A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2019 Sep 25, 18:01 -0700
Ahoy, Chris. Welcome aboard!
For your sight UT/GMT is 8:30:30pm. From your altitude combined with known latitude and the declination, you've calculated the Sun's HA or "hour angle". The result you get expressed as time is 5:19:02pm. As an angle, that's equivalent to 79.758°. You can double-check that this is the correct angle by setting up the standard ZPS triangle and solving for HA. In modern calculator terms (with ZD = 90° - corrected altitude):
- A = cos(ZD) / cos(Dec) / cos(Lat)
- B = tan(Dec) · tan(Lat)
- HA = acos(A - B)
You should find a very close match. So that's good!
This angle of the Sun away from the meridian is not the sort of time that we can compare directly with GMT/UT. That time, 5:19:02pm, is what a sundial would display -- the pure angle from the meridian to the Sun's position in the sky. It's Local Apparent Time. It's what we want: we're turning out sextant into an accurate sundial in this process.
The Sun can be fast or slow, and the difference, of course, is that quantity we call the "Equation of Time". On Sep. 3 at 20h UT, the Sun was fast by about 40 seconds, equivalent to 10 minutes of longitude. Adjust your local time, or adjust your final longitude, and you'll find that everything worked out within a mile, matching what you saw in the StarPilot app. It has to work out. It's the same math.
By the way, in the modern world of celestial navigation, the equation of time correction is simply built into the Sun's GHA. And the time-based math is equivalent to Longitude = GHA +/- HA. The Sun's observed Hour Angle is identical to the difference in longitude between your vessel and the Sun (the Sun's longitude is GHA). Is it add or subtract? Easy for the Sun: add before lunch (noon), subtract after. But you can always just try both and keep the one that makes sense.