Wednesday, April 21, 2010

Ref Mat'l: Asteroidal Tables

........

Habitat to Mars
νRxyDistDistvT Cumm T Mars
DegAUAUAUAUkmkm/secdaysdaysPosition
1.0001.000.00n/an/a32.7n/a057.3°
1.0001.000.020.01752,610,97932.70.920.9257.7°
1.0001.000.030.01752,611,13832.70.921.8558.2°
1.0001.000.050.01752,611,45732.70.922.7758.6°
1.0001.000.070.01752,611,93532.70.923.6959.0°
1.0011.000.090.01752,612,57232.70.924.6259.5°
1.0011.000.100.01752,613,36932.70.925.5459.9°
1.0010.990.120.01752,614,32432.70.936.4760.4°
1.0020.990.140.01752,615,43932.70.937.3960.8°
1.0020.990.160.01752,616,71332.70.938.3261.2°
10°1.0030.990.170.01752,618,14632.70.939.2561.7°
11°1.0030.980.190.01752,619,73832.70.9310.1762.1°
12°1.0040.980.210.01752,621,48932.60.9311.1062.6°
13°1.0040.980.230.01752,623,39932.60.9312.0363.0°
14°1.0050.980.240.01762,625,46832.60.9312.9763.4°
15°1.0060.970.260.01762,627,69632.60.9313.9063.9°
νRxyDistDistvT Cumm T Mars
16°1.0070.970.280.01762,630,08232.60.9314.8364.3°
17°1.0080.960.290.01762,632,62632.50.9415.7764.8°
18°1.0080.960.310.01762,635,32932.50.9416.7165.2°
19°1.0090.950.330.01762,638,19132.50.9417.6565.7°
20°1.0100.950.350.01772,641,21032.50.9418.5966.1°
21°1.0110.940.360.01772,644,38732.40.9419.5366.6°
22°1.0130.940.380.01772,647,72232.40.9520.4867.0°
23°1.0140.930.400.01772,651,21532.40.9521.4367.5°
24°1.0150.930.410.01772,654,86532.30.9522.3867.9°
25°1.0160.920.430.01782,658,67332.30.9523.3368.4°
26°1.0180.910.450.01782,662,63732.30.9524.2868.8°
27°1.0190.910.460.01782,666,75932.20.9625.2469.3°
28°1.0200.900.480.01792,671,03632.20.9626.2069.7°
29°1.0220.890.500.01792,675,47032.20.9627.1670.2°
30°1.0230.890.510.01792,680,06032.10.9728.1370.6°
νRxyDistDistvT Cumm T Mars
31°1.0250.880.530.01792,684,80632.10.9729.1071.1°
32°1.0270.870.540.01802,689,70732.00.9730.0771.6°
33°1.0280.860.560.01802,694,76332.00.9831.0572.0°
34°1.0300.850.580.01802,699,97331.90.9832.0272.5°
35°1.0320.850.590.01812,705,33831.90.9833.0173.0°
36°1.0340.840.610.01812,710,85731.80.9933.9973.4°
37°1.0360.830.620.01822,716,52931.80.9934.9873.9°
38°1.0380.820.640.01822,722,35431.70.9935.9774.4°
39°1.0400.810.650.01822,728,33131.71.0036.9774.8°
40°1.0420.800.670.01832,734,46031.61.0037.9775.3°
41°1.0440.790.680.01832,740,74031.61.0038.9775.8°
42°1.0460.780.700.01842,747,17231.51.0139.9876.3°
43°1.0480.770.710.01842,753,75331.51.0140.9976.8°
44°1.0500.760.730.01852,760,48431.41.0242.0177.2°
45°1.0530.740.740.01852,767,36331.41.0243.0377.7°
νRxyDistDistvT Cumm T Mars
46°1.0550.730.760.01852,774,39131.31.0344.0678.2°
47°1.0580.720.770.01862,781,56531.21.0345.0978.7°
48°1.0600.710.790.01862,788,88731.21.0446.1379.2°
49°1.0630.700.800.01872,796,35331.11.0447.1779.7°
50°1.0650.680.820.01872,803,96531.01.0548.2180.2°
51°1.0680.670.830.01882,811,72031.01.0549.2680.7°
52°1.0700.660.840.01882,819,61930.91.0650.3281.2°
53°1.0730.650.860.01892,827,65930.81.0651.3881.7°
54°1.0760.630.870.01902,835,84030.81.0752.4482.2°
55°1.0790.620.880.01902,844,16030.71.0753.5282.7°
56°1.0820.600.900.01912,852,61930.61.0854.5983.2°
57°1.0840.590.910.01912,861,21530.61.0855.6883.7°
58°1.0870.580.920.01922,869,94730.51.0956.7784.2°
59°1.0900.560.930.01922,878,81330.41.1057.8684.8°
60°1.0940.550.950.01932,887,81330.31.1058.9785.3°
νRxyDistDistvT Cumm T Mars
61°1.0970.530.960.01942,896,94530.31.1160.0785.8°
