MCGRATH%OZ.AI.MIT.EDU@MIT-XX.ARPA ("Jim McGrath") (01/23/86)
This is a followup to a previous message of mine concerning the loss
of momentum (and thus the orbital decay) experienced by an accelerator
placed in low earth orbit (LEO) and designed to accelerate sub-orbital
payloads to low earth orbit velocity. Two obvious solutions suggest
themselves. First is to install reaction motors to accelerate the
structure again. Since they may be far more efficient than those used
in the earth to orbit phase (e.g. ion rockets), you still turn out a
winner. The second is to decelerate payloads from beyond LEO to
sub-orbital speeds. The problem here is that you do not want to be
required to lose mass from the space environment to the earth.
Moreover, it is unlikely that you could balance the traffic in the
early stages of use.
Another solution is possible. If a charge is placed on the
accelerator, then it becomes a gigantic charged particle moving in the
earth's magnetic field. We know that in this case a force is exerted
on the particle, a force that can be used to transfer angular momentum
from the field to the particle, thus making up for the momentum lost
by the payload acceleration. Note that no mass is needed to
accomplish any of this, only a power plant which may not even be
physically coupled to the accelerator.
How much of a charge is needed? The following is a very simple
analysis, correct only to the first approximation. A lot of
simplifying assumptions are used. But the gist should be correct.
Assume throughout that the accelerator is in a circular orbit
concentric and coplanar with the earth. Let delta J = J (final) - J
(initial) [ J = angular momentum of accelerator ]. We know that this
is equal to M*(rf*vf - ri*vi), where M = mass of the accelerator, rf =
final radius of orbit, fi = initial radius of the orbit, vf = final
orbital velocity, vi = initial orbital velocity. Now after the loss
of momentum we charge up the accelerator, resulting in a delta J equal
to rf*Q*vf*B*t, where rf = initial radius of the accelerator before
charging, Q = charge on the accelerator, vf = initial velocity of the
accelerator before charging, B = earth's magnetic field, and t = the
duration that the charge is present. Note that since the velocity is
increasing, and radius decreasing, with time, this is not strictly
correct, but is true in the limit as the mass of the payload becomes a
very small fraction of the mass of the accelerator.
Setting the two equal, we have: M*(rf*vf - ri*vi) = rf*Q*vf*B*t. Using
conservation of linear momentum we have ((M-m)/M)*vi = vf, where m =
mass of the payload. Also, we know that ri = GMe/vi**2, and rf =
GMe/vf**2, where Me = mass of the earth. So we can combine all this
into the following (if I manipulated right):
Q*t = m/B.
Unfortunately, I do not have a good reference value for B. Does
anyone out there?
Jim
-------henry@utzoo.UUCP (Henry Spencer) (01/26/86)
> Another solution is possible. If a charge is placed on the > accelerator, then it becomes a gigantic charged particle moving in the > earth's magnetic field. We know that in this case a force is exerted > on the particle, a force that can be used to transfer angular momentum > from the field to the particle, thus making up for the momentum lost > by the payload acceleration... Small problem: as I recall it, at least for the simple case of motion at right angles to the field lines (close enough, for an equatorial orbit), the force is at *right angles* to the motion. This isn't what's wanted. -- Henry Spencer @ U of Toronto Zoology {allegra,ihnp4,linus,decvax}!utzoo!henry
jrv@MITRE-BEDFORD.ARPA (James R. Van Zandt) (02/02/86)
------------------------------ > The second [solution] is to decelerate payloads from beyond LEO to > sub-orbital speeds. Where do you let them land? Do they all have to be small enough to burn up in the atmosphere, or can you steer them to where they won't hurt anything? > The problem here is that you do not want to be > required to lose mass from the space environment to the earth. Why not? There are a lot of rocks up there. > Moreover, it is unlikely that you could balance the traffic in the > early stages of use. True. > Another solution is possible. If a charge is placed on the > accelerator, then it becomes a gigantic charged particle moving in the > earth's magnetic field. We know that in this case a force is exerted > on the particle, a force that can be used to transfer angular momentum > from the field to the particle, thus making up for the momentum lost by > the payload acceleration. Note that no mass is needed to accomplish > any of this, only a power plant which may not even be physically > coupled to the accelerator. Space isn't a vacuum, only a very tenuous plasma. I'll bet the charged particles in the solar wind would gradually discharge the accelerator, requiring constant recharging. Also, this would not make up for the loss of orbital ENERGY. - Jim Van Zandt