Mars Aerobraking Lab (2D)

Presets

Live readouts

Graphs

Apoapsis altitude vs pass number

Periapsis altitude vs pass number

Peak heat flux per pass

Numerical checks

running...

How to use

Press a preset, then watch the apoapsis graph fall as the passes accumulate. Time warp near periapsis slows automatically so you can see the drag pass.
With Periapsis maintenance burns on the periapsis stays in the heat-flux corridor; switch it off and the first deep pass shows how fast the heating climbs.
Try Too deep (heat spike), Too shallow (almost no braking) and Dust storm (density scatter pass to pass).
Drag area and mass set the ballistic coefficient: more area per kilogram means fewer passes.
The buttons switch the main view between the whole orbit and the periapsis pass. Space pauses, R resets.

The science

An orbiter captured at Mars by a small burn ends up in a long ellipse (about 34 h here). Pushing it into the science orbit with the engine would cost over a kilometre per second of propellant. Aerobraking uses the thin upper atmosphere instead: on every periapsis pass drag removes a little orbital energy, so the apoapsis comes down while the periapsis hardly moves.

a_drag = −½ ρ(h) (C_dA/m) |v_rel| v_rel, ρ(h) = ρ₁₀₀ exp(−(h−100 km)/H), v_rel = v − Ω × r

The page integrates the planar two-body problem (μ = 42828 km³/s²) plus this drag with a fourth-order Runge-Kutta step that shrinks to one second near periapsis. Near periapsis the path is a shallow parabola in altitude, so the density integral along the pass has a closed form (Laplace's method):

∫ ρ ds ≈ ρ_p √(2π H v_p² / r¨), r¨ = v_p²/r_p − μ/r_p², ΔE = −½ (C_dA/m) v_p² ∫ ρ ds

The energy change per pass sets the new semi-major axis, a = −μ/2E, and so the whole campaign: the apoapsis altitude falls roughly exponentially with the pass number, and the number of passes scales with the ballistic coefficient m/(C_dA).

The corridor. Too deep and the heat flux q = ½ ρ v³ (free-molecular, full accommodation) and the dynamic pressure ½ ρ v² exceed what the panels and structure tolerate; too shallow and the campaign takes years. The corridor altitude is where q equals your limit; with maintenance burns on, the spacecraft makes a small tangential burn at each apoapsis to put the periapsis back into the corridor despite density swings (the orbit-to-orbit variability slider, which is a pseudo-random factor drawn once per pass).

Simplifications. Planar orbit, no lift, constant C_d, exponential atmosphere with a single scale height and no winds, no Mars J2 or third-body perturbations, and the stylised heating law; the Mars surface texture is procedural. Real missions fly a periapsis table updated from measured drag after every pass. Numbers are of the right order for a 2 t orbiter, but this is a teaching model, not a mission design tool. In-page checks: Kepler period and energy conservation with drag off; per-pass energy loss at three periapsis altitudes against the closed form; the peak heat flux of a pass flown at the solved corridor; and eight passes of the analytic map against the integrated apoapsis.