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---- /!\ '''Edit conflict - your version:''' ---- The following table is approximate, describing the apses, velocities, and times for construction orbits and in-plane trajectories (I wish ...). Plane changes (cheaper at apogee) require delta V's of $~~ 2 \sin( \delta / 2 ) ~ V_{apogee} $ ---- /!\ '''End of edit conflict''' ---- |
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---- /!\ '''Edit conflict - your version:''' ---- === Lunar Launch Loop === ---- /!\ '''End of edit conflict''' ---- |
Lunar Material and Momentum Supply
I am skeptical about high tech manufacturing in space, especially in the dusty lunar environment. Factories are big, and need a lot of PhDs to keep them running. 100 years from now, there will be many such factories in space, but for now, we have problems locating them in most countries around the world, where there is air and water and food and FedEx.
Assuming we can get material launched from the moon ( 5.5% of the escape energy and launch loop track length ), there are plenty of uses for deadweight mass in space, as ballast and as a source of momentum. Earth launch is expensive, and is deficient in angular momentum compared to destination orbits.
Earth and Moon and interesting orbits |
|||
Earth |
|||
\mu_e |
Earth gravitational parameter |
3.986004418e+14 |
m3/s2 |
r_E |
Earth equatorial radius |
6378137 |
m |
E_e |
Earth escape energy |
-62.494807 |
MJ/kg |
\omega_e |
Earth angular frequency |
7.29211515e-5 |
radians/s |
Geostationary orbit |
|||
r_{GEO} |
GEO radius |
42164172.4 |
m |
v_{GEO} |
GEO velocity |
3074.66 |
m/s |
E_{GEO} |
GEO Energy/kg |
-1.41803E+07 |
J/kg |
H_{GEO} |
GEO Angular momentum/kg |
1.2964E+11 |
m2/s |
M288 Server Sky orbit |
|||
r_{288} |
M288 radius |
12788978 |
m |
v_{288} |
M288 velocity |
5582.79 |
m/s |
E_{288} |
M288 energy/kg |
-4.6751244E+07 |
J/kg |
H_{288} |
M288 angular momentum/kg |
7.1398E+10 |
m2/s |
Moon |
|||
\mu_m |
Lunar gravitational parameter |
4.9027779e+12 |
m3/s2 |
r_m |
Lunar equatorial radius |
1738140 |
m |
E_{m-esc} |
Lunar escape energy |
2.8207037 |
MJ/kg |
a_m |
Lunar orbit semi-major axis |
384399000 |
m |
v_m |
Lunar orbit velocity |
1023.155 |
m/s |
t_m |
Lunar orbit period |
2360591.5 |
seconds |
\omega_m |
Lunar orbit angular frequency |
2.66169954e-6 |
radians/s |
E_m |
Lunar orbit energy/kg |
-5.13522E+05 |
J/kg |
H_m |
Lunar angular momentum/kg |
3.93300E+11 |
m2/s |
Hohmann orbit, moon to GEO r_a = a_m r_p = r_{GEO} |
|||
a_{m-GEO} |
Lunar-GEO semi-major axis |
213281586 |
m |
e_{m-GEO} |
Lunar-GEO eccentricity |
0.8023075 |
|
v_{a-m-GEO} |
Lunar-GEO apogee velocity |
452.7650 |
m/s |
v_{l-m-GEO} |
Lunar-GEO launch velocity |
-2442.6935 |
m/s |
v_{p-m-GEO} |
Lunar-GEO perigee velocity |
4127.7325 |
m/s |
v_{i-m-GEO} |
Lunar-GEO insertion velocity |
-1053.0725 |
m/s |
E_{m-GEO} |
Lunar-GEO energy/kg |
-9.34446E+05 |
J/kg |
H_{m-GEO} |
Lunar-GEO angular momentum/kg |
1.74042E+11 |
m2/s |
\omega_{m-G} |
Lunar-GEO angular freq @ moon |
1.17785E-06 |
radians/s |
\omega_{G-m} |
Lunar-GEO angular freq @ GEO |
9.78967E-05 |
radians/s |
Construction Orbit Apogee
Earth-Launchloop synchronous orbits "return to perigee" at multiples of an 86141 second sidereal day, facilitating synchronized additions of material from a launchloop. These ConstructionOrbits can be fed at apogee from lunar launches, though arrivals will be infrequent and asynchronous, especially due to the 23 degree inclnation of the Earth's orbit, and the extra 8 degrees north inclination of construction orbit apogees (launched from 8 degrees south.
Since the orbits are in a plane matching the launch loop's south latitude with respect to the Earth's center; a launch from the Moon that intersects with this plane will occur at the two times per month when the moon crosses this plane as well. That launch will generally be approximately collinear with 8 degrees south latitude on Earth.
A launch loop near the south pole of the Moon, launching approximately retrograde to the Moon's orbit, can harvest lunar ice in permanently shadowed craters, and connect to rotating photovoltaic arrays in contnuous sunlight. Although the Moon is tidelocked to the Earth, rotating once per sidereal month, a few degrees of north/south adjustment will be needed. Also, the lunar rotation axis is 1.5 degrees from the elliptic poles, and precesses in an 18.6 year cycle. As of this writing, it is pointed about 0.7 degrees away from Delta Doradus in the southern Dorado constellation, and about 24.4 degrees from the Earth's south celestial pole.
Actual mission planning will require much more precision than this. Loop launched surveying satellites and active retroreflectors will help us map the inner solar system to micrometer precision.
