Monday, January 29, 2007

ALPHA LAUNCH TABLE




























NEW MOON: Assume Minimum Lunar Radius
Set origin (0,0) at Earth's initial position.
Time Hab. α ∠Terra ∠Habitat α CoordTerra (♁) CoordDist.
betw.
MOON
PHASE
(t)α))(Xα)(Yα)(X)(Y)(d)
0 dy0.00⁰0.00⁰-354,547 km0 km0 km0 km354,547 km NEW
MOON
4 dy3.96⁰3.95⁰-711,008 km10,305,210 km-354,788 km10,268,843 km358,072 kmWAXING
CRESCENT
7.5 dy7.43⁰7.40⁰-1,606,477 km19,283,565 km-1,246,060 km19,215,785 km366,734 kmFIRST
QTR
11 dy10.89⁰10.85⁰-3,043,248 km28,191,387 km-2,676,127 km28,092,938 km380,093 kmWAXING
GIBBOUS
15 dy14.85⁰14.80⁰-5,341,262 km38,243,609 km-4,963,484 km38,111,458km400,225 kmFULL
MOON
19 dy18.81⁰18.75⁰-8,328,377 km48,113,145 km-7,936,874 km47,949,206 km424,441 kmWANING
GIBBOUS
22.5 dy22.28⁰22.20⁰-11,496,244 km56,562,040 km-11,090,343 km56,372,240 km448,085 kmLAST
QTR
26 dy25.75⁰25.65⁰-15,169,240 km64,804,049 km-14,746,852 km64,590,536 km473,286 kmWANING
CRESCENT
29.5 dy29.21⁰29.11⁰-19,333,932 km72,809,027 km-18,893,122 km72,574,249 km499,434 kmNEW
MOON
Givent × nαt × n [Rα×Cos(θα)]-1AU Rα× Sin(θα) [R×Cos(θ)]-1AU R♁ × Sin(θ)x2+Δy2 )Observed
Rα = 0.9976 AU = 149,243,323.7 km R♁ = 1.0 AU = 149,597,870.7 km



SOURCE DOCUMENT

NEW MOON: Assume Minimum Lunar Radius
Set origin (0,0) at Earth's initial position.
Time aft
Launch
(t)
Hab. α
Ang. Dist. 

