# NavList:

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

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GHAA formula
From: Paul Hirose
Date: 1997 Dec 07, 4:36 PM

```For ordinary navigational purposes, it's possible to simplify the
GHAA formula quite a bit.  Here is the original posted by "WSMurdoch":

GHAA = 0.7790573 + 36,625.0021390T + 0.0000011T^2
- 0.0000122sin(125.0 - 1934.1T) - 0.0000009sin(200.9 + 72,001.7T)

T is elapsed time in Julian centuries (36 525 days per century) since
2000 Jan 1 12 h UT.  The result is in units of revolutions.

What can be removed from the formula?  Well, the sine of an angle is
never more than 1, so the last term cannot affect the result by more
than .0000009 rev, or .02' of arc.  Similarly, the next to last term
has a max effect of about 1/4 minute of arc.  If we drop the last two
terms, the accuracy should still be ample for practical work, and we
no longer need a calculator with trig functions.

The T squared term can be omitted as well, unless you need to cover a
long time span.  Not until we are three centuries from our base year
of 2000 will this term reach 1/4 minute.

The formula now becomes:

GHAA = 0.779 057 + 36 625.002 14 T

Note that I've also rounded the constants to six decimal places.  For
the range 1900 - 2100, that will cause a negligible loss of accuracy,
compared to the terms I deleted.

As long as we remain in the years 1730 - 2270, a ten digit calculator
will be okay for this formula.  Within those years, the calculator
will resolve to .00001 revolution, or .2'.

Note that most navigators use UTC without bothering to convert to UT1.
Whether you're using the almanac or the above formula, that omission
will cause up to 1/4 arc-minute error in GHAA.  See the explanation in
the Nautical Almanac.
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