A capsule meets the top of the atmosphere at eleven or twelve kilometres a second. It cannot slow down by itself, so it lets the air do it: a shock wave stands just in front of the blunt heat shield, the air behind it becomes plasma, and most of the energy goes into that air instead of the capsule. What reaches the shield still makes it glow. Here the flight is computed second by second from the entry speed and angle, and the light on the stage follows the computed heating.
Changing a slider makes it your own entry and recomputes the whole flight. Lift is steered to stop the capsule climbing back out; set lift ÷ drag to 0 for a purely ballistic fall. Sound starts only when you press Sound.
The flight. The capsule is a point mass over a round, non-rotating Earth. From the entry interface at 122 km, the page integrates speed, flight-path angle and altitude with fourth-order Runge–Kutta steps of a tenth of a second: drag ρv²/(2β) per unit mass, where β = m/(CDA) is the ballistic coefficient, lift as a fraction of drag, and gravity falling off with height. Lift points up while the capsule descends and is rolled towards down as its path flattens and starts to climb, which stops it from skipping back out: a crude stand-in for Apollo's guidance, which steered the lift by rolling the capsule. Air density comes from the US Standard Atmosphere 1976 up to 86 km and its tabulated values above (5.6 × 10⁻⁷ kg/m³ at 100 km, 2.2 × 10⁻⁸ at 120 km). The flight ends at 15 km, roughly where parachutes take over, or when the capsule skips back out.
Heating. The heat flux at the nose is Sutton and Graves' stagnation-point formula q = k·√(ρ/rn)·v³ with k = 1.7415 × 10⁻⁴ for air, as in the guide. It is convective heating only: above about 10 km/s the hot gas also radiates onto the shield, which this does not include. The guide's check: Apollo 11's measured peak was 3.2 MW/m² with 301 MJ/m² absorbed over the entry.
Glow. If the surface had to get rid of all the incoming heat by radiating it, its temperature would be T = (q/εσ)1/4 with emissivity ε = 0.85. The shield's colour on the stage is the colour of a black body at that temperature, computed from Planck's law and the CIE 1931 colour-matching functions and converted to screen colour. A real ablator runs cooler than this, because the charring and vaporising material carries heat away; that is why it works.
The shock. The bow shock's distance in front of the nose and its curved shape come from Billig's correlations for blunt bodies: standoff Δ/R = 0.143·e3.24/M², a hyperbola whose far branches approach the Mach angle. In reality the hot, dissociated air behind the shock is denser than an ideal gas would be and the shock sits closer, so this is an upper estimate. The plasma's light and the wake of sparks are drawn, scaled by the computed heating; they are not a spectrum.
A study in long cycles and slow light: one object, one event lasting minutes, a colour that rises to white and falls back to red. It recreates no specific work.