Venus do not appear to be the cause of 2002 VE$_{68}$ entering or leaving the quasi-satellite phase. However, in the cases of both Mercury and the Earth, the distance of closest approach becomes relatively (Mercury) or dangerously close (Earth) to the value of the Hill sphere radius for the respective planet. The Hill sphere radius, $r_H$, is the limiting radius for orbits of planetary satellites in the presence of the Sun’s gravitational field and it is given by: $r_H \approx a (1 - e) (m/(3 M_{\odot}))^{1/3}$, where $a$ is the semi-major axis of the planet, $e$ is the eccentricity of its orbit, $m$ is the mass of the planet and $M_{\odot}$ is the mass of the Sun (Hamilton & Burns 1992). For Mercury, the Hill radius is 0.0012 AU and the closest approach is nearly 0.004 AU (although encounters as close as 0.003 AU are observed in our calculations) but for the Earth, the Hill radius is 0.0098 AU and the closest approaches are at 0.002 AU (0.0018 AU, 9,300 yr from now).

The object is injected into the quasi-satellite dynamical state after a close encounter with the Earth at about 0.007 AU, 11,000 yr ago (not shown in Fig. 