Table 2.

Tidal Polynomials and their Derivatives

${\tilde{f}}_1(\epsilon )=1+\frac{15}{2}ϵ+\frac{45}{8}{\epsilon }^2+\frac{5}{16}{\epsilon }^3$	; $\frac{\partial {\tilde{f}}_1(\epsilon )}{\partial \epsilon }=\frac{15}{2}+\frac{45}{4}\epsilon +\frac{15}{16}{\epsilon }^2$
${\tilde{f}}_2(\epsilon )=1+\frac{31}{2}ϵ+\frac{255}{8}{ϵ}^2+\frac{185}{16}{ϵ}^3+\frac{25}{64}{ϵ}^4$	; $\frac{\partial {\tilde{f}}_2(\epsilon )}{\partial \epsilon }=\frac{31}{2}+\frac{255}{4}\epsilon +\frac{555}{16}{\epsilon }^2+\frac{25}{16}{\epsilon }^3$
${\overline{g}}_1(\epsilon )=\frac{11}{2}+\frac{33}{4}\epsilon +\frac{11}{16}{\epsilon }^2$	; $\frac{\partial {\tilde{g}}_1(\epsilon )}{\partial \epsilon }=\frac{33}{4}+\frac{11}{8}\epsilon$
${\tilde{g}}_2(\epsilon )=9+\frac{135}{4}\epsilon +\frac{135}{8}{\epsilon }^2+\frac{45}{64}{\epsilon }^3$	; $\frac{\partial {\tilde{g}}_2(\epsilon )}{\partial \epsilon }=\frac{135}{4}+\frac{135}{4}\epsilon +\frac{135}{64}{\epsilon }^2$