Venus and the Earth.

On the other hand and after the object leaves its quasi-satellite path, it undergoes multiple transitions between resonant states (see Fig. \[mld3\]). This significant complexity is the result of having high eccentricity and inclination, in this case compound orbits are possible (Namouni 1999; Namouni, Christou & Murray 1999). When moving in a 1:1 mean motion resonance, changes in the values of the semi-major axis, the eccentricity and the inclination are small compared to the variation of the argument of perihelion. Transfers between quasi-satellite, horseshoe and tadpole orbits are the result of the libration of the nodes (Wiegert, Innanen & Mikkola 1998). The argument of perihelion of 2002 VE$_{68}$ is displayed in Fig. \[w\]. During the quasi-satellite phase, its value decreases at a rate of $\dot{\omega} = -0.0005^{\circ}$/yr. This secular change in the value of the argument of perihelion was predicted by Namouni (1999) on theoretical grounds and can be used to precisely track transitions between the quasi-satellite state and any other. Based on the precession of the argument of perihelion criterion and for Model 3, the object enters the quasi-satellite phase at about -14,000 yr and it leaves the phase 555 yr from now.

Regarding the 