energy balance relative to the host planet involved in the various resonant transitions, in Fig. \[energy\] we show the total energy (specific orbital energy) of 2002 VE$_{68}$ relative to Venus. The quasi-satellite dynamical state, even if not bound (the total relative energy is still $>$ 0), is significantly less energetic than the other resonant states (Trojan or any other). If, during the quasi-satellite phase the object suffers any significant decceleration as a result of, for example, drag or a distant interaction with another body (perhaps a pre-existing natural satellite) or ejection of one of the components in a binary asteroid, the object (or one of the components of a hypothetical binary system) may be permanently trapped in a retrograde orbit around the host planet. With no natural satellites, this scenario is unlikely to work for Venus or Mercury (unless the incoming asteroid is a binary) but it may be valid in other cases.

The relatively long-term quasi-satellite dynamical state of 2002 VE$_{68}$ has been further confirmed using control orbits obtained from the nominal orbit by varying the orbital elements within the error range of the observed object (see Table \[elements\]). All the control orbits exhibit consistent behaviour in the time 