control orbits are very close to those of the nominal orbit shown in Figs. \[qs\] and \[mld\]. Mikkola et al. (2004) already pointed out that the orbit of 2002 VE$_{68}$ is quite chaotic. Chaotic orbits are not only sensitive to changes in the initial conditions but also to different dynamical models. Starting from the initial conditions described above, we integrate the orbits up to 20,000 yr in both directions of time although only the time interval (-10,000, 10,000) yr will be displayed in our figures. The output time-step (time resolution) in all the figures is 0.01 yr (3.65 days) and no filtering or smoothing has been applied to the data. Again, this output frequency is not expected to introduce any aliasing in our results. Our calculations do not include any modeling of the Yarkovsky and YORP effects (see, e.g., Bottke et al. 2006).

0.10truecm

  --------------------------------------- --- ------------------------------------
           Semi-major axis, $a$            =    0.7236659191$\pm$0.0000000005 AU
             Eccentricity, $e$             =       0.41035660$\pm$0.00000005
             Inclination, $i$              =    9.005869$\pm$0.000013 $^{\circ}$
   Longitude of ascending node, $\Omega$   =   231.584442$\pm$0.000005 $^{\circ}$
     Argument of perihelion, $\omega$      =   355.463207$\pm$0.000014 $^{\circ}$
             Mean anomaly, $M$             =    202.88183$\pm$0.00003 $^{\circ}$
  --------------------------------------- --- ------------------------------------

  : Heliocentric orbital elements of 2002 VE$_{68}$ used in this research. (Epoch = JD2456200.5, 