On the dynamical evolution of 2002 VE68
  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. 
C. de la Fuente Marcos and R. de la Fuente Marcos
astro-ph.EP