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OT: Ringworld

From:Anton Sherwood <bronto@...>
Date:Tuesday, December 4, 2001, 17:47
> > 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 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 --


Lars Henrik Mathiesen <thorinn@...>