62°1.1000.520.970.01942,906,20730.21.1161.1986.3°
63°1.1030.500.980.01952,915,59730.11.1262.3186.9°
64°1.1060.480.990.01962,925,11430.01.1363.4487.4°
65°1.1100.471.010.01962,934,75729.91.1364.5788.0°
66°1.1130.451.020.01972,944,52429.91.1465.7188.5°
67°1.1160.441.030.01972,954,41229.81.1566.8689.0°
68°1.1200.421.040.01982,964,41929.71.1668.0289.6°
69°1.1230.401.050.01992,974,54529.61.1669.1890.1°
70°1.1270.391.060.02002,984,78629.51.1770.3590.7°
71°1.1300.371.070.02002,995,14129.41.1871.5291.3°
72°1.1340.351.080.02013,005,60729.41.1872.7191.8°
73°1.1380.331.090.02023,016,18329.31.1973.9092.4°
74°1.1410.311.100.02023,026,86529.21.2075.1093.0°
75°1.1450.301.110.02033,037,65129.11.2176.3193.5°
νRxyDistDistvT Cumm T Mars
76°1.1490.281.110.02043,048,54029.01.2277.5394.1°
77°1.1530.261.120.02053,059,52728.91.2278.7594.7°
78°1.1570.241.130.02053,070,61128.81.2379.9895.3°
79°1.1610.221.140.02063,081,78928.71.2481.2295.9°
80°1.1650.201.150.02073,093,05728.71.2582.4796.5°
81°1.1690.181.150.02083,104,41428.61.2683.7397.1°
82°1.1730.161.160.02083,115,85528.51.2785.0097.7°
83°1.1770.141.170.02093,127,37828.41.2886.2798.3°
84°1.1810.121.170.02103,138,98028.31.2887.5698.9°
85°1.1850.101.180.02113,150,65728.21.2988.8599.5°
86°1.1890.081.190.02113,162,40628.11.3090.15100.1°
87°1.1930.061.190.02123,174,22328.01.3191.47100.7°
88°1.1980.041.200.02133,186,10627.91.3292.79101.4°
89°1.2020.021.200.02143,198,04927.81.3394.12102.0°
90°1.2060.001.210.02153,210,05127.71.3495.46102.6°
νRxyDistDistvT Cumm T Mars
91°1.211-0.021.210.02153,222,10627.61.3596.81103.3°
92°1.215-0.041.210.02163,234,21127.51.3698.17103.9°
93°1.220-0.061.220.02173,246,36227.41.3799.54104.6°
94°1.224-0.091.220.02183,258,55427.31.38100.92105.2°
95°1.228-0.111.220.02193,270,78527.21.39102.31105.9°
96°1.233-0.131.230.02193,283,04927.11.40103.71106.5°
97°1.237-0.151.230.02203,295,34227.01.41105.12107.2°
98°1.242-0.171.230.02213,307,66026.91.42106.54107.9°
99°1.247-0.201.230.02223,319,99926.81.43107.97108.6°
100°1.251-0.221.230.02233,332,35326.71.44109.41109.3°
101°1.256-0.241.230.02243,344,71926.61.45110.87109.9°
102°1.260-0.261.230.02243,357,09126.61.46112.33110.6°
103°1.265-0.281.230.02253,369,46526.51.47113.80111.3°
104°1.270-0.311.230.02263,381,83726.41.49115.29112.0°
105°1.274-0.331.230.02273,394,20126.31.50116.79112.8°
νRxyDistDistvT Cumm T Mars
106°1.279-0.351.230.02283,406,55226.21.51118.29113.5°
107°1.284-0.381.230.02293,418,88526.11.52119.81114.2°
108°1.289-0.401.230.02293,431,19626.01.53121.34114.9°
109°1.293-0.421.220.02303,443,48025.91.54122.88115.7°
110°1.298-0.441.220.02313,455,73125.81.55124.43116.4°
111°1.303-0.471.220.02323,467,94425.71.56126.00117.1°
112°1.307-0.491.210.02333,480,11525.61.57127.57117.9°
113°1.312-0.511.210.02333,492,23725.51.59129.16118.6°
114°1.317-0.541.200.02343,504,30625.41.60130.75119.4°
115°1.322-0.561.200.02353,516,31725.31.61132.36120.2°
116°1.326-0.581.190.02363,528,26425.21.62133.98120.9°
117°1.331-0.601.190.02373,540,14225.11.63135.62121.7°
118°1.336-0.631.180.02373,551,94625.01.64137.26122.5°
119°1.340-0.651.170.02383,563,67124.91.66138.92123.3°
120°1.345-0.671.160.02393,575,31224.81.67140.58124.1°
νRxyDistDistvT Cumm T Mars
121°1.350-0.701.160.02403,586,86324.71.68142.26124.9°
122°1.354-0.721.150.02413,598,31924.61.69143.95125.7°
