  Asteroids having perihelion distance $q$ $<$ 1.3 AU are classified as
near-Earth objects (NEOs), which are divided into different sub-groups:
Vatira-class, Atira-class, Aten-class, Apollo-class, and Amor-class. 2020
$AV_2$, the first Vatira (Orbiting totally inside Venus' orbit) was discovered
by the Twilight project of the Zwicky Transient Facility (ZTF) on January 4,
2020. Upon the discovery of 2020 $AV_2$, a couple of orbital studies of the
short-term orbital evolution of 2020 $AV_2$ have been performed and published
(e.g. de la Fuente Marcos & de la Fuente Marcos 2020; Greenstreet 2020). In
this present work, we performed an assessment of the long-term orbital
evolution of known near-Earth objects and known Atiras under the Yarkovsky
effect by using the \textit{Mercury6} N-body code. We considered not only
planetary gravitational perturbation but also the non-gravitational Yarkovsky
effect. Our calculation shows that the NEOs have generally two dynamical
populations, one short-lived and the other long-lived. From our calculation,
the transfer probabilities of Atira-class asteroids to Vatira-class asteroids
for the first transition are $\sim$13.1 $\pm$ 0.400, $\sim$13.05 $\pm$ 0.005,
and $\sim$ 13.25 $\pm$ 0.450 $\%$ for different values of the Yarkovsky force
(i.e. obliquity of 0, 90, and 180 deg.), respectively. It suggests that the
radiation force may play some role in the long-term evolution of this asteroid
population. Finally, our statistical study implicates that there should be 8.14
$\pm$ 0.133 Atira-class asteroids and 1.05 $\pm$ 0.075 Vatira-asteroids of the
S-type taxonomy.
