From: Hal Finney (hal@rain.org)
Date: Fri Jan 03 1997 - 09:33:37 MST
From: Michael Lorrey <retroman@tpk.net>
> After sleeping on it, doing some intentional dreamCAD, I decided that,
> yes the cars, in an absolute sense are following a Hohmann elliptical
> orbit. However relative to the geosynch and ground stations, since we
> are dealing with the earth rotating, they will apear to follow a figure
> eight path, with the crossover point being that point at which the cars
> angular velocity is equal to the rotation of the earth. So, this will
> require good timing in geosynch traffic control to prevent car
> collisions in a high capacity Lorrey Loop.
(-: That's an interesting design technique :-)
I don't think ballistic cars will literally follow a figure eight
trajectory in the earth's rotational frame of reference, although you
are right that the orbit will have a loop in it. Rather, it will be more
like a Spirograph pattern, because the orbit will not form a closed loop
when it comes back to Earth. It will be in a different place because
the Earth has rotated away. So left to itself the car would continue
back on up, loop again, and come back down, repeatedly.
If the period of the elliptical orbit had some simple relationship to
the 24-hour rotational period of the Earth, then eventually the ground
station would catch up with the cars again. But it won't happen on
the first orbit. This suggests that your "ground station" maybe would
be better placed in low earth orbit, otherwise you'll have a lot of
fireballs streaking through the equatorial skies all over the planet.
Another idea would be to put your high station not in geosynch orbit,
but at whatever altitude gives the Hohmann elliptical trajectory exactly
a 24 hour period. This way the cars all come back to the ground station,
and you do have your nice figure eight relative to the rotating earth.
The only problem is that the high station's orbit would not be geosynch.
You could have several high stations and time your launches so that one
would be overhead when the cars get there, or you could have the high
station be in a non-inertial orbit, actively thrusting to stay geosynch.
Maybe the thrust requirements would be small enough to be satisfied
by mirrors.
Hal
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