123°1.359-0.741.140.02413,609,67524.51.70145.65126.5°
124°1.364-0.761.130.02423,620,92724.51.71147.37127.3°
125°1.368-0.781.120.02433,632,06924.41.73149.09128.1°
126°1.373-0.811.110.02443,643,09524.31.74150.83128.9°
127°1.377-0.831.100.02443,654,00224.21.75152.58129.8°
128°1.382-0.851.090.02453,664,78424.11.76154.34130.6°
129°1.386-0.871.080.02463,675,43724.01.77156.11131.4°
130°1.391-0.891.070.02463,685,95623.91.78157.89132.3°
131°1.395-0.921.050.02473,696,33523.81.79159.68133.1°
132°1.400-0.941.040.02483,706,57223.81.81161.49134.0°
133°1.404-0.961.030.02483,716,66023.71.82163.31134.9°
134°1.408-0.981.010.02493,726,59623.61.83165.13135.7°
135°1.412-1.001.000.02503,736,37623.51.84166.97136.6°
νRxyDistDistvT Cumm T Mars
136°1.417-1.020.980.02503,745,99523.41.85168.82137.5°
137°1.421-1.040.970.02513,755,44923.41.86170.68138.4°
138°1.425-1.060.950.02523,764,73523.31.87172.55139.2°
139°1.429-1.080.940.02523,773,84823.21.88174.44140.1°
140°1.433-1.100.920.02533,782,78523.11.89176.33141.0°
141°1.437-1.120.900.02533,791,54223.11.90178.23141.9°
142°1.441-1.140.890.02543,800,11523.01.91180.14142.9°
143°1.444-1.150.870.02553,808,50322.91.92182.07143.8°
144°1.448-1.170.850.02553,816,70022.91.93184.00144.7°
145°1.452-1.190.830.02563,824,70422.81.94185.94145.6°
146°1.455-1.210.810.02563,832,51322.71.95187.90146.5°
147°1.459-1.220.790.02573,840,12322.71.96189.86147.5°
148°1.462-1.240.770.02573,847,53222.61.97191.83148.4°
149°1.466-1.260.750.02583,854,73722.51.98193.81149.3°
150°1.469-1.270.730.02583,861,73622.51.99195.80150.3°
νRxyDistDistvT Cumm T Mars
151°1.472-1.290.710.02593,868,52622.42.00197.80151.2°
152°1.475-1.300.690.02593,875,10622.42.01199.80152.2°
153°1.478-1.320.670.02593,881,47322.32.01201.82153.1°
154°1.481-1.330.650.02603,887,62522.22.02203.84154.1°
155°1.484-1.340.630.02603,893,56222.22.03205.87155.1°
156°1.487-1.360.600.02613,899,28022.12.04207.91156.0°
157°1.489-1.370.580.02613,904,77922.12.05209.95157.0°
158°1.492-1.380.560.02613,910,05722.12.05212.01158.0°
159°1.494-1.390.540.02623,915,11322.02.06214.07159.0°
160°1.497-1.410.510.02623,919,94522.02.07216.13159.9°
161°1.499-1.420.490.02623,924,55321.92.07218.20160.9°
162°1.501-1.430.460.02633,928,93621.92.08220.28161.9°
163°1.503-1.440.440.02633,933,09221.82.08222.36162.9°
164°1.505-1.450.410.02633,937,02121.82.09224.45163.9°
165°1.507-1.460.390.02633,940,72121.82.09226.55164.9°
νRxyDistDistvT Cumm T Mars
166°1.508-1.460.360.02643,944,19421.82.10228.64165.9°
167°1.510-1.470.340.02643,947,43721.72.10230.75166.9°
168°1.511-1.480.310.02643,950,45021.72.11232.86167.9°
169°1.513-1.480.290.02643,953,23321.72.11234.97168.9°
170°1.514-1.490.260.02643,955,78521.72.11237.08169.9°
171°1.515-1.500.240.02653,958,10721.62.12239.20170.9°
172°1.516-1.500.210.02653,960,19721.62.12241.32171.9°
173°1.517-1.510.180.02653,962,05521.62.12243.44172.9°
174°1.518-1.510.160.02653,963,68221.62.13245.57173.9°
175°1.518-1.510.130.02653,965,07621.62.13247.70174.9°
176°1.519-1.520.110.02653,966,23921.62.13249.83176.0°
177°1.519-1.520.080.02653,967,16921.62.13251.96177.0°
178°1.520-1.520.050.02653,967,86621.52.13254.09178.0°
179°1.520-1.520.030.02653,968,33121.52.13256.22179.0°
180°1.520-1.520.000.02653,968,56421.52.13258.35180.0°
Given
l
1+e*cos(ν)
R*cos(ν)R*sin(ν)
√[(Δx)2+(Δy)2]
Dist*(km/AU)
√(Sol
Rν
-μSol
a
)
dν/vΣtνΣtν
Ω
 

