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.

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 construction 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	ratio
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

A higher construction orbit saves delta V, but with a ConstructionPort capture system, angular momentum from lunar delivery provides the insertion delta V needed for loop launch insertion. A lower construction orbit can be accessed from Earth more often, and is less perturbed by lunar tides. North/South delta V from the Moon is needed for plane matching, and that will be smaller if the transfer orbit apogee velocity is smaller.

LunarSupply

Lunar Material and Momentum Supply

Construction Orbit Apogee