We expand notes on Keplerian orbits of binary stars and derive equations of motion for radial velocity and astrometric observations. We primarily follow the right-handed formalism of Murray and Correia, we modify some derivation steps to carefully respect common conventions in the visual binary field, namely that the ascending node is where the secondary crosses the plane of the sky moving away from the observer. We also derive equations for the relative inclination of the stellar orbit and an orbiting circumbinary disk.