OCTANTS
Divide the heavens into 8 octants.
I
II
III
IV
V
VI
VII
VIII
All 8 Octants
OCTANTS Example
Stellar System RA Dec Dist 3D Coord. Time
α δ d x y z t
Origin Sol n/a n/a 0 0 0 0 0
OCTI Groombridge34 4.6° 44° 11.62 8.3 0.7 8.1 18.9
OCTII Wolf 359 164° 7° 7.78 7.4 2.1 0.9 12.9
OCTIII Barnard's Star 270° 5° 5.96 0.1 5.9 0.5 10.1
OCTIV Ross 248 356° 44° 10.32 7.34 0.6 7.2 16.9
OCTV Luyten 7268 25° 18° 8.79 7.5 3.5 2.7 14.4
OCTVI Sirius 101° 17° 8.58 1.6 8.2 2.6 14.4
OCTVII α Centauri 217° 63° 4.37 1.6 1.4 3.8 7.6
OCTVIII Ross 154 283° 23° 9.7 1.9 8.7 3.8 15.9
OBSERVED: α; δ; d d_{CEP } = d × cos(δ)
x = d_{CEP}×cos(α) y = d_{CEP}×sin(α) z = d×sin(δ)
INTERSTELLAR PROFILE TRAVEL TIME:
t = 1 yr + (d.76 LY)/.644c + 1 yr
I  II  III  IV  V  VI  VII  VIII  All 8 Octants 

OCTANTS  Example Stellar System  RA  Dec  Dist  3D Coord.  Time  

α  δ  d  x  y  z  t  
Origin  Sol  n/a  n/a  0  0  0  0  0 
OCTI  Groombridge34  4.6°  44°  11.62  8.3  0.7  8.1  18.9 
OCTII  Wolf 359  164°  7°  7.78  7.4  2.1  0.9  12.9 
OCTIII  Barnard's Star  270°  5°  5.96  0.1  5.9  0.5  10.1 
OCTIV  Ross 248  356°  44°  10.32  7.34  0.6  7.2  16.9 
OCTV  Luyten 7268  25°  18°  8.79  7.5  3.5  2.7  14.4 
OCTVI  Sirius  101°  17°  8.58  1.6  8.2  2.6  14.4 
OCTVII  α Centauri  217°  63°  4.37  1.6  1.4  3.8  7.6 
OCTVIII  Ross 154  283°  23°  9.7  1.9  8.7  3.8  15.9 
x = d_{CEP}×cos(α)  y = d_{CEP}×sin(α)  z = d×sin(δ) 

t = 1 yr + (d.76 LY)/.644c + 1 yr
Upper octants originate at the four quadrants on the Z=0 plane and extend upward.  
Quadrants and Octants. The X,Y axes of a twodimensional Cartesian system divide the plane 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 threedimensional 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.  
Consider notional (X, Y, Z) coordinates in Octant I O = (0, 0, 0) Origin P_{1} = (1, 2, 2); P_{2} = (2, 4, 4); P_{3} = (3, 6, 2) Pythagorean Theorem Compute 3D distances from origin in following manner: D = √(X^{2} + Y^{2} + Z^{2}) D_{0,1} = √(1^{2} + 2^{2} + 2^{2}) = √(1 + 4 + 4) = √(9) = 3 D_{0,2}=√(2^{2}+4^{2}+4^{2})=6 ; D_{0,3}=√(3^{2}+6^{2}+2^{2})=7 Furthermore,quickly determine 3D distances between any two points by further leveraging PTheorem on the coordinate differences. EXAMPLE: compute 3D distances from P_{1} in following manner. D_{a,b} = √[(X_{b}X_{a})^{2} + (Y_{b}Y_{a})^{2} + (Z_{b}Z_{a})^{2}] to P_{2}: D_{1,2} = √[(21)^{2} + (42)^{2} + (42)^{2}] =√[1+4 +4]=3 to P_{3}: D_{1,3}= √[(31)^{2} + (62)^{2} + (22)^{2}] =√[4+16 +0]=4.47 
Sol's neighbors in Octant One.
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.  
to convert astrometrics to three dimension coordinates. 
Compute Leg Distances
Determine two legs of voyage to interstellar destination.EXAMPLE: Leg1 distance from Sol to Hub, G..34; and Leg2 distance is from hub to destination, TStar .
d_{leg} = √[(Δd_{X})^{2} + (Δd_{Y})^{2} + (Δd_{Z})^{2}]
EXAMPLE: d_{leg2} = √[(0.4)^{2} + (7.5)^{2} + (4.5)^{2}] = 8.76 LY

SUMMARY: OCTANTS and HUBS  

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 example, it only shows one of the suggested hubs (i.e., Groombridge 34) in below figure.  
Hub stars are selected to leverage as much as possible the three hub criteria of
1) proximity to Sol,
2) situation to other stars,
3) provision of on site resources.
Hub's stellar names are placed to conveniently designate parent octants; they are not placed to show exact location within each octant.

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