Midnight Meridian Method (M3)
Wikipedia lists 4 commonly accepted methods by which longitude may be determined. We propose for your consideration the possibility of a 5th method based on “midnight meridians” ascribed upon a master star-map of the ecliptic from an observatory on a prime meridian each night at the moment of midnight.
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The Midnight Meridian
As the earth orbits the sun, it also rotates within a “plane of midnight” that sweeps the universe at 360 degrees per solar year or roughly .98 degrees per solar day. Therefore, at the moment of midnight (apparent solar midnight), the slice of stars precisely on the observers N-S line correlates with the local longitude for that day. Subsequently you can predict the exact location for any longitude’s midnight meridian for any day of any year. The ecliptic is the apparent position of the sun.
Proposed Method for Establishing the Midnight Meridian
Let talk about the Gaocheng gnomon-observatory: At the moment of apparent solar midnight, while straddling the N-S line, sight thru the gnomon’s aperture (where the sun appeared exactly ½ day before) and draw that vertical line onto your ecliptic star chart. Continue night after night if only to enhance the accuracy of your midnight meridians and the master star chart itself. What you wind up with is a star map with your prime meridian’s 365 midnight meridians, expressed every .98 degrees (approximately the diameter of two moons).
A traveler to some foreign shore with star map in hand (or astrolabe like device with intertangle disks for each section of sky) then can determine their longitude by repeating the process and computing the distance between the locally determined midnight meridian and that of the master midnight meridian map. Roughly, each arc minute between the midnight meridians corresponds to 10 degrees of longitude. Nights where the midnight meridians fall upon denser clusters of stars offer the greatest potential for resolution.
Goal
Confirm/Proove the Midnight Meridian technique that establishes approximate longitude using little more than a 3rd century Chinese clepsydra, a star chart, and a masonry gnomon/tower straddling a north-south line. The technique does not involve trigonometry, moons or planets or calendars (although you must know current year.)