Incidentally, under a fairly mundane extension of mechanical realisability, the sun is allowed partially to overlap the ring, creating a new crescent-shaped region in which planets rotate counter to those remaining in the old crescent. The new planets require negative radii for previous formulae to work smoothly. WFL On 8/6/15, Fred Lunnon <fred.lunnon@gmail.com> wrote:
On 8/6/15, William R Somsky <wrsomsky@gmail.com> wrote:
Umm.... Ah!
You're setting X_2 = -(sun radius) so that I is all ones, rather than [1, -1; 1, ..., 1], yes?
There's a little more to it than that. My radius sign indicates direction of rotation (rather than of teeth, as one might naïvely expect). With this convention, concentric increment corresponds to the "offset" operation in spherical geometry, in which each oriented sphere (including points and hyperplanes) changes in radius by a constant amount.
WFL