Saturday, March 10, 2007

CYCLERS: Backup Material

Habitats could leverage the highly eccentric Solar orbits of Near Earth Asteroids (NEAs) to become cyclers.  Their orbits could be modified to periodically cross several different planetary orbits. This configuration will enable inexpensive transport throughout the Solar System. Initial cyclers will  routinely transport payloads between Earth and Mars; eventually, cyclers will go to other planetary systems and perhaps to other habitats.
ASTEROIDS AS SPACESHIPS
INTERPLANETARY TRANSPORT!!
To transport large payloads from Earth to Mars, the most cost effective way might be to leverage Near Earth Asteroids (NEAs) which now periodically transit both the orbit of Earth and the orbit of Mars.
Thus, put payload on appropriate NEA, travel at that NEA's orbital speed (about 50,000 mph ≈ 22 km per sec) to Mars orbit.
Of couse, payload would still have to make its way to Mars itself,  but this is still an intriquing idea.

NOTHING IS FREE
While the NEA will provide the infrastructure and energy needed to travel between planetary orbits,  a human enterprise must provide the means (infrastructure and energy) of getting on/off the NEA when near Earth as well as when near Mars.

Trip might take many months which leads TE to conclude that the initial payloads will likely include Artificial Intelligence (AI) devices but probably not humans.

  After asteroids transform into self sustaining habitats,
 look for sizable populations of human travelers.
The first few cyclers will be Near Earth Asteroids (NEAs) refashioned as habitats. Gravity like conditions will be achieved by carefully controlled spin around the cylindrical habitat's longitudinal axis. Like other habitats, cyclers will have lots of room and all the comforts of home. A trip to Mars will take a few months, but it'll be a pleasant few months.

Hopefully, some interplanetary ships will use powerful propulsion systems to provide "equivalence" via gravity force (g-force) acceleration.  These smaller g-force "shuttles" will continuously accelerate/decelerate from departure to destination; typical g-force trips will take days. After g-force spacecraft technology is mature, mankind will have two methods of interplanetary travel; both methods will be used extensively.  While cyclers will continue to provide most transport for most things to other locations within the Solar System (like today's ocean vessels), g-force ships will provide much quicker transport for higher priority payloads (like today's jetliners). 

As a matter of fact, g-force vessels will enhance the use of habitats. Humanity will more easily garner resources from comets and asteroids to create new habitats and enhance old ones. Some habitats will become cyclers.

Intercycler Shuttles.  Cyclers will travel at orbital speeds and will be the main transports of most people and materials between different Solar System positions due to cost considerations. Much like naval helicopters can now shuttle passengers and/or small payloads to many naval vessels throughout their voyages, g-force shuttles will be able to travel to cyclers at anytime during the cycle. 

Thus, economics will force most travelers and payloads to accomplish interplanetary travel at orbital speeds on cyclers, refashioned asteroids. When time is critical, travelers and shipments can go to same destination in days via g-force powered spaceflight which continuously accelerates to midpoint then continuously decelerates to destination.
Cycler Definition
Cycler: Habitat in an eccentric solar orbit which periodically transits circular orbits of interest.
Cycler facilitates a transfer between the departure orbit and destination orbit.
Destinations can include planetary systems.  For example, a Jovian moon would probably be a more useful destination than Jupiter itself. To maintain g-force, the actual destination would most likely be an habitat orbiting the moon.  Frequent expeditions could make short trips to the moon itself, but the vast majority of human's time would be spent aboard the g-force habitat.Other destinations could include other orbital objects such as comets and/or asteroids where the mission might involve harvesting or "mining" resources.  Destinations could even include other habitats on dedicated orbits, i.e., "orbitors".

Cyclers may be small or large, sparse or luxurious, slow or fast, completely passive (simple ballistic orbit) or with limited propulsion capability (course correction drive units).

Cyclic periods depend on Kepler's Law.
The square of the orbital period, T, equals the cube of the semimajor axis, a.
T2 =a3
Stated another way: Semimajor axis, "a", is proportional to cube root of T squared.
=∛(T2)
TE considers following factors:
For simplicity, introduce following artificialities:
  • assume circular Terran orbit.
  • artificially align perihelion of Martian orbit on same solar radius as cycler's perihelion. (on outbound line from Sun, put shortest distance from orbit of Mars as well as shortest distance to orbit of cycler.  This highly unlikely, artificial alignment greatly simplifies the analysis; more realistic parameters can be introduced later. 
Disregard angle of inclination; arbitrarily assume angle = 0° to simplify as 2D case.
Cyclic harmony.orchestrating multiple cyclers for more boarding opportunities. 
Safety Foremost: Engineer cycler orbits to intersect Terran orbit near habitats, Alpha & Omega.
When crossing orbits well away from destination, there are some non g-force options:
At orbit intersection, have shuttle depart cycler and enter concentric orbit (i.e. parallel path):
----enter concentric orbit with shorter radius to gain on destination planet.
----concentric orbit with longer radius to let destination planet gain on shuttle.
For noncycling cycler, see: Hohman Transfer to Mars 

