The moment of mean conjunction can easily be computed from an expression for the average ecliptic length of the Moon minus the average ecliptic length of the Sun (Delauney parameter D). The expression given is based on the ELP2000-85, with the following corrections:
- constant term:
- Applied the constant terms of the aberration to obtain the apparent difference in ecliptic longitudes:
Correction in conjunction: -0.000451 days.
- For UT: at 1 Jan. 2000, Delta-T was +63.83 s; hence the correction for the clock time of the conjunction is:
- quadratic term:
- In ELP2000-85, D has a quadratic term of -5.8681"*T*T; expressed in lunations N, this yields a correction of +87.403E-12*N*N days to the time of conjunction. The term includes a tidal contribution of 0.5* -23.8946 "/cy**2. The most current estimate from Lunar Laser Ranging is: (-25.88 ±0.5) "/cy**2. Therefore I applied the correction -0.9927*T*T" to D. This translates to a correction of +14.79E-12*N*N days, for a total of:
- For UT: analysis of historical observations show that Delta-T has a long-term increase of +31 s/cy**2 . Converted to days and lunations, the correction from ET to UT becomes:
The theoretical tidal contribution to Delta-T is about +41 s/cy**2 ; the smaller observed value is due to changes in the shape of the Earth. The uncertainty of our prediction of UT (rotation angle of the Earth) may be as large as the difference between these values: 11 s/cy**2 . The error in the position of the Moon itself is only maybe 0.5 "/cy**2, or 1 s/cy**2 in the time of conjunction with the Sun.
Periodic perturbations change the time of true conjunction from these mean values. For all new moons between 1601 and 2401, the maximum difference is 0.592 days = 14h13m in either direction.
The duration of a lunation (from new moon to the next new moon) varies in this period between 29.272 and 29.833 days, i.e. -0.259d = 6h12m shorter, or +0.302d = 7h15m longer than average. This range is smaller than the difference between mean and true conjunction, because during the lunation the periodic terms cannot all change to their maximum opposite value.