Sunday, September 18, 2011


Equatorial Anchor 
The optimal location for tether's Marine Anchor is on the Equator where tether will extend vertically to GEO Node. Current plans calls for tether to anchor a slight distance off the Equator (as shown); thus, tether will be almost vertical.
If anchored well away from Equator, the tether will likely angle well away from the equatorial plane which might possibly prove detrimental. Of course, we can currently only speculate about either the equatorial tether or the non-equatorial one.

TE chooses to also speculate about the Ion Beam which would be best based on the Equator, directly under GEO Node. HOWEVER, a non-vertical particle beam could easily locate off the equator with none of the problems of an off equator tether. Thus, Beam Rider's Base Station has much more flexibility than the Tether Climber's Marine Anchor.
Traditional SE Concept is Equatorial
GEO Node is an orbital platform
which stays directly above the Marine Anchor (MA) on the equator,
To do this, orbital platform must be at the correct orbit,
35, 780 km above the Earth's surface;
platform must always reign as the MA's zenith,
and MA must always serve as the platform's nadir.
Thus, the GEO Node, MA, and Earth's center are co-linear.

What if...
...the Marine Anchor anchored well off the Equator?
...the orbital platform had a different path?
Off Equator Anchor Causes "Sub-orbit" 
What if the Marine Anchor (MA) moved 8.7 degrees south of the Equator?
8.7° = 522 NM = 966.7 km = 600 SM
TE assumes centrifugal force maintains co-linearity among GEO Node, MA and Earth's center. Thus, the 35,780 km tether now points to a new, parallel plane 6,357 km below the equatorial plane.
At new plane, GEO Node would trace a new circular path with a slightly reduced diameter.  Due to continued tether restraint, GEO's new position still rotates around the Earth's axis at 15°/hour; thus, it remains geosynchronous. We see this new circular path is no longer equatorial, and it is no longer orbital because this new plane does not pass through Earth's center.
CONCLUSION:  TE chooses to call GEO Node's new circular path a  "sub-orbit".
Centrifugal Force Decreases as Sub-Orbit 
To make one complete rotation in 24 hours, a platform (GEO Node) on the Geosynchronous Equatorial Orbit (GEO) must move about 3.07 kilometers per second (kps). Bound by same tether as for the GEO, sub-orbital platforms will also rotate about the Earth's axis in 24 hours; however, their circumference will be less than the GEO, and their speed will also be less. This speed decreases as the tether's anchor moves away from the equator.  It decreases as the cosine of the latitude.
EXAMPLE:Anchored at latitude of 45°,
v=cos(45°)×3.07 km/sec=.707×3.07kps=2.17 kps 

An object traveling in a circle 
experiences an outward centrifugal force
which depends on velocity-squared over radius (v2/r)
which shrinks as sub-orbit's radius decreases.
CONCLUSION: Tether is best anchored on or near the Equator. As anchor increases distance away from Equator, less and less mass can be suspended by tether.
Thought Experiment (TE) assumes an ocean based particle accelerator can send a constant stream of high speed ions for many minutes and even hours without interruption. TE further assumes continuous, collective momentum of many high speed particles can impart a relatively small acceleration of perhaps one tenth Earth Gravity (.1G) to a vehicle, (i.e. Beam Rider).

Preliminary calculations indicate that at .1G acceleration, the Beam Rider could arrive at midway to the GEO Node (about 18,000 km above Earth surface) in about 100 minutes.  Finally, TE assumes Beam Rider will use internal means to .1G decelerate for another 100 minutes to arrive at GEO Node at relative zero velocity.

SUMMARY:  Base Station's Ion Beam has overwhelming advantage; the entire trip (surface to GEO) would take only 200 minutes versus 7 long days for the tether's climber with an average speed of about 200 km per hour.
Another huge benefit of Beams versus Tethers, is that Beam Base Stations can locate well away from Equator and still propel vehicles to GEO Node on GEO.

Unlike tether dynamics, centrifugal force is not a factor; thus, ion beam angles to where pointed not due to where anchored.

GEO Node restrained not by physical tether but by Kepler's Laws of Orbital Mechanics.  Thus, Base Station can locate literally anywhere and just point the particle stream toward the GEO Node; main consequence for choosing to locate off equator will be a slightly longer flight path.

EXAMPLE: If base station locates 8.7° south, the flight distance would increase from 35,780 km to 35,793 km.  TE speculates this might increase total travel time from 200 mins to perhaps 201 mins, a minuscule amount.
Anchoring tethers well off the equator is not practical; however, basing ion beams in any oceanic location is possible.  If relatively isolated, an oceanic launch location is very practical for Beam Riders on particle beams.



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