Rocket Launch Plume: Ascent Dynamics & Nozzle Expansion (2D)

This 2D companion replaces the 3D version's orbiting smoke render with the physics that actually shapes a rocket's exhaust plume: a real variable-mass ascent equation (thrust, weight, drag) drives the flight while a live nozzle-pressure-ratio (Pe / ambient pressure) readout classifies the plume as under-, over- or perfectly expanded and updates a schematic exhaust drawing to match — so the widening plume everyone recognizes from launch footage is shown as a direct, computed consequence of falling atmospheric pressure with altitude rather than a fixed decorative particle effect.