Friday, June 03, 2011

OCTANTS

Divide the heavens into 8 octants.

I II III IV V VI VII VIII All 8 Octants
OCTANTSExample
Stellar System
RADecDist3-D Coord.
αδdxyz
OriginSoln/an/a0000
OCT-IGroombridge344.6°44°11.628.30.78.1
OCT-IIWolf 359164°7.78-7.42.10.9
OCT-IIIBarnard's Star270°5.96-0.1-5.90.5
OCT-IVRoss 248356°44°10.327.34-0.67.2
OCT-VLuyten 726-8 25°-18°8.797.53.5-2.7
OCT-VISirius101°-17°8.58-1.68.2-2.6
OCT-VIIα Centauri217°-63°4.37-1.6-1.4-3.8
OCT-VIIIRoss 154283°-23°9.71.9-8.7-3.8
OBSERVED:  α;  δ;  ddCEP  = d × cos(δ)
x = dCEP×cos(α)y = dCEP×sin(α)z = d×sin(δ)

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.
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 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 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.
Consider notional (X, Y, Z) coordinates in Octant I
O = (0, 0, 0) Origin
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 (2+ 4+ 42) = (4 +16 +16) = (36) = 6
 D0,3 (3+ 6+ 22) = (9 + 36 + 4) = (49) = 7


Determine 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.
StellarRADecDist.
Systemαδd
G..344.6°44°11.62 LY
T..St43°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 3-D Coordinates
Seq.StardCEPxyz
i =0Sol0  LY0  LY0  LY0  LY
i =1G..348.36 LY8.3 LY0.7 LY8.1 LY
i =2 T..St11.6 LY8.7 LY8.2 LY3.6 LY
Givend×cos(δ)dCEP×cos(α)dCEP×sin(α)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.StardiΔdXΔdYΔdZ 
i =0Sol0  LY0  LY0  LY0  LY
i =1G..3411.62 LY8.3 LY0.7 LY8.1 LY
i =2 T..St12.51 LY 8.7 LY8.2 LY3.6 LY
GivenSee belowXi - X0Yi - Y0Zi - 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.

IIIIIIIVVVIVIIVIIIAll 8 Octants




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




0 Comments:

Post a Comment

<< Home