Thursday, June 26, 2008

LAUNCHING ALPHA from the Moon


Terra, mother of all humanity,
has proven very fertile
and will give some of her children
a promising send off.

Terra's little sister, Luna,
is eager to help
with her ample resources.

Lunar Resources The most obvious lunar resources include the many minerals and materials inevitably found on a large rocky, celestial body.   Even better, Luna's most important resource will be as an invaluable platform to launch habitats.
Routine mining operations can uncover useful materials from Moon. Large areas of Lunar surface are covered with regolith to a depth of several meters. This substance is largely composed of materials shown in following chart. Elements on the lunar surface include: oxygen (O),  silicon (Si),  iron (Fe),  magnesium (Mg),  calcium (Ca),  aluminium (Al), manganese (Mn) and titanium (Ti). Among the more abundant are oxygen, iron and silicon. The oxygen content is estimated at 45% (by weight). Carbon (C) and nitrogen (N) appear to be present only in trace quantities from deposition by solar windNeutron spectrometry data from Lunar Prospector indicate the presence of hydrogen (H) concentrated at the Lunar poles.
Relative concentration of various elements on the lunar surface (in weight %)

Oxygen from the Moon. Oxygen is necessary for breathing, and it has several other uses (for example: rocket fuel). Fortunately, oxygen is the most abundant element in lunar soil. Lunar oxygen can be processed into liquid and stored in tanks made from lunar metals; then, it can be easily launched from the Moon with much less escape velocity then Earth.

Ice on the Moon  Data from the Lunar Prospector spacecraft indicates water ice at both the north and south lunar poles.
This agrees with previous results from the Clementine mission.
Scientists estimate as much as 6 trillion kilograms of lunar ice.

Helium-3. Researchers and space enthusiasts see helium 3 as the perfect fuel: extremely potent, nonpolluting, with virtually no radioactive by-product. While rare on Earth, it's much more plentiful on Luna.

Transformation. Some habitat components would be best manufactured on the Moon; then, launched for immediate use on the habitats. A few examples include:
  • Mirrors for Light.
    Habitat’s critical requirement will be a source of energy. Since habitat  will stay very near the Terran Solar orbit, there should be plenty of sunlight available. Habitat's exterior mirrors must perpetually collect solar energy to light up and energize the habitat's interior.  Thus, one of the very first components to be shipped to these habitats would be a completed, large mirror suitable for reflecting light to desired locations on the habitat.
  • Habitat Hull.  Sections could be manufactured on Lunar surface; then, launched into Lunar orbit for further assembly. As discussed in subsequent text, such modules could be ejected from Lunar orbit and inserted into Solar orbit at well planned times.  Completed modules could even include an ample supply of water which will be needed for its long voyage from Lunar orbit to an eventual parking spot 1 Astronomical Unit (AU) away.  

  • Earth's Soil for Terraformation.  Some items will need transhipment as well as transformation. For example, the first human settlements on Luna will need a means of food production. Most effective agriculture will use Terran soil with the microbes which make possible the growth of Terran flora; thus, initial Lunar agriculture will need to import several tons of Terran soil to be kept in Lunar "greenhouses". Eventually, the "seed" soil from Earth will spread as carefully selected portions of Lunar material mix with it. In turn, portions of this "terraformed" Lunar soil will ship to the habitats to start their own agricultures.

LUNAR LAUNCH: Perhaps Luna's most valuable resource is her position as an excellent launch platform. Thus, assume feasible methods to routinely, launch payloads from Lunar surface to Lunar orbit.  Such methods might include:
1. Traditional chemical, rocket launch (like the Apollo return missions).
Recall that required rocket fuel components (oxygen and hydrogen) are plentiful on Lunar Surface.

2. Lunar Space Elevator.  This concept is similar to the better known Earth-based space elevator idea; however,  engineering requirements for constructing a lunar elevator system can be more easily met due to Luna's much lower gravity.
3. Lunar Mass Driver.  Using magnetic levitation, this engine would accelerate a payload to the necessary speed required to escape the Moon's gravity and orbit Luna.


ENTER SOLAR ORBIT: Once in Lunar Orbit, vehicle must accomplish a carefully planned, well timed insertion into Solar Orbit.  Consider the New Moon phase, when Luna is directly between the Sun and the Earth. (Earth bound observers see a full view of the unlit portion of the moon. Every few years, some see a Solar Eclipse in the daytime when the New Moon is precisely between Sol and Earth.)
NEW MOON
Once per Lunar cycle, the Moon is between Sol and Terra.
The New Moon is the best time each month to lunar launch a vehicle into a solar orbit with slightly less radius then the Terran orbit. According to Newton's universal law of gravitation, this vehicle would have a slightly higher orbital velocity (both angular and linear) than Earth. Thus, once free of gravity influences from Luna and Terra, this vehicle would "lead" Earth in its Solar Orbit and would continually increase this lead until nudged back into Earth's precise orbit.  Once there, this object, the Alpha Habitat (Hab-α) would "park" in a permanent position 60° ahead of Earth.

