numerical integration of the entire solar system thanks to the use of a block-step scheme (Aarseth 2003) in which suitably quantized time-steps enable following the orbits of Mercury or planetary satellites and trans-Neptunian objects simultaneously. The standard versions of these scalar $N$-body codes are publicly available from the IoA web site[^5]. These versions have been modified in order to study the orbital evolution of 2002 VE$_{68}$.

For accurate initial positions and velocities we used the Heliocentric ecliptic Keplerian elements provided by the JPL[^6] and initial positions and velocities based on the DE405 planetary orbital ephemerides (Standish 1998)[^7] referred to the barycentre of the Solar System. Orbits are calculated forward and backward in time. Our reference calculations include the perturbations by eight major planets (Mercury to Neptune) and treat the Earth and the Moon as a single object. As a zeroth order approximation, the Earth and the Moon can be replaced with a ficticious body at their barycentre but, in relative terms, the Moon is the largest satellite in the Solar System and, among satellites, it has one of the largest semi-major axes. Therefore, a better approximation is to resolve the Earth and the Moon as two separate bodies and assume 