  This paper explores the evolutionary behavior of the Earth-satellite binary
system within the framework of the ghost-free parity-violating gravity and the
corresponding discussion on the parity-violating effect from the laser-ranged
satellites. For this purpose, we start our study with the Parameterized
Post-Newtonian (PPN) metric of this gravity theory to study the orbital
evolution of the satellites in which the spatial-time sector of the spacetime
is modified due to the parity violation. With this modified PPN metric, we
calculate the effects of the parity-violating sector of metrics on the time
evolution of the orbital elements for an Earth-satellite binary system. We find
that among the five orbital elements, the parity violation has no effect on the
semi-latus rectum, while the eccentricity and ascending node are affected only
in a periodic manner. These three orbital elements are the same as the results
of general relativity and are also consistent with the observations of the
present experiment. In particular, parity violation produces non-zero
corrections to the eccentricity and pericenter, which will accumulate with the
evolution of time, indicating that the parity violation of gravity produces
observable secular effects. The observational constraint on the
parity-violating effect is derived by confronting the theoretical prediction
with the observation by the LAGEOS II pericenter advance, giving a constraint
on the parity-violating parameter space from the satellite experiments.
