP×sin(α) z = d×sin(δ) INTERSTELLAR PROFILE TRAVEL TIME: t = 1 yr + (d-.76 LY)/.644c + 1 yr

HUBS: Sol's closest stellar neighbors can help humanity travel to even further stars. Vessels can stop there to replenish resources before traveling on.	BEARINGS can help vessels precisely track remaining distance. This will prove essential for decelerating at exact, required distance to destination.
OCTANTS EXTEND BOTH UP AND DOWN FROM ECLIPTIC BASED QUADRANTS
	Upper octants originate at the four quadrants on the Z=0 plane and extend upward.
	Quadrants and Octants. The X,Y axes of a two-dimensional Cartesian system divide the Celestial Equatorial Plane (CEP) into four infinite regions, called quadrants. Each quadrant is bounded by two perpendicular, linear rays which originate at the Origin (0,0) where X = 0 and Y = 0.  Similarly, a three-dimensional Cartesian system uses the X, Y and Z axes to divide space into eight regions, octants. In Thought Experiment (TE) model, the CEP is at the Z=0 plane. Celestial equatorial coordinates are based on the location of stars relative to Earth's equator projected out to an infinite distance. This view describes the sky as seen from the Solar System, and modern star maps almost exclusively use equatorial coordinates. TE assumes CEP to be centered at Sol, but fixed relative to distant stars.
	Lower octants originate at the same four quadrants on the CEP plane but extend downward.
COMPUTE 3-DIMENSIONAL DISTANCES FROM SOL
Consider notional (X, Y, Z) coordinates in Octant I Origin(O) = (0, 0, 0)  P1 = (1, 2, 2); P2 = (2, 4, 4); P3 = (3, 6, 2) Pythagorean Theorem Compute 3-D distances from Sol in following manner: D = √(X2 + Y2 + Z2) D0,1 = √(12 + 22 + 22) = √(1 + 4 + 4) = √(9) = 3 D0,2 = √(22 + 42 + 42) = √(4 +16 +16) = √(36) = 6  D0,3 = √(32 + 62 + 22) = √(9 + 36 + 4) = √(49) = 7

DISTANCES FROM SOL TO NEIGHBOR STARS

	Observed Astrometrics Consider Groombridge 34 (G..34) and Teegarden's Star (T..St), Sol's neighbors in Octant One. Stellar RA Dec Dist. System α δ d G..34 4.6° 44° 11.62 LY T..St 43° 17° 12.51 LY Right Ascension (RA=α) and Declination (Dec=δ) are readily obtained in  decimal degrees. Observed distance are traditionally obtained for nearby stars by carefully measuring brightness and parallax.
COMPUTE THREE DIMENSIONAL COORDINATES
Seq. Star dCEP x y z i =0 Sol 0  LY 0  LY 0  LY 0  LY i =1 G..34 8.36 LY 8.3 LY 0.7 LY 8.1 LY i =2  T..St 11.6 LY 8.7 LY 8.2 LY 3.6 LY Given d×cos(δ) dCEP×cos(α) dCEP×sin(α) d×sin(δ) Use trigonometric functions  to convert astrometrics to three dimension coordinates.	Compute Solar Distances Determine distance from Sol to each neighbor star which should match observed distance. Seq. Star di ΔdX ΔdY ΔdZ  i =0 Sol 0  LY 0  LY 0  LY 0  LY i =1 G..34 11.62 LY 8.3 LY 0.7 LY 8.1 LY i =2  T..St 12.51 LY  8.7 LY 8.2 LY 3.6 LY Given See below Xi - X0 Yi - Y0 Zi - Z0 Use Pythogorean Theorem to obtain leg distances..  dleg = √[(ΔdX)2 + (ΔdY)2 + (ΔdZ)2] EXAMPLE: d2 = √[(8.76)2 + (8.7)2 + (3.65)2] = 12.51 LY

SUMMARY: OCTANTS

Figure shows a small sample of nearby stars in eight octants centered on Sol, our sun. The octants are arbitrarily aligned such that the X axis aligns with the Point of Aries, with Right Ascension (RA) at 0 hours or 000°, and the Y axis aligns with RA at 90°. This random sample only a few of the stars within 15 LYs.  For more details, click on desired octant in below table. I II III IV V VI VII VIII All 8 Octants

SLIDESHOW

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VOLUME 0: ELEVATIONAL
VOLUME I: ASTEROIDAL
VOLUME II: INTERPLANETARY
VOLUME III: INTERSTELLAR

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