A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Tony Oz
Date: 2021 May 31, 07:43 -0700
If the gnomon (the stick) is at 51.2°N (at the latitude equal to star's declination) the shadow will draw the staight East-West line. Parabolas appear if the gnomon is at a latitude where the star is seen as setting/rising. Hyperbolas appear when the gnomon is closer to the equator than the star is (we are moving away from the pole).
(I hope I did not confuse a parabola for a hyperbola!)