OT: Ringworld

> > I have been nformed by many people wiser than myself than the gravity
> > of the inside of a ringworld or a Dyson sphere will be zero.
Lars Henrik Mathiesen wrote:
> I thought this was well known in science fiction circles...
>
> The sphere or ring itself will not exert any gravitational attraction
> on matter inside them ---
True for the sphere, false for the ring, as ought to be obvious from the
informal geometric argument:

From a particle within the sphere, draw a pair of opposing narrow
cones.  Consider the distance along the axis of the cones from the
particle to the sphere in each direction: call them D and d.  The amount
of mass within the cone is proportional to the square of the distance
from the particle to the sphere.  But the force of a given mass is
inversely proportional to distance.  So the force along that axis is
proportional to
        (D^2 / D^2) - (d^2 / d^2)
which is zero.

This argument does not apply to the ring, even in the ring plane;
because the amount of mass within the cone is proportional to D, not
D^2.

See http://www.ogre.nu/images/gringi.jpg for the contours of the ring's
g-field (actually 200 point masses on a circle).  The net force is
perpendicular to the contours.  Unsurprisingly, it's generally toward
the nearest point on the ring.  The central equilibrium point is
unstable: a nudge off the axis will send your test mass falling to the
ring.


--
Anton Sherwood  --  http://www.ogre.nu/

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