(θα)
Terra
Ang. Dist. (θ)
Habitat α
Coordinates
Terra (♁)
Coordinates
Distance
between
(Xα) (Yα) (X) (Y) (d)
0 dy 0.000 0.000 -354,547 km 0 km 0 km 0 km 354,547 km
1 dy 0.990 0.987 -376,834 km 2,578,227 km -22,182 km 2,569,115 km 354,769 km
2 dy 1.980 1.973 -443,689 km 5,155,684 km -88,723 km 5,137,468 km 355,433 km
3 dy 2.971 2.960 -555,091 km 7,731,602 km -199,603 km 7,704,298 km 356,536 km
4 dy 3.961 3.947 -711,008 km 10,305,210 km -354,788 km 10,268,843 km 358,072 km
5 dy 4.951 4.934 -911,393 km 12,875,740 km -554,233 km 12,830,342 km 360,034 km
6 dy 5.941 5.920 -1,156,186 km 15,442,425 km -797,878 km 15,388,036 km 362,412 km
7 dy 6.931 6.907 -1,445,314 km 18,004,498 km -1,085,652 km 17,941,167 km 365,195 km
8 dy 7.922 7.894 -1,778,690 km 20,561,193 km -1,417,468 km 20,488,978 km 368,369 km
9 dy 8.912 8.880 -2,156,215 km 23,111,747 km -1,793,229 km 23,030,712 km 371,921 km
10 dy 9.902 9.867 -2,577,776 km 25,655,398 km -2,212,824 km 25,565,616 km 375,834 km
11 dy 10.892 10.854 -3,043,248 km 28,191,387 km -2,676,127 km 28,092,938 km 380,093 km
12 dy 11.882 11.840 -3,552,491 km 30,718,957 km -3,183,001 km 30,611,929 km 384,679 km
13 dy 12.873 12.827 -4,105,353 km 33,237,351 km -3,733,296 km 33,121,842 km 389,575 km
14 dy 13.863 13.814 -4,701,669 km 35,745,818 km -4,326,849 km 35,621,932 km 394,763 km
15 dy 14.853 14.801 -5,341,262 km 38,243,609 km -4,963,484 km 38,111,458 km 400,225 km
16 dy 15.843 15.787 -6,023,939 km 40,729,978 km -5,643,012 km 40,589,681 km 405,942 km
17 dy 16.833 16.774 -6,749,497 km 43,204,183 km -6,365,231 km 43,055,868 km 411,896 km
18 dy 17.824 17.761 -7,517,720 km 45,665,483 km -7,129,927 km 45,509,285 km 418,068 km
19 dy 18.814 18.747 -8,328,377 km 48,113,145 km -7,936,874 km 47,949,206 km 424,441 km
20 dy 19.804 19.734 -9,181,227 km 50,546,437 km -8,785,832 km 50,374,908 km 430,999 km
21 dy 20.794 20.721 -10,076,015 km 52,964,632 km -9,676,549 km 52,785,670 km 437,722 km
22 dy 21.784 21.707 -11,012,475 km 55,367,008 km -10,608,762 km 55,180,778 km 444,596 km
23 dy 22.775 22.694 -11,990,325 km 57,752,848 km -11,582,193 km 57,559,522 km 451,605 km
24 dy 23.765 23.681 -13,009,274 km 60,121,439 km -12,596,554 km 59,921,195 km 458,732 km
25 dy 24.755 24.668 -14,069,018 km 62,472,073 km -13,651,545 km 62,265,098 km 465,964 km
26 dy 25.745 25.654 -15,169,240 km 64,804,049 km -14,746,852 km 64,590,536 km 473,286 km
27 dy 26.735 26.641 -16,309,612 km 67,116,670 km -15,882,151 km 66,896,819 km 480,685 km
28 dy 27.726 27.628 -17,489,793 km 69,409,246 km -17,057,104 km 69,183,263 km 488,148 km
29 dy 28.716 28.614 -18,709,431 km 71,681,091 km -18,271,364 km 71,449,190 km 495,662 km
29.5 dy 29.211 29.108 -19,333,932 km 72,809,027 km -18,893,122 km 72,574,249 km 499,434 km
Given t × nα t × n [Rα× Cos(θα)]-1AU Rα× Sin(θα) [R×Cos(θ♁)]-1AU R× Sin(θ) (Δx2 +  Δy2 )
Assume Habα
 Mean Motion n
α=0.9902o/dy
Assume Earth
 Mean Motion nα=0.9867o/dy



