A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Rafal O.
Date: 2017 Mar 8, 23:57 -0800
Below are my calculations of latitude and longitude. To calculate time of LAN I used the fact that near this moment trajectory of Sun is like parabola or, in other words, quadratic function:
Hs(t) = a*(t - t0) + hs
Hs(t) = a2*t^2 + a1*t + a0
Using programable calculator that allows to estimate these three parameters (a, t0, hs) or (a2, a1, a0) one can obtain both time of LAN and height of Sun at this moment. I used R program but programable calculator gives t0 and hs as -a1/(2*a2) and a0/a2.
Here I present output of R:
Formula: Hs ~ a * (t - t0)^2 + hs
Estimate Std. Error t value Pr(>|t|)
t0 16.968047 0.002869 5914.69 < 2e-16 ***
hs 41.492687 0.003912 10607.49 < 2e-16 ***
a -1.919479 0.045020 -42.64 1.02e-09 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.008542 on 7 degrees of freedom
Number of iterations to convergence: 3
Achieved convergence tolerance: 3.286e-07
Hence, time of LAN is 16.968047 UTC (16:58:05 UTC) and Hs 41°29.6'. For Sun LL Hc has value of:
Hs[noon] = 41 29.6
IC = -3.8
dip = -4.8
Ha[noon] = 41 21.0
LL = +15.2
Hc[noon] = 41 36.2
From Air Almanac Sun is due south at 12:12:05 UTC. Time differene is 4:46:00 which corresponds to 71°30.0' W. Declination of Sun at this moment is 7°01.2' S. From this one can calculate Lat as 41°22.6' N.
So, the position in question is: 41°22.6' N, 71°30.0' W.