Analytic observation of a star orbiting a Schwarzschild black hole

A star orbiting a Schwarzschild black hole can be used as a toy model for an educational study of the relativistic effects like bending of light, geodesic precession, and frequency shift. Additionally, the finiteness of the speed of light plays a crucial role for the visual appearance of the star. We will develop an analytic method to show the difference between the actual and the apparent position of the star depending on the observation time and the observer’s inclination to the orbital plane.