Table 2.

Computation of angular velocity of moon at syzygy, γ

To compute γ we employ the expression:

where, for full moon and new moon, respectively:

γm = 17.1650, 17.1489 deg⋅day−1

a1 = 0.002326, 0.001663 deg⋅day−1⋅hr−1

a2 = 0.007372, 0.006742 deg⋅day−1

a3 = 0.09323, 0.08706 deg⋅day−1

f1 = 0.4508 ΔTperig − 1.4505 − 0.0254 ΔTperih

f2 = 4.8254 sin (2π ΔTnode/(24.)(27.212220)) − 0.06545

f3 = (1 − cos(2π ΔTperih/365.))

where ΔTperig (in hours), ΔTnode (in hours), and ΔTperih (in days) are,  respectively, the separation-intervals of syzygy from perigee,  lunar node, and perihelion.