---------------- ---------------- --
             Sun             Moon             test particle    
                                              close to $L_5$   
                                              (RTBP)           
  $x_0$      368.666440265   -0.51661666298   -0.91418201074   
  $y_0$      -47.600836868   -0.75733769053   0.06873430889    
  $v_{x0}$   0.93068574512   0.1853827247     -0.02527332186   
  $v_{y0}$   6.40398916643   -0.13621388441   -0.22865309127   
  ---------- --------------- ---------------- ---------------- --

  :  The initial geocentric conditions of the Sun, Moon, and test particle taken from the JPL database. For units, see text.

\[table:epoch\]

In order to monitor the finite time chaotic behaviour and escape dynamics, we place a large number ($\mathrm{9\times10^4}$ to $\mathrm{1\times10^6}$) of particles around the $L_5$ point in the RFBP, see rectangle in Fig. \[fig:coosys\]. All particles start with the same velocity ($v_{x0},\;v_{y0}$) which is equal to the velocity of the $L_5$ point in the circular RTBP.

As is mentioned in Section 1, we want to keep a test particle in a pre-defined region of configuration space using a suitably designed chaos control method. Most of the available chaos control methods, either feedback or delayed, use the fact that there is an accessible system parameter that can be adjusted. However, in our particular problem there are no such parameters. One can only vary the system states, for example the velocity of the spacecraft, during the motion. Therefore, we briefly summarize the basic idea of the two chaos 