In U.S. Naval Institute Proceedings for June 1957 (page 680), Captain P. V. H. Weems and Captain R. E. Jasperson outline a method for finding a position by observing one celestial body only. The principle of the method is to use the observed rate of change of altitude, together with the observed altitude itself, to solve directly for latitude and hour angle, and thus to obtain the position. The authors point out that the parallactic angle, C (the angle at the observed body), in the usual navigational spherical triangle is obtainable from:

sin C = sec (declination) × rate of change of altitude with hour angle.