At 04:43 PM 9/25/01 -0700, Hal wrote:
>The idea is simply not of practical use today.
Quite so. Sorry, I should have made it clear that my own interest in
raising the topic is that I want to plug such a gadget into a post-Spike
future sf novel, which allows me a measure of near-magic physics to help
with drilling and sustaining the tunnel (exotic matter, maybe, how would I
know). But I don't wish to shrug away *all* known physics with, say, an
anti-inertial drive or teleport system.
I find it amusing that some here think the trip will be weightless, others
that the difference in weight will hardly be noticed. So much for physical
intuition. :)
Alex Eremenko, whose site I ref'd, points out to me that
>Indeed, the one-way travel time of a gravity train is
>exactly 1/2 of the time of orbiting the Earth on a low orbit.
>This is easy to figure out without any calculation once the
>fact that the travel time is independent on the destination
>is established. Indeed, conssider the travel to the antipodal point
>(through the center of the Earth). This is the limiting case of
>a Kepler orbit, it can be thought as a very long and thin ellipse.
>According to the Third Kepler Law, the time depends only of the long
>axis of the ellipse. But this long axis is the radius of the Earth,
>the same as for a low circular orbit.
He also commented:
>Speaking of the passengers sensation during the trip, they will depend on
>the distance traveled. For example, on a train from Chicago to
>Detroit they will feel almost nothing special.
>As the distance increases they will feel some decrease of their weight,
>and in the extreme case, a travel through the center of the Earth
>(the longest trip possible, to an antipodal point) they will be
>completely weightless (like in a space orbital trip)
>ALL THE TIME OF THE TRIP.
>There will be never any weight increase in any of these trips, only
>some loss of weight, longer the trip, larger the loss.
>The weight loss will not be constant during the trip[...]
>One more remark: the gravity train running on a chord is not the fastest
>possible one. It only has an amazing property that the time of the travel
>does not depend on the distance. The fastest possible gravity train
>will describe a more complicated curve inside the Earth called
>the brachistochrone, and in this case the time of the travel will
>depend on the distance. Actually the chape of this brachistochrone
>was computed by Newton in his "Principia", but of course he did not mention
>trains.
Damien Broderick
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