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?