NEW MOON: Assume Maximum Lunar Radius
Set origin (0,0) at Earth's initial position.
Time after
Launch
Hab. α
Angular 
Progress
Terra
Angular 
Progress
Habitat α Coord
Terra (♁) Coord
Distance
from Hab-α
 to Terra
t
θα
θ
Xα 
Yα
X Xα d
0 day
0.000⁰
0.000⁰
-406,906 km 0 km 0 km 0 km 406,906 km
1 day 0.991⁰ 0.987⁰ -429,208 km 2,579,529 km -22,182 km 2,569,115 km 407,159 km
2 day 1.981⁰ 1.973⁰ -496,107 km 5,158,287 km -88,723 km 5,137,468 km 407,915 km
3 day 2.972⁰ 2.960⁰ -607,583 km 7,735,502 km -199,603 km 7,704,298 km 409,172 km
4 day 3.963⁰ 3.947⁰ -763,602 km 10,310,405 km -354,788 km 10,268,843 km 410,922 km
5 day 4.954⁰ 4.934⁰ -964,119 km 12,882,226 km -554,233 km 12,830,342 km 413,157 km
6 day 5.944⁰ 5.920⁰ -1,209,073 km 15,450,195 km -797,878 km 15,388,036 km 415,866 km
7 day 6.935⁰ 6.907⁰ -1,498,390 km 18,013,545 km -1,085,652 km 17,941,167 km 419,037 km
8 day 7.926⁰ 7.894⁰ -1,831,985 km 20,571,509 km -1,417,468 km 20,488,978 km 422,653 km
9 day 8.916⁰ 8.880⁰ -2,209,758 km 23,123,323 km -1,793,229 km 23,030,712 km 426,700 km
10 day 9.907⁰ 9.867⁰ -2,631,595 km 25,668,224 km -2,212,824 km 25,565,616 km 431,159 km
11 day 10.898⁰ 10.854⁰ -3,097,371 km 28,205,451 km -2,676,127 km 28,092,938 km 436,011 km
12 day 11.888⁰ 11.840⁰ -3,606,946 km 30,734,245 km -3,183,001 km 30,611,929 km 441,238 km
13 day 12.879⁰ 12.827⁰ -4,160,168 km 33,253,850 km -3,733,296 km 33,121,842 km 446,818 km
14 day 13.870⁰ 13.814⁰ -4,756,872 km 35,763,514 km -4,326,849 km 35,621,932 km 452,731 km
15 day 14.861⁰ 14.801⁰ -5,396,879 km 38,262,486 km -4,963,484 km 38,111,458 km 458,956 km
16 day 15.851⁰ 15.787⁰ -6,079,997 km 40,750,018 km -5,643,012 km 40,589,681 km 465,472 km
17 day 16.842⁰ 16.774⁰ -6,806,024 km 43,225,367 km -6,365,231 km 43,055,868 km 472,259 km
18 day 17.833⁰ 17.761⁰ -7,574,741 km 45,687,793 km -7,129,927 km 45,509,285 km 479,295 km
19 day 18.823⁰ 18.747⁰ -8,385,918 km 48,136,559 km -7,936,874 km 47,949,206 km 486,561 km
20 day 19.814⁰ 19.734⁰ -9,239,314 km 50,570,935 km -8,785,832 km 50,374,908 km 494,037 km
21 day 20.805⁰ 20.721⁰ -10,134,673 km 52,990,191 km -9,676,549 km 52,785,670 km 501,703 km
22 day 21.795⁰ 21.707⁰ -11,071,727 km 55,393,604 km -10,608,762 km 55,180,778 km 509,541 km
23 day 22.786⁰ 22.694⁰ -12,050,196 km 57,780,457 km -11,582,193 km 57,559,522 km 517,532 km
24 day 23.777⁰ 23.681⁰ -13,069,788 km 60,150,034 km -12,596,554 km 59,921,195 km 525,660 km
25 day 24.768⁰ 24.668⁰ -14,130,198 km 62,501,629 km -13,651,545 km 62,265,098 km 533,906 km
26 day 25.758⁰ 25.654⁰ -15,231,109 km 64,834,538 km -14,746,852 km 64,590,536 km 542,256 km
27 day 26.749⁰ 26.641⁰ -16,372,192 km 67,148,063 km -15,882,151 km 66,896,819 km 550,694 km
28 day 27.740⁰ 27.628⁰ -17,553,105 km 69,441,513 km -17,057,104 km 69,183,263 km 559,204 km
29 day 28.730⁰ 28.614⁰ -18,773,495 km 71,714,201 km -18,271,364 km 71,449,190 km 567,774 km
29.5 day 29.226⁰ 29.108⁰ -19,398,381 km 72,842,548 km -18,893,122 km 72,574,249 km 572,076 km
Given t × nα t × n [Rα× Cos(θα)]-1AU Rα× Sin(θα) [R×Cos(θ♁)]-1AU R× Sin(θ) (Δx2y2 )
Assume Habα
 Mean Motion n
α=0.9907o/dy
Assume Earth
 Mean Motion n=0.9867o/dy

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