The moment of mean conjunction can easily be computed from an expression for the mean ecliptical longitude of the Moon minus the mean ecliptical longitude of the Sun (Delauney parameter D). Jean Meeus gave formulae to compute this in his Astronomical Formulae for Calculators based on the ephemerides of Brown and Newcomb (ca. 1900); and in his 1st edition of Astronomical Algorithms based on the ELP2000-85 (the 2nd edition uses ELP2000-82 with improved expressions from Chapront et al. in 1998). These are now outdated: Chapront et al. (2002) published improved parameters. Also Meeus’s formula uses a fractional variable to allow computation of the four main phases, and uses a second variable for the secular terms. For the convenience of the reader, the formula given above is based on Chapront’s latest parameters and expressed with a single integer variable, and the following additional terms have been added:
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