NavList:

I have been thinking of WHY would the Star Path article want the moon to be due east or west of your position.  The givens, stated by Star Path, is that we have two stars and a moon altitude, free of error.

It appears that they want the LOP related to the moon to be a longitude line. That is, in altitudes free of error, the star LOPs will always cross each other in the same relative way, independent of time.  The variable is the time of the moon altitude.  Time is most directly related to longitude, and so, the optimal azimuth for the LOP of the moon is 90° or 270°.

By varying the time of the moon's altitude , the LOP related to the moon will change the where the LOP of the moon crosses the LOP of the stars.  

For this to work well, ideally the stars should be at a maximum 90° cut to each other AND at the maximum cut to the moon.  This puts the stars on 45°, 135°, 225° or 315°.  That is, we want the angle between the azimuths to the stars to be at best cut and then the time sensitivity of the moon LOP to be at maximum.  If the cut between the stars isn't at maxima, or the azimuth to the moon LOP approaches that of either of the star's LOPs, then the sensitivity of the moon relationship to time is reduced.  If the moon's LOP is equal in azimuth to the azimuth of either star's LOP, then the relationship collapses.

Let us begin then with an estimate of the sensitivities.

Time is most responsive to moon altitude variation when the azimuth to the moon is to the east or west, az 90°, 270°.  In the attached spreadsheet, in B4, the azimuth to the moon is entered.  In B7, we find the angular of the moon's azimuth from either 90 or 270.  For example, if the azimuth to the moon is 80°, then the angular cut is 10°.  If the azimuth to the moon is 271°, then the angular cut is 1°.  If the azimuth to the moon is 180° or 90°, it is a latitude and not sensitive to time for the purposes of GMT by altitudes.  It is a simple matter, then to roll off the sensitivity as the cosine of the angle of the moon from 90/270.

Next is the cut between stars.  Ideal is 90° but can range downwards to 0°.  In cells B2 and B3, the azimuths to the two stars are entered.  Once the cut is determined, we call roll off the sensitivity by cos(90°-cut).

Similarly, we can find the cut between the moon and those stars, and roll off the sensitivity as the cosine of that angle.

Multiply those together for the overall in cell B19.  Ideal is 1.  When any of the azimuths overlap, the overall  goes to zero.  

Please be kind to the attached spreadsheet.  I did not try to make it bullet proof.  I merely wrote it to investigate the effects.

Brad

* https://www.starpath.com/catalog/accessories/starpilot/lun_alt.htm