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    Re: Calculating the time when GHA is equals zero?
    From: Jeremy C
    Date: 2020 Mar 14, 03:39 -0700

    Hi Steve,

    As to the "Mer Pass" in the lower right corner.  That is the UTC of meridian passage for the sun or moon at the prime meridian.  The older refences used to call it the local mean time (LMT) at Greenwich, which is essentially the same as GMT and UTC.  The trouble with it is, that you are very rarely on the prime meridian so the number must be adjusted based on your current longitude.  For the sun you can convert your difference in longitude from arc to time using the table in the Nautical Almanac (or mathematically where 15 degrees of longitude is 1 hour of time) and apply it to the time given in Mer Pass.  This will give the UTC time of transit at your location to the nearest minute.  Then you apply your zone description to get the local time of transit.

    For the moon, the process isn't so simple, since the moon moves at not only a different rate than the sun, but also tends to vary a bit depending on the date (this is where that "v-corr" comes in).  The arc to time table will not work.  To do it mathematically, you have to determine the average hourly rate of change in GHA for the given day and then determine how long it will take the moon to cross your meridian.  The nautical almanac’s increments and corrections page is based on an hourly movement of 14 degrees 19.0 minutes.  This is the slowest the moon moves.  The v-correction is added to this.  So at 1900 on March 4th, 2020, the moon is moving 14 degrees 19.0 minutes plus 7.0 for a total of 14 degrees 26.0 minutes per hour.  At 2000 on the same date, the moon moves only 14 degrees 25.9 minutes, and continues to slow as the day progresses.  It is quite a process to track this change in the movement until the moon reaches your local meridian.

    If you need an exact time for the moon's transit, I would suggest ignoring the Mer Pass table and use the "GHA method" where you determine the time at your longitude where LHA is zero for an upper transit, or 180 for a lower transit.   This is similar to what you were doing in your example to find a time of a given GHA. I will work through a problem with this if you are not familiar with the method.

    To be honest, if you are just learning, I’d leave the moon alone for now.  Once you have a firm grasp of how Local Apparent time, Local Mean time, Zone time, and UTC all work, then you can start to tackle the moon, which tends to break the rules.

    Let’s do an example with the Sun.  Say it’s March 4, 2020 and you are at 85 deg W longitude.  What is the time of LAN?

    The Mer pass table says 1212 UTC.  Converting 85 degrees longitude is 5h 40m (85/15=5.666=5h 40m).  So add that time to 1212 and you get 1752 UTC.  At 85W you should be keeping ZD +6, so applying that in reverse gives you 1152 ZT.

    In Eastern longitude, you just subtract the arc to time conversion from the given UTC.  So, 1212 minus the 5h 40 minutes is 0632 UTC Plus the 6 hours for ZD is 1232 ZT.

    I hope this helps.

    Jeremy

       
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