Saturday, March 16, 2013


Why go???
Kuiper Belt will likely prove a bountiful source of raw materials.
Kuiper Belt (KB) is a vast reservoir of icy bodies beyond the orbit of Neptune (30 AU) to 55 AUs from Sol. Some have highly elliptical orbits; some periodically visit the inner solar system as comets. It's named after Gerard Kuiper (1905–1973), Dutch-born American astronomer.
 Kuiper Belt Objects (KBOs) are remnants of the original plantesimals, building blocks of the outer planets. Being well past the gas giants (Jupiter, Saturn, Uranus, Neptune), they were neither incorporated into the planets nor ejected from the Solar System. KBOs are thus relics from the Solar Nebula, the original disk of gas and dust that gave rise to the Solar System.
History. Since the discovery of Pluto, many have speculated about the region now called the Kuiper belt.
•  In 1930, Frederick C. Leonard was the first astronomer to suggest the existence of a trans-Neptunian population. Soon after Pluto's discovery, he pondered whether it was "… first of a series of ultra-Neptunian bodies...".
•  In 1943 and 1949, Kenneth Edgeworth (1880-1972) proposed a trans-Neptunian comet belt. Primordial material beyond Neptune is too sparse to condense into planets but still dense enough for many smaller bodies. Occasionally one "wanders from its own sphere” and visits the inner solar system as a comet.
•  In 1951, Gerard Kuiper (1905-73) proposed a region beyond Neptune where leftover plantesimals might have existed for many eons. He speculated a similar disc formed early in the Solar System's evolution; ironically, he did not believe such a belt now exists.
IN SITU RESOURCES. Eventually, we will harvest raw material from numerous Solar objects: comets, asteroids, moons and even planetoids (i.e., Pluto, etc.) Kuiper Belt has all these objects in abundance.
The Kuiper Belt can serve as an excellent source of raw materials for space borne enterprises; "icy bodies" can provide lots of liquids for life support and fuel. All bodies will provide plenty of structural material.
We've already manufactured and launched many extraterrestrial spacecraft from Earth's surface; most missions were accomplished by robotic devices, and all traveled via transfer orbits.
While near future missions will continue in this matter, necessity will eventually compel us to more efficiently manufacture and fuel spacecraft from space resources. Thus, some space vessels will become "habitats"; large, rotating structures which can accommodate large human populations. Most habitats will orbit Sol, planets or even moons via fixed orbits; however, some will travel throughout the Solar System via transfer orbits which can take years.

       Habitable habitats will need following resources:
• Plenty of consumables
: air, water and food. All these can be shipped and stored, but persistent supplies of air and food require creation in situ (within habitats). Discussed further below.
• Living space. Vessel's internal volume must accommodate reasonable sized human populations (> 10,000).
• Earth like gravity. Deliver g-force for their populations via carefully planned rotation to impart g-force via centrifugal force.
Typical hull will be at least one meter thick due to
  1) Structural integrity      2)  Protection from radiation.
Such a hull requires enormous amounts of raw material which would be highly impractical to launch from Earth's surface. It will probably prove practical to ship from Luna, Earth's moon, with one sixth the gravity of Terra, our planet. Even more practical, move comets and asteroids from KB to the habitats and extract desired materials.
Grow Food in Space. For successful agriculture, habitats will require “seed soil”; proper amounts of Earth's soil with fertile combinations of microbes, bacteria, seeds, insects, worms, etc. Hopefully, this fertile mix will readily replicate in raw material from space objects. Indeed, this soil may prove necessary to "terraform" celestial destinations.
Trees Produce Oxygen. Large forests are the "lungs of Earth" because they supply the vast majority of Earth's oxygen. Space borne habitats will accommodate large tree populations to provide essential oxygen as well as many other useful materials. Arbology (study of trees) will be essential for life on habitats.
Harvest Water in Space.
"Water, water everywhere, but not a drop to drink!"
There's a lot of water in the ocean & many comets in the KB.
Like ocean water, comet water will need treatment.
• In 1962, physicist Al G.W. Cameron postulated the existence of “a tremendous mass of small material on the outskirts of the solar system.”
• In 1964, Fred Whipple (recall: "dirty snowball" hypothesis of cometary structure) proposed a "comet belt" massive enough to affect physical events in the inner Solar System.
• In 1980, Julio Fernandez proposed a comet belt from 35 to 50 AU to account for vast majority of comet observations.
• In 1988, Canadians Martin Duncan, Tom Quinn and Scott Tremaine used Fernandez's proposal to perform computer simulations which confirmed that most observed comets could have come from this region. Tremaine named this region the "Kuiper Belt".
• In 1992, Jewitt and Luu discovered the first Kuiper belt object" (15760) 1992 QB1. Dr. Jewitt later proposed the region to be renamed in honor of Dr. Fernandez who more accurately predicted the true nature of the Kuiper Belt.
On January 19, 2006, the New Horizons (NH) spacecraft mission was launched. NH arrived at Pluto on July 14, 2015. NH then proceeded to another KBO for further study.
Physical Properties. Disk-shaped belt contains numerous small icy bodies orbiting the Sun beyond the orbit of Neptune; these KBOs orbit from 30 to 55 AU from the Sun. The Kuiper Belt is quite thick, with the main concentration extending as much as ten degrees outside the ecliptic plane and a more diffuse distribution of objects extending several times farther. KB more resembles a torus versus a belt. Its mean position is inclined to the ecliptic by 1.86 degrees.
Like the traditional Asteroid Belt (between Mars and Jupiter), KB consists mainly of small bodies (remnants from the Solar System's formation). However, Kuiper Belt is 20 to 200 times as massive as the asteroid belt.
ANOTHER DIFFERENCE: Asteroid belt objects are mainly rock and metal, the Kuiper Belt Objects (KBOs) are mostly frozen volatiles (i.e. "ices"), such as methane, ammonia and water. Over a thousand KBOs have been discovered since 1992; however, more than 70,000 KBOs over 100 km in diameter are likely.
KB has at least three dwarf planets: Pluto, Haumea and Makemake.


