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» Online Classroom   » Celestial Navigation   » Public Discussion of Cel Nav   » Trig help

Author Topic: Trig help

 - posted September 23, 2020 04:19 PM      Profile for JACK2           Edit/Delete Post 
Newbie here-
The following two trig formulas determine Z, but they appear to differ by 7’. Did I make mistakes? Is 7’ significant? Which is “more correct”?

L = DR latitude 15 degrees
d = declination 22 degrees
t = meridian angle 55 degrees
Hc = 37.63652 degrees (37 degrees 38 minutes)

Example 1 from “Commonsense Celestial Navigation” by Hewitt Schlereth
His formula:
sin-1 Z = cosine of d x sine of t divided by cosine Hc

Plugging in the numbers -
cos 22 x sin 55 = 0.759505 divided by cos 37.63652 = 0.959091
sin-1 = 73.554812 (73 degrees 33.3 minutes)

Example 2 from “Practical Celestial Navigation” by Susan P. Howell.
Her formula:
cos-1 Z = sin d - sin L x sin Hc divided by cos L x cos Hc

Plugging in the numbers -
sin 22 - sin 15 x sin 37.63652 divided by cos 15 x cos 37.63652 = 0.281135
cos-1 0.281135 = 73.67204 (73 degrees 40.3 minutes)

40.3’ - 33.3’ = 7’. Where did I go wrong?

BTW, he calls “t” the meridian angle and she calls “t” the LHA - how can they be the same?

Should I just go with NAO? Thanks, Jack

David Burch

 - posted September 23, 2020 04:33 PM      Profile for David Burch           Edit/Delete Post 
Very sorry, but we cannot check the results from other textbooks. We have our own textbook, which we support, and we have a book of extensive exercises of real cel nav sights (Hawaii by Sextant), which we also support.

We also have formulas online that can be used to compute Hc and Zn. See www.starpath.com/glossary and look up Navigator's Triangle in the cel nav section.

LHA and meridian angle are not the same. LHA is 0 to 360 measured westward from your meridian. Meridian angle (t) is 0 to 180 measured east or west from your meridian and labeled as such. Both terms are in our online Glossary.

From: Starpath, Seattle, WA
David Burch

 - posted September 23, 2020 04:37 PM      Profile for David Burch           Edit/Delete Post 
You can also check to see which answer is correct at www.starpath.com/calc

Choose sight reduction and pre-computation

From: Starpath, Seattle, WA

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