This formula was adopted by M. Chapront-Touze & J. Chapront in the shortened version of the ELP lunar theory in their “Lunar Tables and Programs. Title: Lunar tables and programs from B.C. to A.D. Authors: Chapront- Touzé, M.; Chapront, J. Publication: Lunar tables and programs from B.C. Michelle Chapront-Touze is the author of Lunar Tables and Programs from B.C. to A.D. ( avg rating, 0 ratings, 0 reviews, published ).
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The first set provides time-dependent expansions of the longitude, latitude, and radius vector of the Moon, referred to the mean ecliptic and equinox of date. These tables are intended for the user who does not need high precision.
Lunar Tables and Programs from B. It could be useful for those interested in the prediction proggams lunar occultations. The accuracy of the longitude in degrees, for each kind of precision, for a date in ephemeris time for various time spans for Lunar Tables and Programs from B.
The programs and data files are protected under United States Copyright Law but are not copy protected. For historians and others who do not need this full precision, procedures are given for computing peograms and low-precision coordinates that use a much smaller number of terms of the tables with low-precision, 72 terms for the three coordinates inclusively.
The second set of tables provide expansions of the semimajor axis, eccentricity, sine of half the inclination, longitude of perigee, longitude of node, and mean longitude, referred to the mean ecliptic and equinox date.
These tables include a large number of terms in order to ensure a sufficient precision in the present period for most users.
Lunar Tables and Programs from 4000 B.C. to A.D. 8000
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C to A. Included are formulae for computing coordinates referred to other reference frames, in particular the true equator and equinox of date, and for corrections of aberration.
Formats and Editions of Lunar tables and programs from B.C. to A.D. 
These programs are available only to purchasers of the book. These programs display menus which allow easy computation of lunar coordinates in various reference frames and orbital elements.
It is a work of great value and utility and I am more than pleased at being allowed to keep the review copy. As well as the practical information given in the tables and programs, a considerable amount of lunar orbital theory is given that may be chaprpnt use to those who have an interest in the details of celestial mechanics.
For better precision, formulae for computing the osculating orbital elements from the full tables of the first set are given. You must use the order form located at the back of the book and it must show the serial number for prograsm book to purchase the program.
I cannot suppose that anyone will seek to better the book for a generation or more.