  Minor planet 2002 VE68 was identified as a quasi-satellite of Venus shortly
after its discovery. At that time its data-arc span was only 24 days, now it is
2,947 days. Here we revisit the topic of the dynamical status of this
remarkable object as well as look into its dynamical past and explore its
future orbital evolution which is driven by close encounters with both the
Earth-Moon system and Mercury. In our calculations we use a Hermite integration
scheme, the most updated ephemerides and include the perturbations by the eight
major planets, the Moon and the three largest asteroids. We confirm that 2002
VE68 currently is a quasi-satellite of Venus and it has remained as such for at
least 7,000 yr after a close fly-by with the Earth. Prior to that encounter the
object may have already been co-orbital with Venus or moving in a classical,
non-resonant Near-Earth Object (NEO) orbit. The object drifted into the
quasi-satellite phase from an L4 Trojan state. We also confirm that, at
aphelion, dangerously close encounters with the Earth (under 0.002 AU, well
inside the Hill sphere) are possible. We find that 2002 VE68 will remain as a
quasi-satellite of Venus for about 500 yr more and its dynamical evolution is
controlled not only by the Earth, with a non-negligible contribution from the
Moon, but by Mercury as well. 2002 VE68 exhibits resonant (or near resonant)
behavior with Mercury, Venus and the Earth. Our calculations indicate that an
actual collision with the Earth during the next 10,000 yr is highly unlikely
but encounters as close as 0.04 AU occur with a periodicity of 8 years.
