Longitude: How do yo tell what the exact ships time is.
You must synchronize your ship''s clock with UTC. The Naval Observatory has the precise time as well as many other sources. I suspect your computer is linked to one of these sites so it can keep precise time. I know my Mac does.
You DO NOT reset your clock to peak sun. This is local solar time (also called sundial time). High noon will vary according to your position.
The rest here is an aside:
Sundial time was the problem in Colonial days when people could more quickly get from one part of the state to another. It was the railroads that instituted time zones in 1863 in this country to avoid scheduling confusion and to prevent train wrecks. England had already started railroad time in 1840. Greenwich Mean Time was started in 1847, but I don''t think the US switched over to it ''til after 1883 (I suspect this since Lewis and Clark used Washington, DC as their longitude reference in charting the West using the stars and a "crude" chronometer)