A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2017 Mar 29, 04:35 -0700
You asked: “Can you really extract those fifteen seconds of time from the raw data given by Frank, without knowing the longitude à priori? Aren't you pulling more information out of the data than that data contain?”
Expanding on what Frank responded; The 15 seconds is not pulled from the data. It’s the known offset between the time of peak altitude and Local Apparent Noon (LAN) which is common to all observers at the given latitude and dos not depend on longitude. Another question to ask might be “can a fit to the data locate the time of the peak altitude to within 15 seconds?” to which I feel pretty confident that the answer is yes.
You can retrace my own voyage of discovery on the need for this correction if you follow the thread starting here. Antoine “Kermit” Couëtte gave an expression for the offset in plain text
" ΔT culmination-transit (s) = 48/π * (tan Lat - tan Dec) * ( d/dt Lat ['/hour] - d/dt Dec ['/hour] ) "
In his original formulation of the problem Frank reminds us of the need for this correction when he states “Incidentally, my "northing" speed was zero, but the Sun is northbound at about 1 knot this time of year.”