Lunar Launch Parameters

Lunar 
 radius fm 
 Earth Center (rL)
Solar 
 radius fm Sun_Center(RS)
Linear Velocity
Angular Velocity
Time till Destination
Lunar
 Phase
Vsec
VDay
ω
Δω
T
Max407,000km0.99728AU29.855km/sec0.017243AU/day0.9907o/day0.0040o/day41.1yearsNEW_MOON
400,000km0.99733AU29.854km/sec0.017242AU/day0.9906o/day0.0039o/day41.8years
360,000km0.99759AU29.850km/sec0.01724AU/day0.9902o/day0.0035o/day46.5years
Min357,000km0.99761AU29.850km/sec0.01724AU/day0.9902o/day0.0035o/day46.9yearsNEW_MOON
Given1.0 AU - rL
(μSol

R
)
VSec×86,400sec/dy

149,597,870.7 km/AU
57.3×VDay

R
ωα - ω
60°

Δω
×1 year

365.25dy
During New Moon, Min/Max values for lunar radius are most likely. 
For shortest time to destination, the Max is best distance to release Habitat from Earth-Moon system 
 on its way to Alpha, 60o ahead of Earth in its Solar Orbit. HOWEVER, "Min" value suffices for effective Launch.
Lunar Launch to Alpha (α) happens at New Moon; thus, vehicle (Habitat-α) can instantaneously achieve a slightly smaller Solar Orbit for a slightly quicker orbit. Thus, a New Moon launch enables a vehicle to lead Mother Earth in Earth's own orbit. Vehicle's travel must be planned so that it rejoins Earth's orbit at precisely the desired position.

In this case, target would the Sol-Terra L-4 point. If habitat separates from the Luna-Terra system and maintains the small daily rate of 4 thousandths of a degree, then it would take 15,000 days (about 41 years) to reach 60° from Earth's orbital position. Thereafter, habitat Alpha can leverage the inherent L4 stability to maintain 60° lead from Earth. The lengthy transit time can be put to good use with lots of construction going on with materials being supplied by following launches from Luna.

Special Spatial Concerns:
1. LAUNCH SIZE. For first few launches, minimize risk with small mass; thus, worst case scenario (launched mass actually impacts Earth) will cause minimal damage. As confidence increases, launched mass (for subsequent additions to habitat) can increase.
2. DANGER TO TERRA. Launch point will be from carefully chosen position on Luna at a carefully chosen position in Luna's orbit about Terra. This puts initial position of launched habitat at perhaps 354,000 km from Terra. If launch vectors put habitat into appropriate Solar orbit, habitat will escape the gravity pull of the Terra-Luna system.
3. DANGER FROM LUNA. Will the moon (our launch platform) come around and impact our habitat on the next Lunar orbit? Assuming successful orbital insertion, simple tables of likely separation distances indicate this is highly unlikely.  See Alpha Launch Tables.
After Lunar Launch, note continual increase of  linear separation (distance, d)
of habitat from Terra throughout first lunar cycle.
Assume Near Moon happens exactly when Terra crosses line from Sol to “Point of Aries” as shown.
Further assume minimum Lunar radius (RL) of 354,000 km.
If Hab-α carefully launches from Luna at New Moon phase, it achieves a Solar Orbit of 1 AU - R.
1 AU - R =  149,597,870.7 km - 354,000 km
1 AU - R =  1 AU - .00237 AU  = 0.99763 AU
For convenience assume angular velocity of time × mean motion for both Terra and Hab-α.
Assume Habα  Mean Motion: nα = 0.9902o/dy
Assume Earth Mean Motion:  n♁ = 0.9867o/dy
Inset rectangle shows Hab-α progress during first Lunar Cycle (New Moon to New Moon), a duration of 29.5 days.
During New Moon at Aries, Hab-α launches “aft” side of Luna.  Assume enough propulsion to barely escape gravity of Terra-Luna system and maintain Solar orbit of 0.99763 AU.  Slightly lesser radius than Terra will cause greater angular velocity and Hab-α will gradually increase its lead to Terra. 
CONSIDER Will Hab-α avoid Lunar collision during this critical first Lunar Cycle?
Inspection of most likely Hab-α progress indicates that such collision is unlikely. Immediate Lunar motion is distinctly away from Hab-α in its Solar Orbit; thus, collision is unlikely as long as Hab-α escapes Luna’s gravity.
Remaining question:  Will Luna collide with Hab-α when it returns to New Moon position. Again, this is very unlikely.
EXAMPLE:  During Full Moon phase when Hab-α and Luna are on opposite sides of Terra (thus, safely far apart); Hab-α is over 400,000 km from Terra, very near the max lunar radius of 407,000 km from Earth’s center.

By the time Luna returns to New Moon position and thus near Hab-α ‘s Solar radius, Hab-α has already increased its distance from Terra to over 499,000 km, well out of Luna’s reach.  Now, Hab-α must just await 40+ years until it reaches 60⁰ ahead of Terra, and it modifies its Solar Radius to exactly 1.0 AU to maintain that 60⁰ lead.

Subsequent Opportunities
Previous diagrams indicate that Luna holds no danger for newly launched habitats. Thus, Luna can accomplish follow on launches during subsequent New Moons to add more modules to Habitat-α. During the 40+ years that Habitat-α travels from Luna to 60° ahead of Terra, a crew of humans and AI devices can productively use this time to fully assemble their habitat and conduct unique scientific research.
TRANSITION: In next chapter, Landing Omega ...., we discuss Lunar Launches from Lunar orbit to Solar orbit during subsequent months and years throughout the 40+ year duration from Lunar launch to Solar parking at 60°  (a full AU) from Terra.



VOLUME I: ASTEROIDAL
VOLUME II: INTERPLANETARY
VOLUME III: INTERSTELLAR




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