.require "memo.pub[let,jmc]" source
.at "qDv" ⊂"%AD%2v%1"⊃
.FONT B "ZERO30";
.TURN ON "↑"
.at "qm" ⊂"%B.%2m%1"⊃
.cb A SKYHOOK SUPPORTED BY ORBITING PARTICLES

.cb "Marvin Minsky, M.I.T."
.cb "John McCarthy, Stanford University"

	This essay proposes a skyhook idea that will work with weaker
materials than the synchronous or rotating skyhooks.  The idea is to
support a platform by a continuous stream of orbiting particles which
are deflected downwards -- to hold up the platform at a stationary
point, some 800 kilometers above a point on the equator.  Then, a
cable is run from the platform down to the ground.


	There are several variants of the idea:

	1. Each particle is in an equatorial elliptic orbit with
perigee just above the atmosphere.  Soon after perigee and at an
altitude of a few hundred miles above the top of the atmosphere, the
particle encounters a deflector which deflects it towards the earth
but only about 20 degrees and not changing its speed and hence its
energy.  The deflector is accelerated away from the earth by the
reaction but is constrained by skyhook cable anchoring it to the earth
This reaction is what keeps the cable and skyhook up.  The particle
goes around the earth again on an orbit congruent to the previous one
but precessed relative to it.  By the time it reaches the place in the
new orbit corresponding to the place where it was deflected before,
the deflector anchored to the earth has rotated with the earth to the
new place and deflects it again.

	A new particle reaches the deflector each tenth of a second
so that the deflector and skyhook are continuously supported.  Each
successive particle is in a new orbit congruent to the others but
rotated with respect to it by the amount the earth rotates in a tenth
of a second.

	2. The second variant involves ⊗n skyhooks in a regular
%2n%1-gon around the equator.  The particles travel at many times
orbital velocity and closely follow the %2n%1-gon.  The higher
the velocity, the less mass is invested in the particle stream.
The mathematics for a hexagon is as follows:

	⊗v is the velocity of the particles.

	qDv is the change in velocity at each deflection.

	⊗g is the acceleration of gravity.

	⊗r is the distance to the deflector from the center of the earth.

	⊗T is the time of flight of a particle between deflectors.

	⊗M is the mass of a skyhook including deflector.

	⊗m is the mass of the particle stream between two skyhooks.

	qm is the rate of flow of mass by a skyhook.

	%2k = m/M%1 is the ratio of mass of particles to mass of skyhooks.

	The first group of equations are valid for any %2n%1-gon.

!!a2:	%2qmqDv = Mg%1

!!a3:	%2qmT = m.

	For the hexagon we have

!!a1:	%2T = r/v%1

!!a7:	%2qDv_=_v%1.


(())	All this gives

!!a4:	%2k = gr/v↑2%1,

and if we take %2g = 10%1, %2r = 7 x 10↑6%1 and %2v = 2 x 10↑4%1, all
in mks units, we get

!!a5:	%2k = 0.7%1,

i.e. the mass of particles is about the same as the mass of skyhook.
Lower velocity particles would require more mass in the particle
stream.


	As in other skyhook schemes, objects and material can climb
the cable on an elevator.  However, because this skyhook ends only a
few hundred miles up (how many depends on the strength of available
materials) , the matter is not in orbit, so we have to consider what
to do next, and there are two main possibilities.

	The first possibility is that there is another skyhook whose
bottom is at the top of the first one - and so on up to synchronous
altitude.  This ladder is like the original skyhook concept except
that the ladder is supported at each rung.

	The other possibility is that a mass driver is supported from
one or several skyhooks that accelerates mattter and/or people to orbital
velocities.

	We have not determined the optimal size of particle or
whether magnetic or electrostatic deflection is preferable.  They
need to have mass enough so that the reaction will support the
cable, so they shouldn't be ions.

	More elaborate schemes are possible involving several
deflectors, and these may permit skyhooks above places on the earth
that are not on the equator.  These would be optimal for communication
"satellites".  For this application the cable might be dispensed with
and the position of the station maintained entirely by reaction.  For
example, consider two communication satellites could be symmetrically
disposed far apart from the equator.  They could be supported by
particles passed from one to the other and reflected back; the
positions must be selected so that the reaction vector serves both to
support the satellites vertically while and push them away from the
equator.


       Launching: because the system would fall if any part is
missing, perhaps the easiet launch method is to assemble the system at
near-geosynchrouous orbit.  Then the reaction particles are inserted
at low velocities and the system is lowered slowly, increasing the
number and speed of the particles as the vertical loads grow.
Of course, some rockets will be needed to correct for the
higher natural speed of lower orbits.

As for the skyhook cable, presumably one begins with a very
minimal one, and then uses it to hoise the
materials for larger ones.

Problems:
	stabilization of orbits -- use of planar nets.
	building the reflector -- superconductors.
	supplying launch power -- electric cable or solar