Garmaine Staff asked 2 years ago

This answer to Is there a name for the great circle where latitude and longitude are equal? says (in part):

More generally, a clélie is the name given to any spherical curve where the longitude $\varphi$ and colatitude $\theta$ have the relationship $\varphi=c\theta,\quad c>0$, and the curve of Viviani corresponds to the locus of a geosynchronous orbit, $c=1$.

Is it really true that a polar geosynchronous orbit (displayed in a synodic or rotating frame) is described by Viviani's curve? Can this be demonstrated mathematically?

File:Viviani-fenster-1.svg construction of Viviani's curve Source