#format jsmath
= 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, shielding, and a source of angular momentum.  Earth launch is expensive, and is deficient in angular momentum compared to destination orbits.

||<-4> '''Earth and Moon and interesting orbits'''                              ||
||<-4> ''Earth''                                                                ||
|| $ \mu_e    $ || Earth gravitational parameter || 3.986004418e+14 || m^3^/s^2^||
|| $ 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||
||<-4> ''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     || m^2^/s   ||
||<-4> ''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      || m^2^/s   ||
||<-4> ''Moon''                                                                 ||
|| $ \mu_m    $ || Lunar gravitational parameter || 4.9027779e+12   || m^3^/s^2^||
|| $ 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     || m^2^/s   ||
||<-4>''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     || m^2^/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 [[HighApogeeConstruction | 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} $

||<-6:> construction orbit                              ||<-3:> Earth Loop launch  ||<-5:> Moon launch to construction apogee  ||
|| period   ||  km ||<-2> radius km ||<-2> velocity m/s ||<-3:> velocity m/s       ||<-4:> velocity m/s           ||<|2>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 ||
[[ attachment:LunarSupply.ods | spreadsheet ]]

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.  

That said, the less we launch from the Moon, the smaller the lunar launcher can be, so a higher ratio of Earth-to-Moon mass is also desirable.  I'll leave the tradeoffs to future mission planners, who are likely to imagine far more clever ways to optimize this.

== Lunar Launch ==

We can go about this two ways - Large vehicles and a launch loop, or tiny packets and a mass driver,  In either case, we can "curl the end" post-acceleration to change launch angle.  With some care to exclude lunar dust from the mechanisms, both can be placed near the lunar surface.  

Typical launch velocities of 2400 m/s would require a 100 km launch path at 3 gees.  Following the lunar polar radius of 1736 km, vehicles would experience about 0.34 gees of radial acceleration near the exit.   An additional 100 km of curved track with 30 degrees of launch azimuth selection can help change the orbital plane, but with a lateral acceleration of 3 gees.

An alternative might involve a launch into an orbit that re-encounters the Moon weeks later, skimming the lunar surface and deflecting into a different angle.  For nonvolatile bulk cargo from the Moon, this adds delay and complication, but the "time is money" delay might be cheaper than a high gee deflection system.

Large 100 kg-scale vehicles will use magnet-based launch sleds and have thrust packages.  They will extract launch energy and momentum from a velocity-transformer launch loop.  The vertical axis loop can be designed to circle past multiple banks of solar panels, designed to capture the Sun from different angles as the moon rotates.  It may be cheaper to install multiple banks of panels than to make a few large sets of pivoting Sun-tracking panels, especially given the vulnerability of pivots to lunar erosion.  For a 100 kW average power supply and 80% efficiency, a velocity transformer loop could launch about one 100 kg vehicle per hour.

Alternately, a loop can also be used for power storage, and energy can be extracted with a different linear generator to power a long coilgun for gram-scale pellets, perhaps 30 per second.  These pellets might be small aluminum cones, perhaps a micrometer thick, designed to shield a lump of lunar ice from the Sun, and radiate heat into 2.7 Kelvin deep space.  They might have a tiny PV cell powering a microchip, which receives mm-wave instructions and powers tiny electrochromic "thrusters" resembling [[http://serversky.com | server sky ]] thinsats.  These "smart pellets" maneuver into a destructive high speed collision with a catcher at the construction station destination.  1000 m/s arrival velocity is 500KJ/kg or 120 calories per gram.  If the pellet is cold enough, it won't vaporize, instead thermalizing and heating a long, narrow, and curving target cavity, perhaps expending some of the energy by bouncing inelastically off the walls. '''KLUDGE!'''  

=== Lunar Ice for Shielding ===

Hydrogen is the best shielding for galactic cosmic rays and solar flares; both are mostly high energy protons, and protons shed the most energy when they collide with other protons (as opposed to heavy nuclei).  Liquid hydrogen provides the best shielding per weight, but is bulky and difficult to keep cold.  Next best is liquid methane (25% hydrogen by weight), but also a cryogen, and not dense.  

High density polyetheylene (HDPE) is around 15% hydrogen by weight, is dense, reasonably strong, and can tolerate high temperatures, so it is the best bulk shielding material for launch from Earth.

Water (and ice) is 11% hydrogen by weight, and ice is weaker and melts 80C colder than HDPE.  However, there is ice on the Moon, but very little carbon.   Spacecraft shielding will probably be water/ice contained in HDPE, shielded from the Sun, with expansion space for ice to expand and contract between freezing and melting.

Properly aimed ice launched from the Moon '''adds''' angular momentum, and adds shielding.  Water is oavailable near the lunar south pole.  Not much; I imagine a small American town uses more water per year than the entire Moon has captured, so lunar ice should be used sparingly, until we can replenish it by deflecting Earth-threatening icy comets into the Moon.  Ice must never be processed into hydrogen rocket fuel; ice crystal exhaust plumes in Earth orbit are dangerous space debris, especially for optical and millimeter-wave surfaces.