Top-down view of photon and massive-particle geodesics near a Schwarzschild black hole — click anywhere to launch a trajectory.
Each trajectory is a numerically integrated Schwarzschild geodesic in the equatorial plane — the canonical 2D representation of orbital motion around a non-rotating black hole. The radial equation (dr/dλ)² = Ẽ² − V²eff(r) is advanced with 4th-order Runge–Kutta, with V²eff = (1−Rs/r)(1+L̃²/r²) for a massive particle and the rest-mass term dropped for a photon. Low impact parameter falls past the photon sphere (1.5 Rs) and is captured; high impact parameter deflects and escapes; intermediate values near the photon sphere orbit many times before deciding. Massive particles below the ISCO (3 Rs) plunge, and bound orbits above it precess — the same physics behind Mercury's perihelion shift and the black-hole shadow imaged by the Event Horizon Telescope.