  With the discovery of now more than 500 exoplanets, we present a statistical
analysis of the planetary orbital periods and their relationship to the
rotation periods of their parent stars. We test whether the structure of
planetary orbits, i.e. planetary angular momentum and orbital periods are
'quantized' in integer or half-integer multiples with respect to the parent
stars' rotation period. The Solar System is first shown to exhibit quantized
planetary orbits that correlate with the Sun's rotation period. The analysis is
then expanded over 443 exoplanets to statistically validate this quantization
and its association with stellar rotation. The results imply that the
exoplanetary orbital periods are highly correlated with the parent star's
rotation periods and follow a discrete half-integer relationship with orbital
ranks n=0.5, 1.0, 1.5, 2.0, 2.5, etc. The probability of obtaining these
results by pure chance is p<0.024. We discuss various mechanisms that could
justify this planetary quantization, such as the hybrid gravitational
instability models of planet formation, along with possible physical mechanisms
such as inner discs magnetospheric truncation, tidal dissipation, and resonance
trapping. In conclusion, we statistically demonstrate that a quantized orbital
structure should emerge naturally from the formation processes of planetary
systems and that this orbital quantization is highly dependent on the parent
stars rotation periods.
