Top-down view of a non-rotating black hole: a test mass on a precessing orbit, the effective potential it moves in, and light rays bending around the photon sphere. Radii are in Schwarzschild radii r_s.
The science
Scales. The Schwarzschild radius is r_s = 2GM/c^2 (2.95 km per solar mass). The photon sphere sits at 1.5 r_s and the innermost stable circular orbit (ISCO) at 3 r_s.
Orbits. In units G = c = 1 and lengths in GM/c^2, with u = 1/r, a test mass obeys u'' + u = 1/h^2 + 3u^2 (derivative with respect to the orbital angle). The extra 3u^2 term makes the periapsis advance by about 6 pi GM / (c^2 a (1 - e^2)) per orbit; the radial motion is governed by the effective potential V(r) = (1 - 2/r)(1 + h^2/r^2) compared with E^2.
Light. Photons follow u'' + u = 3u^2. Far from the hole the deflection is 4GM/(c^2 b); rays with impact parameter below b_c = (3 sqrt 3 / 2) r_s are captured.
Simplifications. Non-rotating hole, test particle (no gravitational radiation), no accretion disk, schematic scale. The 3D page shows the disk; this view shows the geodesics.