The Longitude Problem as the Unification of Space and Time with Special Application to the Island of St Helena

Determination of the longitude is the unification of space and time. The course note is presented to understand the points in the longitude problem within the framework of 16–8 Centuries. Establishing local time is difficult, because there are leads and lags of the Sun’s culminations, known as ‘Equation of Time.’ The Sun’s motion in the celestial sphere is nonlinear because of geometrical and gravitational reasons. The novel algorithm is proposed to get the rigorous Equation of Time. Three brilliant astronomers had stayed in St Helena. They themselves determined the longitude of the island by different methods. By use of their and other observations of astronomical events the new calculations are available. These are the sources of the exercises. Edmond Halley states the island in 7 degrees west of London. There are three observations of the Transit of Mercury on 7th November 1677: 5◦53′21′′W by Towneley data and 6◦26′44′′W by Avignon data. Nevil Maskelyne determined the longitude to be 5◦49′W based on eclipses of Jupiter’s satellites in 1761. Using observations of the total lunar eclipse on 18th May 1761 at the island, Cape and Stockholm, one obtains 5◦49′05′′W. Manuel John Johnson reached the conclusion of 5◦43′39′′W by the lunar distance method (1830–33). Using observations of the total solar eclipse on 27th July 1832 at the island, one obtains 5◦27′51′′W.