  We determine three invariants: Arnold's $J^+$-invariant as well as
$\mathcal{J}_1$ and $\mathcal{J}_2$ invariants, which were introduced by
Cieliebak-Frauenfelder-van Koert, of periodic orbits of the second kind near
the heavier primary in the restricted three-body problem, provided that the
mass ratio is sufficiently small.
