NavList:

Hello all,

I am relatively new to celestial navigation but very much deep into it. As an engineer, I make a point in making sure that all my calculations are precise. So far everything has worked out very nicely. But I’m now challenged by a mathematical error that I can’t figure out. It might just be the precision of the tables versus mathematical calculation. I would appreciate your input on it.

Here’s the problem.

I want to get the azimuth of the sun at sunrise at a specific position in the Northern Atlantic to verify the error of my compass.

Date: June 16^th, 2022

My position: N 48° 17.0’ W 062° 28.0’.

At this position, the sun will rise at exactly 8h08 TU (3h58 + 4)

Option 1. Using HO-249 the same way I do for any other sightings.

I enter the table with DEC N 23° 23.0 / Latitude N 48° / LHA 239°. The azimuth is 052°, which makes sense.

Option 2. Using Bowditch Tables

I enter the table with DEC 23° and Latitude 48°. The azimuth is 054.3°. It also makes sense.

Option 3. Finally, I use the amplitude formula instead of the Bowditch table

A°= arcsin (sin DEC / cos a-Lat)

A°= arcsin (sin 23° 23.0’ / cos 48° 17’)

A°= arcsin (sin 23.383° / cos 48.283°)

A°= 36.6°

Z = 090 – 36.6° = 53.4°

Here’s my question: The three results make sense but are slightly different (052°, 054.3° and 053.4°). Is it only due to the precision of the tables or is there something I forget to consider. Also, when using the first method, while the azimut (052°) seems to make sense, I get a Hc of  -1° 15’. It seems to me that Hc should be very close to 0°

Thanks for your input!

Francois