Odd thought on a non-orbital tether (long)

Hi all,

I had an odd thought last night, that I think might work to position
a tether to an anchor, which is fixed at 500 km above the poles.
This is a refinement on my orbiting ring idea, but much stranger. I
might be missing something, as it was a 2:00 AM thought. I've not
encountered anything quite like it. I'll start simply, and hopefully
won't lose anybody. It is a very odd thought.

If you have a craft in circular polar orbit, and over the pole you
thrust radially, toward the earth's center, the craft's angular
momentum is unchanged. The pole becomes the descending node, the
equator is crossed at perigee, and the other pole is the ascending
node. If you again thrust radially over the other pole, with twice
the impulse, you can recreate the previous path. Doing this, both
poles are acting as both the ascending and descending nodes, and the
equator marks the perigee, twice per orbit. The crafts angular
momentum is unchanged, and since the radial velocity is mirrored at
each pole, the total energy in the orbit is constant.

If you replace the craft with many, many tiny craft, you can
accomplish the same thing, as long as some impulse is applied
radially, over each pole. What you end up with is a bunch of objects
in a patched elliptical orbit, which looks like a football, with the
pointing ends of the ball aligned with the poles. I'm doing this
over the pole so the tether won't move relative to the ground, the
orbital mechanics would work anywhere else, though.

If the orbit is instead filled with a stream of particles, like BB's,
we can position a flat plate at each end of the football, horizontal
to the pole, exactly perpendicular to vertical (In reality the
reaction between particle and plate must be done electromagnetically,
but it's easier to start with a perfectly elastic impact against a
flat plat). The particles impact the plate, with the angle of
incidence of course equaling the angle of reflection, so their is no
resultant impulse, tangential to the plate.

This means the angular momentum of the particle is absolutely
unaffected by the impact. The impulse normal to the plate is simply
the change in the particles radial velocity. This change is twice
the particle's incoming radial velocity. Each particle's mass, times
this change in radial velocity, is the impulse delivered by the
particle, to the plate. This impulse is purely normal to the surface
of the plate, providing an vertical, upward force on the plate. The
sum of the impulses per second equals gives the force on the plate.
If this impulse equals the force on the plate due to gravity, at the
altitude of the plate, the plate remains in a fixed location. The
kinetic energy of the particles is unaffected, since it's an elastic
collision, and the angular and radial particle energies are
conserved. The energy in the plate (all potential) is likewise
conserved, since the plate doesn't move.

This means that an object can be held aloft in a fixed position, by
riding the "wave" of a stream of particles in patched elliptic
orbits. Two plates can be levitated at the two ends of the football
orbit. The force, due to gravity, on the levitated object, is used
to provide the radial impulse to the particles, which is just like a
radial burn on a spacecraft. In a way, we've built both a wing, and
its "airstream", in theory having an infinite lift/drag ratio.
Though not quite true, having to be cleaned up with small
electromagnetic impulses to the particles, this is the simple model.

If the delivered impulse/mass of the particles varies, no great
problem occurs. The particles that receive less impulse merely move
along a less eccentric orbit. The location of the particle's
ascending and descending nodes, the two target platforms, is
unaffected. In essence, we don't care much about the exact perigee
altitude of the particles, or each particles exact impulse/mass
ratio. We have slop to work with. In between the two nodes, we can
have a verticle cloud of particles. They will always come back
together over the poles.

If the particles start in a circular polar orbit at 500 km altitude,
and we then provide an impulse at each pole, to put the pergiee at
200 km over the equator, we should have an incoming and outgoing
radial velocity of about +-336 m/sec. The total radial delta V is
672 m/sec.

Given a mass of particles that sums to 100,000 kg, about 1 Saturn V's
worth, the force on each plate should be roughly 2500 lbs. If the
orbit is made more eccentric, the ratio of the levitated mass to
particle weight goes up significantly, but at a significant increase
in required tether length.

Assuming you could get a useful mass levitated, along with a cable,
then the cable could haul up new particles, and also transmit the
power required to accelerate the particles into the same orbit as the
others. If, in this scenario, 10% of the levitated mass was
particles being transported upward at 300 miles per hour, then the
mass of the orbiting particles would double about every 33 days. I'm
ignoring having to increase the mass of the cable, which is swamped
by the mass of added particles.

So the mass of the system, and deliverable payloads, is doubling once
a month, and at the end of the year is about 4000 times greater than
at the start. After one year our simple system should be able to
haul up 13,600 tons per day. This is somewhat like launching 136
Saturn V's per day, but remember, we still haven't accelerating
anything, except the particles, to orbital velocity.

Fix 1: To keep the acceleration of new particles from accelerating
the platform, there must be three streams of particles. Two outside
streams rotate in one direction, while the central stream rotates in
the other. This allows us to cancel the external forces and torques
on the platforms.

Fix 2: Particles that slow down, due to atmosphereic drag, will
impact the cable, unless a dual, gapped cable is used. For this
reason, each particles mass must be very small. Small particles will
ablate the cable, hopefully at a slow rate than the cable is being
grown. Large particles will be like gunfire, or artillery, which is
not good.

Fix 3: If the impulse/drag ratio on the particles is not infinite,
provision will have to be made to either keep them re-accelerated, or
two dump slow movers back into the atmosphere, at some small leak
rate. This would be less of a problem for a lunar cable.

Question 1: The poles are full of ice, and not much else. Could
water, or seperate H and O ions, be reflected electrostatically?

Question 2: Is putting history's two largest lightning rods in the
middle of the incoming solar wind, at the pole, a really bad idea?

Question 3: The mass of the 300 mile cable is certainly way less
than the proposed, though unbuildable, geosynchronus tether. But
even at this, is is buildable?

Question 4: If not, could part of the tether be levitated by fixed
lasers hitting reaction mass (ice), which is carried up the cable?

To Orbit: The problem of accelerating the objects to orbital velocity
can be done with either a more efficient plasma or VASIMIR drive, or
by depending on another ring system for support and reaction (really
complex dynamically). In this scenario, half the payloads are
accelerated, relative to the ring, so as to slow down the ring. The
other half of the payloads are accelerated the opposite direction, to
re-accelerate the ring. Whether this ring should be particles or
solid, I don't know.

Best Regards, and hope this wasn't too stupid, since I might be
overlooking something obviously wrong.

George Turner