From: Michael Lorrey (retroman@tpk.net)
Date: Tue Dec 31 1996 - 16:06:27 MST
Hal Finney wrote:
>
> From: Michael Lorrey <retroman@tpk.net>
> > Essentially, you have one station at geosynch, that is say a hundred
> > miles long, containing a main EM rail system, and an
> > accelerator/decellerator rail in parallel. On the opposite side of the
> > planet, you've got a ground station, with a similar EM setup.
> > [...]
> > The cars would, when reaching the geosynch station, be traveling at the
> > same velocity as the station, from which they can either dump their
> > load, accept a load, or be switched to the parallel system for
> > changeover to an accelerator for transition to higher orbit or
> > interplanetary trajectory.
>
> My orbital mechanics is pretty rusty, but I think the cars would
> actually have a significant velocity relative to the geosynch station
> (having climbed all the way up from Earth), and similarly would need a
> big kick on leaving the station so that they would drop out of geosync
> orbit all the way down to a perigee of 1 earth radius. This is quite
> a big drop. My very rough calculations came out with a value of about
> 10,000 m/s for the velocity differential between the circular orbit and
> the elliptical one at apogee. Maybe that is tolerable with your EM rail,
> if it is long enough. A similar velocity differential exists at the
> Earth side as well. (Obviously you need greater than LEO speed there,
> which is about 7000 m/s.)
>
> Hal
Your numbers are wrong. The cars would be going at their very slowest at
their highest altitude (read keplers law) and fastest at the ground. I
am actually concerned that they wont be going fast enough at geosynch,
as they need to be going slow enough to fall back to earth, rather than
staying in geosynch, even though at apogee they will be tangential to
the geosynch orbit.
Opening my _Introduction to Space Dynamics_ by William Tyrrell Thomson,
I see that my deduction is right. Essentially, the cars will be
following a Hohmann transfer orbit, with lower orbit tangential point at
earth ground (perigee) and upper point at Geosynch station, where the
velocity of the cars would be less than the velocity of the station, so
the station would catch up to the cars as they reach their peaks, add a
little momentum to keep them, and then drop them off the back, regaining
the momentum when they are returning a car. If you drop off a car every
time you pick up a car, you lose or gain zero momentum at the station.
Give me a little time and I'll give you some accurate velocity
calculations. If your equations are right, I think that you just have
apogee and perigee mixed up.
--
TANSTAAFL!!!
Michael Lorrey
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