Clélie

In mathematics, a Clélie or Clelia curve is a curve on a sphere with the property:

If the surface of a sphere is described as usual by the longitude (angle ${\displaystyle \varphi }$) and the colatitude (angle ${\displaystyle \theta }$) then

${\displaystyle \varphi =c\;\theta ,\quad c>0}$.

The curve was named by Luigi Guido Grandi after Clelia Borromeo.

Viviani's curve and spherical spirals are special cases of Clelia curves. In practice Clelia curves occur as the ground track of satellites in polar circular orbits, i.e., whose traces on the earth include the poles. If the orbit is a geosynchronous one, then ${\displaystyle c=1}$ and the trace is a Viviani's curve.