# NavList:

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

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Re: determination of longitude and the prime vertical
From: Paul Hirose
Date: 2007 Apr 12, 16:14 -0700

George Huxtable wrote:
>
> | Date:     1 May, 2007
> | UT:       20:41:45
> | Position: N40 W60
> | Hc:       24d 00!2
> | Az:       270.00
> | LHA:      71d 09!5
> | dec:      15d 09!5

I'll work the computation with the USNO MICA program, using the
Terrestrial Time scale for best accuracy. IERS Bulletin A predicts UT1
will be .11 second behind UTC on that date. In addition, UTC will be 33
seconds behind TAI, and TAI 32.18 seconds behind TT.

Delta T = .11 + 33 + 32.18 = 65.29 seconds. So 20:41:45 UT1 = 20:42:50.3 TT.

For that time MICA gives RA 2h 34m 40.568s and dec. +15° 09′ 29.53″ with
respect to the true equator and equinox of date.

At 20:41:45 UT1, MICA says the Greenwich apparent sidereal time is 11h
19m 20.1896s. (UT1, not TT, is the better time scale to use here.)
Subtracting RA Sun gives GHA 131° 09′ 54″, and subtracting longitude
gives LHA 71° 09′ 54″. That's only a tenth minute off what George's
calculator gave.

To be consistent with the TT time scale, the observer's longitude must
be moved west by delta T times the solar / sidereal ratio, converted to
arc. I.e., 65.29 * 1.002738 * 15″ = 16′ 22″. So the adjusted position is
40° 00′ 00″ N 60° 16′ 22″ W. From that point on 2007 May 1 20:42:50.3
TT, MICA gives altitude 24° 00′ 03″, azimuth 270° 00′ 02″.

Everything gets much simpler if you input UT1 throughout and let MICA
use its internal delta T table. MICA 2.0, the one I have, is a full
second of time in error, but that affects only the Sun's position
relative to the stars. To navigational accuracy, the end result is
identical.

Incidentally, the latest MICA version is 2.1, released in December 2006.
http://aa.usno.navy.mil/software/mica/micainfo.html

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