# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Time of meridian passage accuracy
From: Antoine Cou�tte
Date: 2009 Sep 25, 23:43 -0700

```George is right : Time of Meridian passage may be significantly different from time of Culmination.

Well known formula (although first order approximation). Let :

- "Delta Time" be the difference is seconds of time between culmination and Meridian Transit, and

- "Lat" the Observer's Latitude at Transit time, with "vLat" his hourly
Latitude speed is arcminutes per hour, and

- "Dec" the Body's Declination at Transit Time, with "vDec" the hourly
Declination change in arcminutes per hour, then

Delta Time = 48/Pi * (tan. Lat - tan. Dec) * (vLat - vDec) . First coefficient
often published as 15.35 or 15.3

Nothing new : this formula has already been posted here and it has been taught
for probably (almost and maybe more) one century now.

Let us take a somewhat 'extreme' but still realistic example : Lat = North 15?
with vLat = -30 and Dec = 15? South  with vDec = + 12 (Moon case), then we
find that Delta Time =  22.5 seconds (actual value does differ by just a few
seconds of time)

What are the practical implications on position accuracy if and when Meridian
transit time not equal to Culmination time ?

If the vessel has a significant north/south speed component, such as in the
extreme case listed here-above, then :

Body declination may have changed by up to 1/15 arc minute during that time
period, so it is (almost) negligible for conventional Celnav, and

Vessel's latitude will have changed by 0.2 ' during that time period. You may
start wanting to take it in account.

Antoine

Antoine M. "Kermit" Couette

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