\begin{table}%t5
\caption{\label{t:amplitudesceres}Coefficients of the periodic terms in the analytical solution for Ceres. }
\small%\centering
\par
\begin{tabular}{@{}ccrrrrr@{}}
\hline\hline\noalign{\smallskip}
&& \multicolumn{5}{c}{\underline{\hspace{5cm} Coefficient \hspace{5cm} }} \\
\multicolumn{1}{c}{Frequency $(i,j)$} & \multicolumn{1}{c}{Period (days)} & \multicolumn{1}{c}{$M/\epsilon$} & \multicolumn{1}{c}{$\Lambda/\epsilon$} & \multicolumn{1}{c}{$\mu-\delta$} & \multicolumn{1}{c}{$\nu$} & \multicolumn{1}{c}{$\lambda$}  \\
\hline
$(2,0)$  & $840.250$   & \multicolumn{1}{c}{---} & $ 9.4943\times 10^{+04}$       & $-1.0836\times 10^{-05}$  & $-4.4828\times 10^{-08}$  &\vphantom{$K^{K^K}$} $ 1.0896\times 10^{-05}$ \\
$(2,-1)$ & $0.35380$   & $-7.6334\times 10^{-02}$     & $-1.5267\times 10^{-01}$     & $ 2.4028\times 10^{-06}$  & $-2.4028\times 10^{-06}$  & $-8.7482\times 10^{-12}$\\
$(0,1)$  & $0.35365$   & $ 7.6249\times 10^{-02}$     & \multicolumn{1}{c}{--} & $ 2.4001\times 10^{-06}$  & $-2.4001\times 10^{-06}$  & $-8.7265\times 10^{-12}$\\
$(2,1)$  & $0.35350$   & $ 5.2298\times 10^{-05}$     & $-1.0460\times 10^{-04}$     & $ 1.6462\times 10^{-09}$  & $-1.6462\times 10^{-09}$  & $-1.8014\times 10^{-14}$\\
$(2,-2)$ & $0.17686$   & $-7.2861\times 10^{-05}$     & $-7.2861\times 10^{-05}$     & $ 2.2935\times 10^{-09}$  & $-2.2935\times 10^{-09}$  & $ 1.1475\times 10^{-17}$\\
$(0,2)$  & $0.17683$   & $-9.9901\times 10^{-08}$     & \multicolumn{1}{c}{--} & $-3.1446\times 10^{-12}$  & $ 3.1446\times 10^{-12}$  & $ 1.1465\times 10^{-17}$\\
$(2,2)$  & $0.17679$   & $-3.4244\times 10^{-11}$     & $ 3.4244\times 10^{-11}$     & $-1.0779\times 10^{-15}$  & $ 1.0779\times 10^{-15}$  & $ 7.8652\times 10^{-21}$\\
\hline
\end{tabular}
\tablefoot{The coefficients of $M$ and $\Lambda$ are scaled by $\epsilon=-5.40548\times10^{15}~{\rm kg~m^2/s^2}$ and are given in seconds; those of the angles are not scaled and are given in radians.} 
\end{table}