Continuous black curves are obtained from the original solid angle Eq. (9), while the dashed red curves are from the polynomial approximation in Eq. (30). Different panels are for R = 3r_s and R = 5r_s and three different inclination angles, i = 30°, i = 60°, and i = 80°. The dotted blue line helps distinguishing trajectories without a turning point (i.e., 0 ≤ cosα ≤ 1) from those with a turning point (i.e., π/ 2 ≤ α ≤ α_max). The lower panels show the difference between the curves from the original and approximate equations. The dotted-dashed lines represent the difference between the curves from the original and Beloborodov (2002) equations.