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Murray,

In addition to Robin's comments (Reduction-occultation-stars-Stuart-jan-2018-g41143), I wish to add the following information if it may help:

• Good if not excellent theoretical treatment of Stars Occultations by the Moon is given in various books. The ones I can recommend are:
  • Spherical Astronomy (Cambridge University Press) by W.M. Smart (1931). In my 6th edition copy (1976) Occultations are covered under Chap XV. And:
  • Astronomie Générale by André Danjon (1959), in my 1980 reprint Occultations are covered under Chap XIV.
    • Both Authors depict the William Bessel's method just described by Robin. André Danjon has the immense advantage of closely looking into the refraction effects which are not so easy to deal with when you use William Bessel's method.
• And also, Mathematical Astronomy with a Pocket Calculator (John Wiley and Sons, 1978) by Aubry Jones FRAS lists 2 calculator Programs (including a Grazing Occultations program) given in Appendix (end of the book) and claimed as yielding "rigorous calculation of a star by the Moon at any given place". I have not used any of these programs, but given the overall excellent quality of this book, I would certainly trust them.
• In his excellent Astronomical Algorithms (William Bell), Jean Meeus does not cover Occultations, at least in my 1991 Edition. Maybe he did address them in some subsequent edition. Can anybody confirm this or not?
• And this is the Gold Mine for Occultations:
  • http://www.lunar-occultations.com/iota/iotandx.htm , you can even download an occultation program here:
    • http://www.lunar-occultations.com/iota/occult4.htm
• And I would simply conclude with the use of Frank E. Reed's Lunar Calculator ( http://reednavigation.com/lunars/lunars_v4.html )
  • While it is an outstanding Lunar Calculator for Lunar Distances superior to about 7° to 10°, and while Frank E. Reed has clearly indicated that it is not an Occultation tool, it can still deliver reasonably decent Occultations results provided you use it through an iteration method, which is a variant of the one described in " http://fer3.com/arc/m2.aspx/First-MoonStar-Lunar-corrected-version-Couëtte-dec-2017-g41041 " . Let us proceed with one example:
    • http://www.lunar-occultations.com/iota/iotandx.htm lists the following details for an upcoming Aldebaran occultation: seen from Moncton Airport Canada (N46°07.0' W064°40.7' Alt 232') Aldebaran will disappear behind the Moon at 16h00m40s UT1 on Feb 23rd, 2018. I can confirm these data since my own determination is 16h00m37s. 
      • If you load Frank's Calculator with the Moncton position, with a "0" Distance and a starting UT equal to 16h00m00s, you will get the following result: Error in Lunar: -0.3'      Approximate Error in Longitude: 0° 08.6'. Simply multiply the Error in Longitude by 4 to get a correction to your UT in seconds of time, here a + 34.4 second correction, everything else remaining unchanged. Then:
        • 16h00m34.4 UT Error in Lunar: -0.2'       Approximate Error in Longitude: 0° 06.0'.  Let us continue ...
        • 16h00m58.4 UT Error in Lunar: -0.1'       Approximate Error in Longitude: 0° 04.2'
        • 16h02m00.0 UT Error in Lunar: 0'           Approximate Error in Longitude: 0° 00.2', which is about the best you can get for this example.