It will likely prove optimal
to use space borne resources
to construct space facilities
as much as possible.

Kuiper Belt resources will go to most habitats;
 however, most habitats will not go to Kuiper Belt. 
To optimally leverage KB resources,
humanity will need g-force vessels.
Orbiting habitats can take years
to complete their journeys.
However, g-force interplanetary travel
will take days or weeks.

TE  assumes g-force acceleration
comes from onboard particle accelerators;
furthermore, accelerator performance will improve. 

Exhaust particle speed (VExh) will increase;
thus, spaceship's range will increase
(further explained in following text).
BINARIES.  KB contains many binary objects (two objects of similar mass which orbit "each other"). The most notable example is the Pluto-Charon binary. Scientists estimate over 1% KBOs (a relatively high percentage) are binaries.
DWARF PLANET. Pluto is now classified as a dwarf planet. Pluto's orbit, icy composition, and size qualify it as a giant KBO, KB's largest known member.
PLUTINOS include KBOs which share Pluto’s orbital resonance with Neptune.  Gravitational disturbances by Neptune likely cause most short-period comets, solar orbits less than 200 years.

Kuiper Belt greatly contrasts with the Oort Cloud, a thousand times more distant. KBOs, members of the scattered disc, potential objects from the Hills cloud or Oort cloud are often called Trans-Neptunian Objects (TNOs).
Other Stars. 15-20% of solar-type stars are observed with infrared excess believed to indicate massive Kuiper Belt like structures.  For more about Kuiper Belt.

Particle's Exhaust Speed
is given as decimal light speed:
VExh = dc  c
Decimal component of light speed is dc .

Let exhaust particle velocity (VExh) = 86.6% c;
then, dc = 86.6% = .866
For Table-1, dc is the Independent Variable (IV).

Exhaust Particles
experience relativistic growth
per Lorentz Transform:
mr = 1/(1-dc²)

Thus, particle mass in one sec of fuel flow consumed at rest (ffsec) grows as it accelerates to become larger particle mass in one second of exhaust fuel flow (ffExh).
ffExh =   ffsec / (1-dc²) = mr × ffsec 

Let dc = 86.6% = .866;
ffExh = ffsec  / (1-.866²)  =  2.0 ffsec  = mr  × ffsec 
Then, exhaust fuel flow mass doubles
due to relativistic growth.
Brief Bio: Gerard Peter Kuiper
"Father of Modern Planetary Science"

G. P. Kuiper, 1905–73, American astronomer, born in the Netherlands. Kuiper is the father of modern planetary science due to his wide ranging studies of the solar system. He is best known for his namesake, the Kuiper Belt.
He proposed (1951) the existence of a disk-shaped region of minor planets outside the orbit of Neptune (now called the Kuiper belt) as a source for short-period comets—those making complete orbits around the sun in less than 200 years.
Kuiper was the editor of two encyclopedic works, The Solar System (4 vol., 1953–58) and Stars and Stellar Systems (9 vol., 1960–68).
During the 1960s, Kuiper served as chief scientist for the Ranger lunar-probe program, choosing crash-landing sites on the moon; by analyzing Ranger photographs, he also participated in the Surveyor and Apollo programs.
A pioneer in the field of infrared astronomy, he was honored posthumously when National Aeronautics and Space Admin (NASA) named its airborne infrared telescope the Kuiper Airborne Observatory (1975).
Early Life. Kuiper, the son of a tailor in the village of Tuitjenhorn in North Holland, had an early interest in astronomy. With extraordinarily sharp eyesight, he could see stars of magnitude 7.5 stars, about four times fainter than visible to normal eyes.

1924.  He entered Leiden University and befriended fellow students Bart Bok and Pieter Oosterhoff.  His instructors included: Ejnar Hertzsprung, Antonie Pannekoek, Willem de Sitter, Jan Woltjer, Jan Oort and the physicist Paul Ehrenfest.

1927.  He received his B.Sc. in Astronomy and continued straight on with his graduate studies.

1933.  Kuiper finished his doctoral thesis on binary stars with Hertzsprung.  Then, he traveled to Lick Observatory, in California, to work as a fellow under Robert Grant Aitken.

