From: henry@spsystems.net (Henry Spencer)
Newsgroups: sci.space.tech
Subject: Re: Sub Orbital Platform
Date: Wed, 9 Feb 2000 23:48:08 GMT

In article <38A15CFD.9063DC7A@peterlynnkites.co.nz>,
Robert Lynn  <robert@peterlynnkites.co.nz> wrote:
>> "The Ringworld is un-STA-ble..."
>> Well, you get the idea. The instability is non-intuitive...
>
>It's actually a pretty well known result in first year physics that as
>you move towards the centre of a planet the gravitational effects of all
>the material above the radius you happen to be at cancels out...

Correct so far.

>I think this can be generalised to the ringworld in that the ringworld
>feels the gravity of everything inside its radius, but is insensitive to
>its location.

Nope, it's worse than that.  The Ringworld is not just neutrally stable,
it is *unstable*.  Not only is there no restoring force, there is an
anti-restoring force:  any deviation from the central position of the star
tries to get worse.  Your intuition that you can, so to speak, turn the
problem inside out is basically correct... but your intuition that spheres
and rings work the same way is not.

Suppose you're at the center of a spherical shell, and then move 1km
northward.  (The directions and distance are arbitrary, but it helps to be
able to talk about them concisely.)  Clearly the shell is symmetrical
around you in all non-north/south directions, so the only issue is whether
its gravity from the north still balances that from the south.  You are
closer to the part that's north of you, so courtesy of the inverse-square
law, it pulls more strongly, and contrariwise for the south part.  On the
other hand, there is now *less* of the shell north of you, and more of it
south of you:  a 1km strip above the equator used to be north of you and
is now south of you.  For a spherical shell, these effects balance.

For a ring, it doesn't work.  There's less mass off to the sides, and
hence proportionally more to the north and south, so the change in
distance has a stronger effect.  The equatorial strip is now just two
little patches, so moving them to the south has a weaker effect.  Net
result, a northward force.
--
The space program reminds me        |  Henry Spencer   henry@spsystems.net
of a government agency.  -Jim Baen  |      (aka henry@zoo.toronto.edu)