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␈↓ α∧␈↓␈↓ u1


␈↓ α∧␈↓α␈↓ βvA SKYHOOK SUPPORTED BY ORBITING PARTICLES

␈↓ α∧␈↓α␈↓ ¬jMarvin Minsky, M.I.T.

␈↓ α∧␈↓α␈↓ ¬
John McCarthy, Stanford University

␈↓ α∧␈↓␈↓ αTThis␈α∩skyhook␈α∪idea␈α∩will␈α∪work␈α∩with␈α∩weaker␈α∪materials␈α∩than␈α∪the␈α∩synchronous␈α∪or␈α∩rotating
␈↓ α∧␈↓skyhooks.␈α
 The␈α
idea␈α
is␈α
that␈α
a␈α
continuous␈α
stream␈α
of␈α
orbiting␈α
particles␈α
are␈α
deflected␈α
downwards␈αby␈α
a
␈↓ α∧␈↓deflector at the top of the cable, and the reaction supports the cable.

␈↓ α∧␈↓␈↓ αTThere are several variants of the idea:

␈↓ α∧␈↓␈↓ αT1.␈α∞Each␈α∞particle␈α∞is␈α∞in␈α∞an␈α∞equatorial␈α∞elliptic␈α∞orbit␈α∞with␈α∞perigee␈α∞just␈α∞above␈α∂the␈α∞atmosphere.
␈↓ α∧␈↓Soon␈α
after␈α
perigee␈α
and␈α
at␈αan␈α
altitude␈α
of␈α
a␈α
few␈α
hundred␈αmiles␈α
above␈α
the␈α
top␈α
of␈α
the␈αatmosphere,␈α
the
␈↓ α∧␈↓particle␈αencounters␈αa␈α
deflector␈αwhich␈αdeflects␈αit␈α
towards␈αthe␈αearth␈αbut␈α
only␈αabout␈α20␈α
degrees␈αand
␈↓ α∧␈↓not␈αchanging␈αits␈αspeed␈αand␈αhence␈αits␈αenergy.␈α The␈αdeflector␈αis␈αaccelerated␈αaway␈αfrom␈αthe␈αearth␈αby
␈↓ α∧␈↓the␈α
reaction␈αbut␈α
is␈α
constrained␈αby␈α
skyhook␈α
cable␈αanchoring␈α
it␈αto␈α
the␈α
earth␈αThis␈α
reaction␈α
is␈αwhat
␈↓ α∧␈↓keeps␈αthe␈αcable␈αand␈αskyhook␈αup.␈α The␈αparticle␈α
goes␈αaround␈αthe␈αearth␈αagain␈αon␈αan␈αorbit␈α
congruent
␈↓ α∧␈↓to␈αthe␈αprevious␈αone␈αbut␈αprecessed␈αrelative␈αto␈αit.␈α By␈αthe␈αtime␈αit␈αreaches␈αthe␈αplace␈αin␈αthe␈αnew␈αorbit
␈↓ α∧␈↓corresponding␈αto␈αthe␈αplace␈α
where␈αit␈αwas␈αdeflected␈αbefore,␈α
the␈αdeflector␈αanchored␈αto␈αthe␈α
earth␈αhas
␈↓ α∧␈↓rotated with the earth to the new place and deflects it again.

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

␈↓ α∧␈↓␈↓ αT2.␈α∞The␈α∞second␈α∞variant␈α∞involves␈α∞␈↓↓n␈↓␈α∞skyhooks␈α
in␈α∞a␈α∞regular␈α∞␈↓↓n␈↓-gon␈α∞around␈α∞the␈α∞equator.␈α
 The
␈↓ α∧␈↓particles␈α⊃travel␈α⊃at␈α⊃many␈α⊃times␈α⊃orbital␈α⊃velocity␈α⊃and␈α⊃closely␈α⊃follow␈α⊃the␈α⊃␈↓↓n␈↓-gon.␈α⊃ The␈α⊃higher␈α⊂the
␈↓ α∧␈↓velocity,␈α∞the␈α∞less␈α∞mass␈α∞is␈α∞invested␈α∞in␈α∞the␈α∞particle␈α∞stream.␈α∞ The␈α∞mathematics␈α∞for␈α∞a␈α∞hexagon␈α∞is␈α∞as
␈↓ α∧␈↓follows:

␈↓ α∧␈↓␈↓ αT␈↓↓v␈↓ is the velocity of the particles.

␈↓ α∧␈↓␈↓ αT␈↓	D␈↓↓v␈↓ is the change in velocity at each deflection.

␈↓ α∧␈↓␈↓ αT␈↓↓g␈↓ is the acceleration of gravity.

␈↓ α∧␈↓␈↓ αT␈↓↓r␈↓ is the distance to the deflector from the center of the earth.

␈↓ α∧␈↓␈↓ αT␈↓↓T␈↓ is the time of flight of a particle between deflectors.

␈↓ α∧␈↓␈↓ αT␈↓↓M␈↓ is the mass of a skyhook including deflector.

␈↓ α∧␈↓␈↓ αT␈↓↓m␈↓ is the mass of the particle stream between two skyhooks.

␈↓ α∧␈↓␈↓ αT␈↓
.␈↓↓m␈↓ is the rate of flow of mass by a skyhook.

