\begin{table}%t6
\par
\caption{Number of single- and multiple-planet systems detected and measured by Gaia as a 
   function of $\sigma_\psi$.
\label{sigdegrad}}
%\centerline
 {
   \begin{tabular}{rrrrrrr}
       \hline\hline\noalign{\smallskip}
       $\sigma_\psi$$^a$ ($\mu$as)& 
       $N_\star$$^b$ & 
       $N_{\rm d}$$^c$ &  
       $N_{\rm m}$$^d$ & 
       $N_{\rm d,~mult}$$^e$ &  
       $N_{\rm m,~mult}$$^f$ & 
       $N_{\rm copl}$$^g$\\
              \noalign{\smallskip}
       \hline
       \noalign{\smallskip}
       8    &   500~000 &   8000  &  4000  &  1000  &   500   &  159   \\
      12    &   148~148 &   2370  &  1185  &   296  &   148   &   47   \\
      16    &   62~500  &  1000   &  500   &  125   &   62    &  19    \\
      24    &   18~519  &   296   &  148   &   37   &   18    &   5    \\
      40    &   4000   &   64    &  32    &   8    &   4     &  1     \\
      80    &   500    &   8     &  4     &  1     &  0      & 0      \\
     \hline\noalign{\smallskip}
   \end{tabular}}
\par
   \smallskip
   $^a$ {Single-measurement precision.}\\
   $^b$ {Number of stars within the 
   useful distance, assumed to scale with the cube of the radius (in pc) of a 
   sphere centered around the Sun.}\\
  $^c$ {Number of single-planet systems detected.}\\
  $^d$~{Number of single-planet 
       systems whose astrometric orbits are measured to better than 15\% accuracy.}\\
   $^e$  {Number of multiple-planet systems detected.}\\
   $^f$  {Number of multiple-planet systems with orbits 
       measured to better than 15--20\% accuracy.}\\
   $^g$  {Number of multiple-planet systems for which successful 
   coplanarity tests (with $i_{\rm rel}$ known to better than $10{\degr}$ accuracy) 
   can be carried out.}
\end{table}