\begin{table}%t3
    \caption{\label{phys_par}The physical parameters of $\psi$ Cen 
    obtained using either the first or
    the final solution for the orbital parameters.}
\par
    %\centering
\par
    \small\begin{tabular}{c c c c c}
    \hline
    \hline\noalign{\smallskip}
    Parameters & First values & Errors & Final values & Errors\\
    \hline
    $a_1$ & $31.187$ & $0.059$~$R_{\rm sun}$ & $31.293$ & $0.075$~$R_{\rm sun}$\\
    $a_2$ & $51.393$ & $0.306$~$R_{\rm sun}$ & $51.030$ & $0.114$~$R_{\rm sun}$\\
    Total~mass & $5.022$ & $0.056$~$M_{\rm sun}$ & $4.975$ & $0.025$~$M_{\rm sun}$\\
    Mass~ratio & $1.648$ & $0.010$ & $1.631$ & $0.005$\\
    $M_1$ & $3.126$ & $0.042$~$M_{\rm sun}$ & $3.084$ & $0.016$~$M_{\rm sun}$\\
    $M_2$ & $1.897$ & $0.067$~$M_{\rm sun}$ & $1.891$ & $0.030$~$M_{\rm sun}$\\
    $R_1$ & $3.632$ & $0.014$~$R_{\rm sun}$ & $3.621$ & $0.007$~$R_{\rm sun}$\\
    $R_2$ & $1.807$ & $0.007$~$R_{\rm sun}$ & $1.804$ & $0.004$~$R_{\rm sun}$\\
    $\log{g_1}$ & $3.815$ & $0.006$ & $3.811$ & $0.003$\\
    $\log{g_2}$ & $4.204$ & $0.016$ & $4.206$ & $0.007$\\
    \hline
    \end{tabular}\vspace*{5mm}
    \end{table}