🚀 go-pugleaf

I'm cross-posting to sci.space. Scott said that they were having a
similar discussion. I haven't been keeping track there. I hope this
is a help and not a hindrance there.

In article <l7ukasINNaem@pollux.usc.edu>, srobiner@pollux.usc.edu
(Steven Robiner) writes:
|>
|>Excuse me, but isn't something missing from this "Tethered Satellite"
|>experiment?  The shuttle is at one end, and the satellite is at the 
|>other, right?  But that's an open circuit, so where's the load
|>joining the ends of this 'generator.'?
|>

Why should this bother you anymore than seeing something like:
                    -----------|

                             -----
                              ---
                               -
On a circuit diagram? Where's the load for a grounded circuit?
How do you get a power supply that guarentees you the input is at
+9V?

The difference here is that we appeal to a novel source of EMF rather
than something more standard like a battery or a power supply.

Now if you want to get to the nitty gritty, you should ask, well lets
follow the electrons and see what happens. So lets try that. The tether
will soak up electrons (I'm assuming a polarity here, I may have it reversed)
then transports it to the shuttle. Since the shuttle will have an excess
of electrons, it will shed them when its potential compared to the
local plasma is higher than the work function for the shuttle surfaces.
So now you have the "infused" electrons into the flux tube that contains
the shuttle. Eventually normal plasma-plasma and plasma-neutral interactions
will allow the electron to move back to its original flux tube. This however
may take some time. So the circuit is really completed in the same sense
that grounded circuits are completed, except here we don't have a good ground
because of magnetic insulation. The critical question becomes, what is
the maximum current I can pull off of this circuit. That is the voltage is
fixed, so the power output depends on the maximum current. Well if you
pull enough current fast enough, you will create a charge imbalance between
the flux-tubes and shut down the circuit. Two things will determine this
limit. The first is the relaxation time mentioned above and the second is
the motion of the shuttle itself. The shuttle is moving across the magnetic
field, so if it saturates the local flux-tube with excess electrons then
it cannot draw extra current until its orbital motion takes it to another
flux tube. Now I am not sure whether natural relaxation time or orbital
motion sets the limit on power extracted.

Now for some numbers (order of magnitude only). Suppose the spacecraft has
an orbital velocity of ~10,000 meters/sec and the geomagnetic field is 
~10 Gauss. The relevant expression(cgs) is E = V X B / C = 333E-6 statvolt/cm
= 10 Volt/meter = 16,000 Volt/mile of tether. This is pretty close to the 
quoted numbers. The actual orbital velocty is probably closer to 5000m/s.

Now lets talk about how the tether might affect the orbit of the satellite.
Imagine a local coordinate system where: V = - |v| \hat{y} ; B = |B| \hat{z}
and the tether is extended in the -x direction. In this cooridnate system,
an equatorial satelite is moving east-to-west (pardon the heresy), the
magnetic field points from the south to the north and the tether is lowered
earthward. The electric field is VXB/c. Therefore it points earthward (-x
direction). E is parallel to J by Ohm's law. The force on the tether is
JXB/c therefore it points in the + y direction. It acts to slow down the
spacecraft. Now the thing to ask is how large. Well that depends on the
resistivity in the tether, since that will determine J. It don't have that
number in my head. Perhaps someone else will comment.

|>Conspiracy Theory:
|>------------------
|>The whole thing is Top-Secret high-tech fishing trip: just stick
|>a satellite out on a long string and see if any 'UFO's bite.  ;)
                 
Be careful what you wish for, you may get it. :>

john w. cobb
jwc@fusion.ph.utexas.edu