Continue Semi-Orbits

Increase Hohman Transfers

SOSemimajor axisOrbit
Time
Angle
Diff
Cumm.
Angle
HTPerihelionAphelionTransfer TimeAngle
Diff
Cumm
Angle
(i)atδΔ(i)qQtδΔ
1 1.003 AU0.502Yr0.7°0.7°1 1.003 AU1.004 AU0.502Yr0.9°0.9°
2 1.003 AU0.502Yr0.7°1.4°2 1.004 AU1.005 AU0.503Yr1.2°2.0°
3 1.003 AU0.502Yr0.7°2.2°3 1.005 AU1.006 AU0.504Yr1.5°3.5°
4 1.003 AU0.502Yr0.7°2.9°4 1.006 AU1.007 AU0.505Yr1.8°5.3°
5 1.003 AU0.502Yr0.7°3.6°5 1.007 AU1.008 AU0.506Yr2.1°7.3°
6 1.003 AU0.502Yr0.7°4.3°6 1.008 AU1.009 AU0.507Yr2.4°9.7°
7 1.003 AU0.502Yr0.7°5.0°7 1.009 AU1.010 AU0.507Yr2.7°12.3°
8 1.003 AU0.502Yr0.7°5.8°8 1.010 AU1.011 AU0.508Yr2.9°15.3°
9 1.003 AU0.502Yr0.7°6.5°9 1.011 AU1.012 AU0.509Yr3.2°18.5°
10 1.003 AU0.502Yr0.7°7.2°10 1.012 AU1.014 AU0.510Yr3.5°22.0°
11 1.003 AU0.502Yr0.7°7.9°11 1.014 AU1.015 AU0.511Yr3.8°25.9°
12 1.003 AU0.502Yr0.7°8.6°12 1.015 AU1.016 AU0.511Yr4.1°30.0°
GivenAU + rL(2a)3/2
5.656
(t-.5)*360°ΣδiGiven1AU+i*rΔq + rΔ(q+Q)3/2
5.656
(t-.5)*360°Σδi
rL =384,000 km = 0.0026 AUrΔ =164,000 km = 0.0011AU
12 Semi-Orbits take 6.02 years for 8.6° lag.Estimate total of 43 yrs for 30° lag.12 Hohman Transfers can take 6.08 years for 30.0° lag.It depends on size of rΔ.

aaa

Mass of Sun and EarthSmith, Peter J. The Earth. New York: Macmillan Company, 1986.

MSol = 2 × 1030 kg

which dominates rest of Solar System is dominated by the Sun

For example, :

MSol = 343,000 * MEarth

Also, from circular motion, v = 2 π r /T, where is T is the "period" of circular motion.

Mean distance of Moon from Earth's center is 384,400 kms.

Moon/Earth/Sun Comparison

Bulk parameters Moon'>http://solarsystem.nasa.gov/planets/compchart.cfm?Object1=Moon">Moon Earth(kg)

7.35 x 1022

5.97 x 1024

2 x 1030

μ (=GM)(km3/s2)

xxx x 106

3.986 x 105

1.327 x 1011

Volume (km3)

2.20 x 1010

1.083 x 1012

1.412 x 1018

Equatorial radius (km)

1,738

6,378

est. 696,000

Polar radius(km)

1,736

6,356

working

Mean density (kg/m3)

3,350

5,515

1,408

Surface gravity (m/s2)

1.62

9.80

274.0

Escape velocitykm/s

2.38

11.2

617.7

Orbital velocitykm/s

1.023*

29.81**

n/a

* Lunar orbital speed for orbit around Earth.
**Terran orbital speed for orbit around Sun.

orbit around Earth

Orbital Dimensions

Perigee*

Semimajor axis

Apogee*

363,300 kms

384,400 kms

405,500 ms

Orbital Period

Revolution

Synodic

27.322 days

29.53 days

Orbital velocity

Min.

