.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 skyhook idea will work with weaker materials than
the synchronous or rotating skyhooks.  The idea is that a
continuous stream of orbiting particles are deflected downwards by
a deflector at the top of the cable, and the reaction supports
the cable.

	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,
a
the 
consider a pair of two communication satellites at nearly geosynchronous altitude, but symmetrically disposed far apart from the equator.
These are supported by particles passed froom one to the other and reflected back.  The reactionn vector serves to (1) support the satellites ver
back.