Table 1.

Values of Doodson Numbers, Delaunay Angles, Tidal Arguments, Tidal Frequencies ($\omega$), and Integer Sets $j_{Mq}$, $j_{Wq}$, and $j_{\mathrm{\Omega }q}$ (See Text), for the 14 Tidal Constituents Used in Our Orbital Dynamics Model ^a

Constituent	Doodson number	Delaunay angle	Tidal argument	Frequency $\omega$	$j_M$	$j_W$	$j_{\mathrm{\Omega }}$
Long‐period tides
${\mathrm{M}}_f$	075,555	$2F+2\mathrm{\Omega }$	$2L$	$2n$	2	2	2
${\mathrm{M}}_m$	065,455	$l$	$l$	$\frac{dl}{dt}=n-\frac{d\overline{\omega }}{dt}$	1	0	0
Diurnal tides
${\mathrm{K}}_1$	165,555	Constant	$\theta$	${\omega }_E$	0	0	0
${\mathrm{O}}_1$	145,555	$2F+2\mathrm{\Omega }$	$\theta -2L$	${\omega }_E-2n$	2	2	2
${\mathrm{P}}_1$	163,555	$2F+2\mathrm{\Omega }-2D$	$\theta -2L^{\prime }$	${\omega }_E-2n^{\prime }$	0	0	0
${\mathrm{Q}}_1$	135,655	$2F+2\mathrm{\Omega }+l$	$\theta -2L-l$	${\omega }_E-2n-\frac{dl}{dt}={\omega }_E-3n+\frac{d\overline{\omega }}{dt}$	3	2	2
$\mathrm{\Omega }$ (${\mathrm{K}}_1$ nodal)	165,565	$\mathrm{\Omega }$	$\theta -\mathrm{\Omega }$	${\omega }_E-\frac{d\mathrm{\Omega }}{dt}$	0	0	1
$L+F$ (${\mathrm{O}}_1$ nodal)	145,545	$2F$ + $\mathrm{\Omega }$	$\theta -L-F$	${\omega }_E-\frac{d(L+F)}{dt}={\omega }_E-2n+\frac{d\mathrm{\Omega }}{dt}$	2	2	1
Semi‐diurnal tides
${\mathrm{K}}_2$	275,555	Constant	$2\theta$	$2{\omega }_E$	0	0	0
${\mathrm{M}}_2$	255,555	$2F+2\mathrm{\Omega }$	$2\theta -2L$	$2{\omega }_E-2n$	2	2	2
${\mathrm{S}}_2$	273,555	$2F+2\mathrm{\Omega }-2D$	$2\theta -2L^{\prime }$	$2{\omega }_E-2n^{\prime }$	0	0	0
${\mathrm{N}}_2$	245,655	$2F+2\mathrm{\Omega }+l$	$2\theta -2L-l$	$2{\omega }_E-2n-\frac{dl}{dt}=2{\omega }_E-3n+\frac{d\overline{\omega }}{dt}$	3	2	2
$\mathrm{\Omega }$ (${\mathrm{K}}_2$ nodal)	275,565	$\mathrm{\Omega }$	$2\theta -\mathrm{\Omega }$	$2{\omega }_E-\frac{d\mathrm{\Omega }}{dt}$	0	0	1
$L+F$ (${\mathrm{M}}_2$ nodal)	255,545	$2F+\mathrm{\Omega }$	$2\theta -L-F$	$2{\omega }_E-\frac{d(L+F)}{dt}=2{\omega }_E-2n+\frac{d\mathrm{\Omega }}{dt}$	2	2	1

^a Doodson numbers follow the convention used in J. G. Williams and Boggs (2016, see their page 98) and Petit and Luzum (2010, see their Table 6.7).