␈↓ α∧␈↓␈↓ αT␈↓↓k = m/M␈↓ is the ratio of mass of particles to mass of skyhooks.

␈↓ α∧␈↓␈↓ αTThe first group of equations are valid for any ␈↓↓n␈↓-gon.
␈↓ α∧␈↓␈↓ u2


␈↓ α∧␈↓1)␈↓ αt ␈↓↓␈↓
.␈↓↓m␈↓␈↓	D␈↓↓v␈↓ = Mg

␈↓ α∧␈↓2)␈↓ αt ␈↓↓␈↓
.␈↓↓m␈↓T = m.

␈↓ α∧␈↓␈↓ αTFor the hexagon we have

␈↓ α∧␈↓3)␈↓ αt ␈↓↓T = r/v␈↓

␈↓ α∧␈↓4)␈↓ αt ␈↓↓␈↓	D␈↓↓v␈↓ = v.

␈↓ α∧␈↓␈↓ αTAll this gives

␈↓ α∧␈↓5)␈↓ αt ␈↓↓k = gr/v␈↓#
2␈↓#␈↓,

␈↓ α∧␈↓and if we take ␈↓↓g = 10␈↓, ␈↓↓r = 7 x 10␈↓#
6␈↓#␈↓ and ␈↓↓v = 2 x 10␈↓#
4␈↓#␈↓, all in mks units, we get

␈↓ α∧␈↓6)␈↓ αt ␈↓↓k = 0.7␈↓,

␈↓ α∧␈↓i.e.␈αthe␈α
mass␈αof␈αparticles␈α
is␈αabout␈αthe␈α
same␈αas␈αthe␈α
mass␈αof␈αskyhook.␈α
 Lower␈αvelocity␈αparticles␈α
would
␈↓ α∧␈↓require more mass in the particle stream.

␈↓ α∧␈↓␈↓ αTAs␈α⊂in␈α⊂other␈α⊂skyhook␈α⊂schemes,␈α⊂objects␈α⊃and␈α⊂material␈α⊂can␈α⊂climb␈α⊂the␈α⊂cable␈α⊂on␈α⊃an␈α⊂elevator.
␈↓ α∧␈↓However,␈α∞because␈α∂this␈α∞skyhook␈α∂ends␈α∞only␈α∞a␈α∂few␈α∞hundred␈α∂miles␈α∞up␈α∞(how␈α∂many␈α∞depends␈α∂on␈α∞the
␈↓ α∧␈↓strength␈αof␈α
available␈αmaterials),␈αthe␈α
matter␈αis␈α
not␈αin␈αorbit,␈α
so␈αwe␈α
have␈αto␈αconsider␈α
what␈αto␈αdo␈α
next,
␈↓ α∧␈↓and there are two main possibilities.

␈↓ α∧␈↓␈↓ αTThe␈αfirst␈αpossibility␈αis␈αthat␈αthere␈αis␈αanother␈αskyhook␈αwhose␈αbottom␈αis␈αat␈αthe␈αtop␈αof␈αthe␈αfirst
␈↓ α∧␈↓one␈α∂-␈α∂and␈α∞so␈α∂on␈α∂up␈α∞to␈α∂synchronous␈α∂altitude.␈α∞ This␈α∂ladder␈α∂is␈α∞like␈α∂the␈α∂original␈α∂skyhook␈α∞concept
␈↓ α∧␈↓except that the ladder is supported at each rung.

␈↓ α∧␈↓␈↓ αTThe␈αother␈α
possibility␈αis␈αthat␈α
a␈αmass␈αdriver␈α
is␈αsupported␈αfrom␈α
one␈αor␈αseveral␈α
skyhooks␈αthat
␈↓ α∧␈↓accelerates mattter and/or people to orbital velocities.

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

␈↓ α∧␈↓␈↓ αTMore␈α⊂elaborate␈α⊃schemes␈α⊂are␈α⊃possible␈α⊂involving␈α⊃several␈α⊂deflectors,␈α⊃and␈α⊂these␈α⊃may␈α⊂permit
␈↓ α∧␈↓skyhooks␈α∂above␈α∞places␈α∂on␈α∞the␈α∂earth␈α∞that␈α∂are␈α∂not␈α∞on␈α∂the␈α∞equator.␈α∂ These␈α∞would␈α∂be␈α∂optimal␈α∞for
␈↓ α∧␈↓communication␈α∪"satellites".␈α∪ For␈α∪this␈α∩application␈α∪the␈α∪cable␈α∪might␈α∩be␈α∪dispensed␈α∪with␈α∪and␈α∩the
␈↓ α∧␈↓position␈αof␈αthe␈αstation␈αmaintained␈αentirely␈αby␈αreaction.␈α For␈αexample,␈αa␈αthe␈αconsider␈αa␈αpair␈αof␈αtwo
␈↓ α∧␈↓communication␈α∞satellites␈α∞at␈α∞nearly␈α∞geosynchronous␈α∞altitude,␈α∞but␈α∞symmetrically␈α∞disposed␈α∞far␈α
apart
␈↓ α∧␈↓from␈αthe␈α
equator.␈α These␈α
are␈αsupported␈α
by␈αparticles␈α
passed␈αfroom␈α
one␈αto␈α
the␈αother␈α
and␈αreflected
␈↓ α∧␈↓back.  The reactionn vector serves to (1) support the satellites ver back.