Comet Atmospheric Passage: Drag, Ablation and Airburst Profile (2D)

Presets

Live readouts

Graphs

Speed against altitude

Deceleration against altitude

Energy deposited per kilometre of altitude

Numerical checks

running...

How to use

Choose a preset or set diameter, density, strength, speed and angle. The side view shows the trajectory through the atmosphere, coloured by ram pressure; the three graphs mark the current point. Try: (1) the Stony airburst preset and read the main energy release height; (2) switch off breakup and watch the same body reach much lower; (3) a 1 cm grain: it vanishes near 90 km; (4) raise the entry angle and see the energy release move down; (5) press Reset (or R) to replay. Space pauses.

The science

Equations of entry. A body of mass m, speed v and flight-path angle γ below the horizontal, at height h, in an exponential atmosphere ρ_a = ρ₀ e^-h/H (ρ₀ = 1.225 kg/m³, H = 7.16 km) obeys

m dv/dt = -(1/2) C_D ρ_a A v² + m g sinγ, dγ/dt = -(g/v) cosγ + (v/(R_E+h)) cosγ, dh/dt = -v sinγ dm/dt = -C_H ρ_a A v³ / (2Q) (heat of ablation Q, heat-transfer coefficient C_H)

Gravity is g = 9.81 (R_E/(R_E+h))² m/s² and the Earth is curved, so a shallow trajectory bends upward in the flat-earth picture. The code integrates these with a fourth-order Runge-Kutta scheme.

Ballistic limit (Allen-Eggers). With constant area, no ablation, no gravity and a straight path, the speed has the closed form

v(h) = v₀ exp[ -(ρ₀ H / (2 β sinγ)) (e^-h/H - e^-h₀/H) ], β = m / (C_D A)

and the maximum deceleration occurs where ρ_a(h*) = β sinγ / H, i.e. h* = H ln(ρ₀ H / (β sinγ)). Heavy compact bodies (large β) pass this height lower down or reach the ground; light or weak ones are stopped high up.

Breakup and the pancake model. When the ram pressure ρ_a v² exceeds the strength σ, the body is assumed to break into a cloud of fragments that spreads at dr/dt = v √(ρ_a/ρ_m). The frontal area grows as π r², the drag soars, and most of the kinetic energy is released in a short altitude range: an airburst. Energy deposition per kilometre is taken from the kinetic energy lost in each 1 km altitude bin and is quoted in kilotons of TNT (1 kt = 4.184 TJ).

Checks (run in the page). (1) the numerical speed at 60 km against the Allen-Eggers closed form; (2) the altitude of maximum deceleration against H ln(ρ₀ H /(β sinγ)); (3) convergence of the full model with halved time step; (4) energy conservation of the equations in vacuum; (5) ablated mass against the integral of C_H ρ_a A v³/(2Q).

Simplifications. A single intact body or a single pancaking cloud (no discrete fragments, no wake shielding, no rotation or lift); constant C_D and C_H (real values change with Mach and Knudsen number at high altitude); an isothermal exponential atmosphere; kinetic energy lost is counted as deposited even though a part leaves as light and a part heats the body. The presets are of the right order for well-known events, not fits to them. Educational physics only: inanimate rock and ice, no damage or casualty modelling.