  The distribution of angular momentum of planets and their host stars provides
important information on the formation and evolution of the planetary system.
However, mysteries still remain, partly due to bias and uncertainty of the
current observational datasets and partly due to the fact that theoretical
models for the formation and evolution of planetary systems are still
underdeveloped. In this study, we calculate the spin angular momenta of host
stars and the orbital angular momenta of their planets using data from the NASA
Exoplanet Archive, together with detailed analysis of observation dependent
biases and uncertainty ranges. We also analyze the angular momenta of the
planetary system as a function of star age to understand their variation in
different evolutionary stages. In addition, we use a population of planets from
theoretical model simulations to reexamine the observed patterns and compare
the simulated population with the observed samples to assess variations and
differences. We found the majority of exoplanets discovered thus far do not
have the angular momentum distribution similar to the planets in our Solar
System, though this could be due to the observation bias. When filtered by the
observational biases, the model simulated angular momentum distributions are
comparable to the observed pattern in general. However, the differences between
the observation and model simulation in the parameter (angular momentum) space
provide more rigorous constraints and insights on the issues that needed future
improvement.
