A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Peter Hakel
Date: 2020 May 10, 16:26 -0700
Hello Antoine, you asked: “how did you tackle this possible LHA indetermination trap in your spreadsheets?”
My short answer is: I didn’t.
Now the longer answer:
The attached images depict a special case showing that, besides the four input numbers in green, additional piece of information is needed to decide between the two mathematically valid values of LHA. I have done so in my meridian-passage-related spreadsheets by specifying upper vs. lower transit, but here I chose not to go as far for this (already rather academic) problem. My one_body_fix.xls spreadsheet always chooses the |LHA| < 90° value, since the other solution would usually place the celestial body below the horizon.
In fact, the noon-sight / meridian-transit problem is a special case of such a "one-body fix", in which the navigation triangle collapses to a line since the azimuth is known to be either 0 or 180.
That said, for the original Dave Walden problem, I looked at a globe to verify that the computed solution made sense before posting the result.