Galactic Mining Industries, Inc. – Business Plan Development ...
"REVENUE GENERATING ACTIVITIES" lists 12.
Interplanetary Cycler Challenges
1. SPACE BASED CONSTRUCTION. Orbital construction is most practical with space-based raw resources. Possibilities include:
--Orbit the Moon. Glean resources from a moon based mining colony. 
--Orbit the Earth. Deliver some Terran resources via a cost effective manner such as a space elevator.
--Orbit the Sun. Cohabits Earth's Solar orbit; gets resources from asteroids and/or comets.  From Earth, this Orbitor would appear static.
--Cycler Orbit. Ongoing construction during Cycler Orbit.  As soon as possible enter cycler orbit. Would need certain prerequisites: 1 g at inner hull due to longitudinal spin, agriculture and other life support needs.
2. RIGHT SIZE THE ORBIT. For example, to achieve an optimal orbit between Earth and Mars, cycler must acheive an elongated orbit with perihelion inside the Earth orbit and aphelion outside the Martian orbit; period must be at least  two years. A practical cycler must periodically adjust its orbit to leverage best orientations of Earth and Mars.
LIMITED USE. A typical cycler orbit takes 2.5 years. So the Cycler will not be a quick solution for getting to Mars, but it might prove the optimum solution for passengers and cargo with some time on their hands.  For example, a two year trip would be a great opportunity to conduct some college classes.  
(NOTE: In his book, Mining the Sky...., John Lewis suggests a carefully orchestrated system of 6 cylers with 2 year orbits; these Cyclers orbits would be sequenced for one cycler to rendezvous with Earth every four months.)
3.  RENDEZVOUS MANUEVER.  For hours, days or even weeks prior to Cycler passing near Earth, a transfer vehicle (i.e., "shuttle") shall be in a slightly larger, concentric Solar orbit.  Thus, the shuttle's path shall parallel the Cycler's path at a slower speed. The difference between the cycler's velocity and shuttle's velocity can be called the "differential" velocity, and from the shuttle's viewpoint the cycler shall be approaching at this differential speed.
First Burn. At a certain distance, shuttle must employ slight thrust for specified delta Vee (ΔV1) toward planned intersection point where shuttle's path will intersect Cycler's orbit. 
Second Burn. This intersection should occur precisely after Cycler passes through; then, shuttle must employ another thrust (ΔV2) to fly in close formation on Cycler's "tail".
Third Burn(s).  Finally, shuttle will engage in a series of extremely mild burns (ΔV3a, ΔV3b, ΔV3c, ....) to dock with cycler.  Then, payload transfers can take place as planned over a fairly lengthy duration.
When shuttle wishes to disembark (might be Mars, might be near asteroids in the Belt, might be Earth after a complete Cycler orbit), it needs to accomplish above in reverse: carefully separate from Cycler; enter a different orbit; then orbit about destination.
Since a cycle will take at least two years, it makes eminent good sense to plan for a dedocking and a docking manuever to both happen during every rendezvous.  There are many ways to accommodate this, and this will be the subject of a later chapter.
4. COURSE CORRECTIONS. Cycler might need nuclear powered engines to make orbital adjustments.
DELTA VELOCITY. To speed up a space ship to catch the cycler and then slow down at the other end requires a large delta velocity which will take a lot of energy; more energy then demonstrated from chemical or ion engines. A fission engine might work; unfortunately, fission engines are still theoretical.
Gravity assists...
5. LOGISTICS. Re-supplying the cycler will be much more difficult then resupplying the ISS. The most practical method of resupply will be during the very short transition windows in the orbits of Earth and Mars. In short, our cycler will be an autonomous, independent entity and will for the most part have to make do with what's onboard. Fortunately, asteroids will likely have a lot of indigenous materials already "onboard".
Cycler might encounter comets or other asteroids; however, it would be impractical to immediately "glean" resources from these other bodies. If the cycler deployed a vessel to mine resources, the vessel would have to stay with the target until another cycler came close enough to recover it. By the time the mining vessel lands at its target, the original cycler must continue on its orbit and would have already traveled far beyond recovery range. On the other hand, this might prove a useful methodology for detecting and claiming planetisimal resources. (Recall the Biblical injunction: "Ye who sows shall not reap.") However, economic transactional arrangements could be made for original cycler to be compensated for initial investment (dropping off mining vessel and crew).
A rendezvous craft must be able to accelerate and match the cycler's velocity. Once onboard the cycler, craft can use its engines to assist cycler for course corrections. To travel safely to/from the cycler, this craft must be a radiation shielded can with a robust life support system. However, radiation shielding isn't perfect, and materials can accumulate radioactivity - after ten years cycling through hard radiation, will likely have to decontaminate.
Consider final dispostion of the rendezvous craft. You might land the entire craft (with life support) to contribute to the Martian base. On the other hand, rendezvous spacecraft will also be needed for return trips (back to Earth), and Martians won't be able to manufacture them for a while.