1935, he left Lick to work at the Harvard College Observatory.

June 20, 1936, he married Sarah Parker Fuller who he met at Harvard.

1937,  he took a position at the Yerkes Observatory of the University of Chicago and became an American citizen.

1949, Kuiper initiated the Yerkes - McDonald asteroid survey (1950 - 1952).
Ship's Gross Weight
can be determined by momentum equilibrium.
MShip × VShip  = MExhaustFuel × VExhaustFuel
On each side, divide one term by one second:
Ship's velocity:  VShip ÷ 1 sec = g
We choose ship's velocity to increase 9.8065 meters per sec;
thus, g = acceleration due to gravity.
MExhaustFuel ÷ 1 sec = Exhaust fuel flow per sec = ffExh
On each side, redefine the other term:
Exhaust fuel particle speed: VExhaustFuel  = dc c
Ship's Mass = GWt = Gross Weight for each day, t
GWt × g = ffExh × dc c
GWt = mrffsec × dc c ÷ g

Daily Difference (Δ) 
Ship's mass (i.e. GW) decreases
due to consumption of at rest fuel (ffSec).
One day’s consumption: ffDay = ffsec × 86,400 sec/Day
Daily diff as constant percentage:  Δ = ffDay ÷ GW

Previous work enables following substitutions:

Δ=86,400sec ffSec

mrfSec × dc c/g

mr × dc

Theoretical G-force Range
can be readily approximated with exponents.
GWt =(1-Δ)t

If g-force propulsion requires 1%GW/day (Δ);
compute theoretical GW for 50th day of powered flight.
GW50 = (1-.01)50 = (.99)50 = (.605) = 60.5% GW0
At 1%/day fuel burn for 50 days,
theoretical mass reduces to 60% original mass, GW0 .

Practical G-force Range
Consider inevitable inefficiency and max fuel load.
Assume propulsion efficiency (E) = 25%.
thus, efficiency factor: ε = 1/E = 4
Assume available fuel is 40% of original mass, GW0.
Find practical range, t, from available fuel
t = log(1-%TOGW) ÷ log(1-εΔ)
Find t from fuel = 40% of ship's original GW:
t = log(1-.4)÷log(1-4×.01) = log(.6)÷log(.96) = 12.6 days
G.P. Kuiper Discoveries include:
1. Uranus's satellite      
    Miranda (1948)
2.  Neptune's satellite Nereid (1949).
3.  Carbon dioxide in the atmosphere of Mars (1948).
4.  Methane in atmosphere of Saturn's satellite Titan (1944).
5.  Airborne infrared observing(via a Convair 990 in the 1960s).
6.  Several binary stars which received "Kuiper numbers" to identify them, i.e., KUI 79.
Kuiper spent much of his career at the University of Chicago, but he moved to the University of Arizona in 1960 to found the Lunar and Planetary Laboratory; he was Director until his death in 1973. 
For more about Dr. Kuiper.

TABLE-1: G-force Gets Us to Kuiper Belt Quickly!
Original fuel flow:
ffSec = 1.0 kg/sec
Original fuel load:
%TOGW = 40%
Efficiency factor:
ε = 4 = 100% ÷ %Out
daysec× g

= 86,400 s/day ×9.8065 m/s2

299,792,458 m/s
Gross Wt.
G-force Flight Profile
2 way trip time
10.0% c1.005 kg3,072 mT2.81%/Day4.3 dayAt minimum distance of .5 AU, 2 way trip to Mars could take 4 days of g-force.
27.0% c1.039 kg8,603 mT1.00%/Day12.6 dayWith typical distance of 5 AU, two way trip to Jupiter would take 12.7 days.
50.0% c1.155 kg17,650 mT0.49%/Day25.3 dayWith typical distance of 20 AU, two way trip to Uranus would take 25.3 days.
75.0% c1.512 kg34,664 mT0.25%/Day31.0 dayWith typical distance of 30 AU, two way trip to Neptune would take 31 days.
86.6% c2.000 kg52,950 mT0.16%/Day56.6 dayWith typical distance up to 100 AU, two way trip to KB could take up to 57 days.



t = 4 × (d ÷ g)

g = .5 AU/day2
Accelerate to midway (dAcc =d/2) for high velocity and quick trip:tAcc = (2dAcc/g)
To regain orbital velocity, decelerate same distance to destination:tDec = (2dDec/g)=tAcc
Recall 2dAcc=d=2dDec ; thus, compute total one way trip time:t1way=tAcc+tDec =2(d/g)
Total two way travel is twice one way travel time:t2way = 4(d/g)

High speed exhaust particles exchange momentum with the space vessel; thus, g-force.
Two Examples Follow. 
E-1:  At a particle exhaust speed (VExh) of .10c, Mars is sometimes within reach. 
E-2:  At much higher exhaust speeds (i.e., VExh = .866c);
trips to the planets become routine,
and mining expeditions to the Kuiper belt become practical.


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