Mean

Max.

0.964 km/sec

1.023 km/sec

1.076 km/sec

Inclination to ecliptic

5.145o

Inclination to equator

Min.

Mean

Max.

18.28o

23.47o

28.58o

Orbit eccentricity

0.055

Sidereal rotation period

27 days 7.73 hrs

Obliquity to orbit

6.68o

Recession rate from Earth

3.8 centimeters per year

* Apogee and perigee values are for an average orbit. Lunar orbit changes over the course of the year so the distance from the Moon to Earth ranges from roughly 357,000 km to 407,000 km.







 

 

Transits 13-24

Continue Semi-Orbits

Static Hohman Transfers

SOSemi-Orbit
Time
Angle
Diff
Cumm.
Angle
HTAphelionPerihelionSemimajor axisTransfer TimeIncr. Ang. DiffCumm. Ang. Diff.
(i)tδΔ°(i)QqatδΔ
13 0.502Yr0.7°9.4°13 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°32.0°
14 0.502Yr0.7°10.1°14 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°33.9°
15 0.502Yr0.7°10.8°15 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°35.8°
16 0.502Yr0.7°11.5°16 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°37.7°
17 0.502Yr0.7°12.2°17 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°39.7°
18 0.502Yr0.7°13.0°18 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°41.6°
19 0.502Yr0.7°13.7°19 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°43.5°
20 0.502Yr0.7°14.4°20 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°45.4°
21 0.502Yr0.7°15.1°21 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°47.4°
22 0.502Yr0.7°15.9°22 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°49.3°
23 0.502Yr0.7°16.6°23 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°51.2°
24 0.502Yr0.7°17.3°24 1.016 AU1.012 AU1.014 AU0.505Yrs1.9°53.2°
Given(2a)3/2
5.656
(t-.5)*360°
year
ΣδiGiven1AU+i*rΔQ - rΔQ+q
2
(1+a)3/2
5.656
(t-.5)*360°
year
Σδi
a =1.0026 AU rΔ = 500,000km =0.0033AU
24 Semi-Orbits take 12.05 years for 17.3° lag.
Estimate 43 yrs for 30° lag.
24 Hohman Transfers take 12.1 years for 53.2°lag.

 


Transits 25-32

Continue Semi-Orbits

Decreasing Hohman Transfers

SOAngle
Diff
Cumm.
Angle
HTAphelionPerihelionSemimajor axisTransfer TimeIncr. Ang. DiffCumm. Ang. Diff.
(i)δΔ°(i)QqatδΔ
25 0.7°16.6°25 1.012 AU1.011 AU1.012 AU0.504Yrs1.6°54.7°
26 0.7°17.3°26 1.011 AU1.009 AU1.010 AU0.504Yrs1.4°56.1°
27 0.7°18.0°27 1.009 AU1.008 AU1.008 AU0.503Yrs1.2°57.3°
28 0.7°18.7°28 1.008 AU1.006 AU1.007 AU0.503Yrs1.0°58.3°
29 0.7°19.5°29 1.006 AU1.005 AU1.005 AU0.502Yrs0.8°59.0°
30 0.7°20.2°30 1.005 AU1.003 AU1.004 AU0.502Yrs0.5°59.6°
31 0.7°20.9°31 1.003 AU1.001 AU1.002 AU0.501Yrs0.3°59.9°
32 0.7°21.6°32 1.001 AU1.000 AU1.001 AU0.500Yrs0.1°60.0°
Given
(t-.5)*360°
year
ΣδiGiven1AU+i*rΔQ - rΔQ+q
2
(1+a)3/2
5.656
(t-.5)*360°
year
Σδi
t =0.502 yr per Semi-Orbit rΔ = 233,333km =0.0016 AU
32 Semi-Orbits take 16.06 years for 21.6° lag.32 Hohman Transfers take 16.2 years for 60.0°lag.

Static Circular Orbit
TimeAng. Disp
(T)α
1 yrs1.28°
2 yrs2.56°
3 yrs3.84°
10 yrs12.78°
20 yrs25.57°
30 yrs38.35°
40 yrs51.14°
44.4 yrs60.0°
GivenT*365.25*ω
ω =0.0035°/dy

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