Olendirk
Hour angle is nothing to do with how long an astronomical body is visible! It is one co-ordinate of a position on the celestial sphere (the other being declination), the equivalent of longitude on the Earth's surface although measured 000°-360° to the West instead of 000°-180° East or West.
[aside to Aspidustra : This angle may be "... conventionally expressed in units of time" but it is not for the purpose of the General Navigation syllabus! Unless we wish to go deeper into a discussion of how to actually navigate by the stars, way beyond what most pilots here need, then we should leave it as Oxford Blue and I, both Gen Nav instructors, have stated.]
The question you describe, Olendirk, does not come within the scope of JAA Navigation, it requires knowledge far beyond the learning objectives. Do you need to go deeper into astro navigation than the JAA ATPL syllabus? If so I would suggest a more specialised site for your question, a visit to the military forum where some military navs may be able to help, or a specific heading asking for those with knowledge (such as ocean yachtmasters' certificate holders!) of real astro navigation. It has not been in common use for civil aviation for many years.
Send Clowns
Gen Nav, BCFT