ALPHA LAUNCH TABLE

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NEW MOON: Assume Minimum Lunar Radius
Set origin (0,0) at Earth's initial position.
Time	Hab. α ∠	Terra ∠	Habitat α Coord		Terra (♁) Coord		Dist. betw.	MOON PHASE
(t)	(θα)	(θ♁)	(Xα)	(Yα)	(X♁)	(Y♁)	(d)
0 dy	0.00⁰	0.00⁰	-354,547 km	0 km	0 km	0 km	354,547 km	NEW MOON
4 dy	3.96⁰	3.95⁰	-711,008 km	10,305,210 km	-354,788 km	10,268,843 km	358,072 km	WAXING CRESCENT
7.5 dy	7.43⁰	7.40⁰	-1,606,477 km	19,283,565 km	-1,246,060 km	19,215,785 km	366,734 km	FIRST QTR
11 dy	10.89⁰	10.85⁰	-3,043,248 km	28,191,387 km	-2,676,127 km	28,092,938 km	380,093 km	WAXING GIBBOUS
15 dy	14.85⁰	14.80⁰	-5,341,262 km	38,243,609 km	-4,963,484 km	38,111,458km	400,225 km	FULL MOON
19 dy	18.81⁰	18.75⁰	-8,328,377 km	48,113,145 km	-7,936,874 km	47,949,206 km	424,441 km	WANING GIBBOUS
22.5 dy	22.28⁰	22.20⁰	-11,496,244 km	56,562,040 km	-11,090,343 km	56,372,240 km	448,085 km	LAST QTR
26 dy	25.75⁰	25.65⁰	-15,169,240 km	64,804,049 km	-14,746,852 km	64,590,536 km	473,286 km	WANING CRESCENT
29.5 dy	29.21⁰	29.11⁰	-19,333,932 km	72,809,027 km	-18,893,122 km	72,574,249 km	499,434 km	NEW MOON
Given	t × nα	t × n♁	[Rα×Cos(θα)]-1AU	Rα× Sin(θα)	[R♁×Cos(θ♁)]-1AU	R♁ × Sin(θ♁)	√(Δx2+Δy2 )	Observed
			Rα = 0.9976 AU = 149,243,323.7 km		R♁ = 1.0 AU = 149,597,870.7 km

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

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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♁)

√(Δx2+Δy2 )

Assume Habα  Mean Motion nα=0.9907o/dy

Assume Earth  Mean Motion n♁=0.9867o/dy