![/!\](/moin_static198/modernized/img/alert.png "/!\"){kind=small}
Edit conflict - other version:
Edit conflict - other version:
The following table is approximate, describing the apses, velocities, and times for construction orbits and in-plane trajectories (I wish ...). Plane changes (cheaper at apogee) require delta V's of 2 \sin{ \delta / 2 } ~ V_{apogee}
Edit conflict - your version:
The following table is approximate, describing the apses, velocities, and times for construction orbits and in-plane trajectories (I wish ...). Plane changes (cheaper at apogee) require delta V's of ~~ 2 \sin( \delta / 2 ) ~ V_{apogee}
End of edit conflict
construction orbit |
Earth Loop launch |
Moon launch to constr. apogee |
|||||||||||
period |
km |
radius km |
velocity m/s |
velocity m/s |
velocity m/s |
ratio |
|||||||
sid.days |
semi |
peri. |
apo. |
peri. |
apo. |
peri. |
apo. |
insert |
apo. |
peri. |
launch |
insert |
|
1 |
42164 |
8378 |
75950 |
9257 |
1021 |
10666 |
907 |
114.2 |
584.9 |
2961 |
2420 |
-1939 |
16.98 |
2 |
66931 |
8378 |
125484 |
9445 |
631 |
10835 |
558 |
72.9 |
714.4 |
2188 |
2399 |
-1558 |
21.36 |
3 |
87705 |
8378 |
167032 |
9519 |
477 |
10902 |
421 |
56.0 |
792.6 |
1824 |
2390 |
-1347 |
24.07 |
4 |
106247 |
8378 |
204116 |
9560 |
392 |
10939 |
346 |
46.3 |
848.1 |
1597 |
2385 |
-1205 |
26.01 |
5 |
123289 |
8378 |
238199 |
9588 |
337 |
10963 |
297 |
40.0 |
890.8 |
1437 |
2382 |
-1100 |
27.51 |
6 |
139223 |
8378 |
270068 |
9607 |
298 |
10980 |
263 |
35.5 |
925.1 |
1317 |
2380 |
-1019 |
28.73 |
7 |
154292 |
8378 |
300205 |
9621 |
269 |
10993 |
236 |
32.0 |
953.6 |
1221 |
2379 |
-953 |
29.74 |
8 |
168657 |
8378 |
328935 |
9633 |
245 |
11003 |
216 |
29.3 |
977.9 |
1143 |
2378 |
-897 |
30.60 |
9 |
182434 |
8378 |
356489 |
9642 |
227 |
11011 |
199 |
27.1 |
998.9 |
1077 |
2377 |
-851 |
31.35 |
10 |
195709 |
8378 |
383039 |
9650 |
211 |
11018 |
186 |
25.3 |
1017.4 |
1021 |
2377 |
-810 |
32.01 |
Edit conflict - other version:
Edit conflict - your version:
The following table is approximate, describing the apses, velocities, and times for construction orbits and in-plane trajectories (I wish ...). Plane changes (cheaper at apogee) require delta V's of ~~ 2 \sin( \delta / 2 ) ~ V_{apogee}
construction orbit |
Earth Loop launch |
Moon launch to constr. apogee |
|||||||||||
period |
km |
radius km |
velocity m/s |
velocity m/s |
velocity m/s |
ratio |
|||||||
sid.days |
semi |
peri. |
apo. |
peri. |
apo. |
peri. |
apo. |
insert |
apo. |
peri. |
launch |
insert |
|
1 |
42164 |
8378 |
75950 |
9257 |
1021 |
10666 |
907 |
114.2 |
584.9 |
2961 |
2420 |
-1939 |
16.98 |
2 |
66931 |
8378 |
125484 |
9445 |
631 |
10835 |
558 |
72.9 |
714.4 |
2188 |
2399 |
-1558 |
21.36 |
3 |
87705 |
8378 |
167032 |
9519 |
477 |
10902 |
421 |
56.0 |
792.6 |
1824 |
2390 |
-1347 |
24.07 |
4 |
106247 |
8378 |
204116 |
9560 |
392 |
10939 |
346 |
46.3 |
848.1 |
1597 |
2385 |
-1205 |
26.01 |
5 |
123289 |
8378 |
238199 |
9588 |
337 |
10963 |
297 |
40.0 |
890.8 |
1437 |
2382 |
-1100 |
27.51 |
6 |
139223 |
8378 |
270068 |
9607 |
298 |
10980 |
263 |
35.5 |
925.1 |
1317 |
2380 |
-1019 |
28.73 |
7 |
154292 |
8378 |
300205 |
9621 |
269 |
10993 |
236 |
32.0 |
953.6 |
1221 |
2379 |
-953 |
29.74 |
8 |
168657 |
8378 |
328935 |
9633 |
245 |
11003 |
216 |
29.3 |
977.9 |
1143 |
2378 |
-897 |
30.60 |
9 |
182434 |
8378 |
356489 |
9642 |
227 |
11011 |
199 |
27.1 |
998.9 |
1077 |
2377 |
-851 |
31.35 |
10 |
195709 |
8378 |
383039 |
9650 |
211 |
11018 |
186 |
25.3 |
1017.4 |
1021 |
2377 |
-810 |
32.01 |
End of edit conflict
Lunar Launch Loop
Edit conflict - your version:
Lunar Launch Loop
End of edit conflict