The optimum shape for a rigid rotating shell enclosing an isotropic spherical planetary mass
Abstract
Analysis of the Dyson Sphere, an extremely advanced civilization's hypothetical construct entirely surrounding a star, shows that new stress inward to the star increases to maxima at the poles if the sphere is rotating. This is because the centrifugal force in the rotating frame of reference vanishes at zero rotational radius, which occurs at the poles. There is less of the centrifugal force at high latitudes than low to offset the star's gravity. A form is derived for a thin, rigid, rotating shell, surrounding a large pointlike mass and/or charge, which will experience the least possible net stress at every point upon it  a shape on which every point not on the shell's equator is as near as possible to being in orbit. In orbit, whose plane passes through the primary body's center of mass or of charge, F(grav), or Fg, is exactly opposite in direction to F(centrif), or Fc, and is equal in amount. At all points not on the equator, Fc will not entirely offset Fg, because of Fg's vector decomposition. However, both forces are always constrained to be equal in absolute amount everywhere on the shell, equator included. The derived shape, given by the figure of revolution around the xaxis of x = square root (y172), will prove useful in largescale space construction. Also, various engineering problems are discussed.
 Publication:

Resources of NearEarth Space
 Pub Date:
 1991
 Bibcode:
 1991rnes.nasa...36C
 Keywords:

 Center Of Mass;
 Centrifugal Force;
 Gravitation;
 Planetary Mass;
 Rotation;
 Spheres;
 Thin Walled Shells;
 Construction;
 Decomposition;
 Equators;
 Isotropy;
 Polar Regions;
 Radii;
 Lunar and Planetary Exploration