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

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Re: Formula to determine GHA of Sun?
From: Bill B
Date: 2014 Sep 07, 15:51 -0400

```On 9/6/2014 7:31 PM, Samuel L wrote:
> I can calculate Dip and Refraction with my calculator but I'd like to
> know how to easily and accurately calculate GHA for the Sun. I can
> approximate GHA using a general Longitude and improve upon it for the
> minutes of time from the Tables of Increments and Corrections but I'm
> usually off by 25 minutes of arc.
>
> Can you recommend a formula that'll do it? That is- one that a math
> dummy would understand?

The concepts are basically the same as put forth in my 8 August answer.

You do not specify what is off by 25 arc seconds? Your intercept, your GHA?

If you are using the increments and corrections tables correctly, the
arc degrees and arc minutes past the whole hour GHA  will be accurate to
withing 3 arc seconds.

Keep in mind the cosine formula uses LHA, which is derived from GHA (GHA
- west AP longitude = LHA). If your assumed-position longitude is off,
your intercept will be off (except for LAN observations).

As to a calculator formula, portion of the hour expressed as a decimal
x 15 = decimal degrees. (The Sun's GHA changes approximately 15 degrees
per hour, so the fraction of the hour multiplied by 15 = change in degrees.

How to:

In any event, remember minutes and seconds time are base 60 (sexagesimal
system) like arc minutes and seconds.

*Enter the minutes and seconds of time into the calculator the same way
you would arc minutes and seconds.(DMS)
*Convert to decimal degrees (DD) (Decimal arc minutes/seconds
interchangeable with time minutes/seconds thanks to base 60.)
*Multiply by 15
*Add to the DD equivalent of the GHA at the whole hour used.
*Convert the total to degrees, minutes and seconds (DMS)

Cook-book example on TI-30XA, 7 September 2014, 18:14:55 UT

* Enter 0.1455 (14 minutes and 55 seconds time)
* Convert to decimal degrees: 2nd DMS-DD keys (will display 0.24861...)
* x 15 = (will display 3.72916...) If converted to DMS, 3d 43' 45"
displayed--within 3" of tabular method--but do NOT convert to DMS yet
* + 90.3048 2nd DMS-DD (GHA at 18:00 UT 90d 30.8' aka 90d 30' 48")
* = 2nd DD-DMS (94.2425 DD then 94d 14' 33" DMS displayed)

Easy peasy once you grasp the DD and DMS concept. We want to input and
output DMS, and this calculator does its thing in DD.

```
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