Let there be light.  System of large mirrors could use sunlight perhaps as far as the orbit of Mars.  Beyond that distance from Sol, habitats may have to use Helium 3 (He3) in nuclear fussion power generators.  He3 could perhaps be harvested from the gas giants.
May the Force be with you.  G-force is essential for long term habitat dwellers. Centrifugal vs. centripedal.

The Aldrin Cycler is a well known, fundamental concept for notional cyclers to periodically transit the orbits of Earth and Mars. Aldrin has worked with McConaghy and LonguskiPurdue engineers, to research possible cycler applications.
Like an ocean liner on a regular trade route, a cycler will glide perpetually along its predictable orbit.


Buzz Aldrin: cyclers could be a "new class of spacecraft that would serve as orbiting hotels perpetually cruising between Earth and Mars".

"We believe these regular planetary flybys would create an entirely new economic and philosophic approach to space exploration," the researchers wrote in NASA's Jet Propulsion Laboratory. "Reliable, reusable and dependable cycler transportation can be the key to carry humanity into the next great age of exploration, expansion, settlement and multi-planetary commerce."

"The cycler would orbit the sun for regular flybys of Earth and Mars,"  Dr. James Longuski, Purdue's Professor of Aeronautics and Astronautics. "Once in an orbit, cycler continues on its own momentum between Earth and Mars. Vessel might sometimes need some propellant for an occasional adjustment, but it's pretty much a free ride."

Like an ocean liner on a regular trade route, a cycler will glide perpetually along its beautifully predictable orbit.

The cycler spacecraft would have to encounter Mars and Earth at precisely the right distance and speed. If a cycler approached Mars too fast or at the wrong distance, too much fuel would be needed for steering rockets and it would be more difficult for "taxi" spacecraft to dock with the cyclers as they sped by.

A cycler might fly past the Earth at about 6 kilometers per sec, or roughly 13,000 miles per hour. Small shuttle spacecraft would have to rendezvous with the speeding cycler to provide "taxi" service to arriving passengers as well bring return passengers and exchange cargos.

The outbound trip to Mars would take six to eight months. Thus, cyclers would rotate slowly to create artificial gravity and maintain Earthlike conditions.
The spacecraft also would be roomy enough to make the trip tolerable. The earliest versions of the space hotels might accommodate up to 50 passengers.

By the time that craft arrived at Mars, the two planets would have moved much farther apart, making a return trip impractically long.

Rather, a family of perhaps three cyclers, continuously providing outbound and inbound flights, would ensure that passengers could get to Earth and Mars within a reasonable amount of time, Longuski said.
elements of Cycler orbit.

Resonant cyclers would have orbits in even multiples of years.  Thus, they return near Earth at same date during those particular years. 
PROBLEM: Mars orbit is not resonant, thus, the relative position of Mars varies during every encounter.

Synodic Cyclers.  For cyclers with periods exactly 2.135 Earth years, their period would coincide with the Mars's synodic orbit about Earth. Thus, everytime the synodic cycler intersected Earth's orbit, the Earth-Mars angular relationship would be the same as the previous such intersection. Unfortunately, this intersection point would not always coincide with Earth's position.

For a Synodic Cycler, perhaps one orbit of seven would bring the cycler close to Earth. 
Orbital Elements
Mars Solar Orbit
AphelionQ=1.6659 AU =a + c
Perihelionq=1.3815 AU=a - c
Semi-major axisa=1.5237 AU
Given
Semi-minor axisb=1.5170 AU =(a2 - c2)1/2
Focusc=0.1422 AU =a × e
Eccentricity=0.0933
Given
Semi-latus Rectum =1.5104 AU=b2 /a
Sidereal PeriodT =1.88  Yr=(a3)1/2
Angular Velocity ωM =0.524 °/day =360°/T
Orbital Elements
Earth-Mars Resonant Cycler
AphelionQ=2.5530 AU =a + c
Perihelionq=0.6218 AU =a - c
Semi-major axisa=1.5874 AU =(T2)1/3
Semi-minor axisb=1.2599 AU =(l × a)1/2
Focusc=0.9656 AU =(a2 - b2)1/2
Eccentricity=0.6053 =c / a
Semi-latus Rectum =1.0000 AU
Given
PeriodT =2.000 Yr
Given

Terran Orbital Elements
Assume Circular Solar Orbit
AphelionQ=1.0 AU =a + c
Perihelionq=1.0 AU=a - c
Semi-major axisa=1.0 AU
Given
Semi-minor axisb=1.0 AU
Given
Focusc=0.0 AU =(a2 - b2)1/2
Eccentricity=0.0=
c / a 
Semi-latus Rectum =1.0 AU=b2 /a
Sidereal PeriodT =1.0 Yr=(a3)1/2
Angular Velocity ωE =0.986 °/day =360°/Txxx

Cycler Table

Rν=lC


1 + eC × cos(ν)
Vν

=√(
Sol

Rν
+
μSol

aC
)

Cycler Relevant Positions
Pos.TimeRangeCycler
Velocity
ν
Days
AU
km/sec
00.614 AU 48.6
90°501.000 AU 35.2
127°1121.611 AU23.8
180° 3922.703 AU11.02
Given
Deg
AU
km/sec


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