Module: 1 (Foundations)
Concepts: Newton's Laws, Numerical Integration, Atmospheric Physics
| Concept | Application |
|---|---|
| Newton's 2nd Law | How F=ma governs rocket acceleration |
| Drag Equation | Why rockets experience Max Q |
| Gravity Variation | g decreases with altitude (1/r²) |
| Mass Depletion | Why rockets accelerate faster as fuel burns |
| RK4 Integration | Industry-standard numerical method for trajectories |
This physics-based simulation models a multi-stage rocket ascent, accounting for:
- Variable Gravity: g decreases with altitude (inverse-square law)
- Atmospheric Drag: Air density decreases exponentially
- Mass Depletion: Rocket accelerates as fuel burns (F=ma)
- Thrust Vectoring: Gravity turn maneuver for orbit insertion
| Agency | Vehicle | Similar Physics |
|---|---|---|
| SpaceX | Falcon 9 | Max Q throttling, booster recovery |
| NASA | SLS | Gravity turn to orbit, staging events |
| ESA | Ariane 6 | Atmospheric drag modeling |
| JAXA | H3 | Trajectory optimization |
pip install -r requirements.txt
python simulation.pyThe simulator provides an interactive dashboard with:
- Overview: Key flight metrics at a glance
- Altitude: Height vs time with apogee marker
- Velocity: Speed profile including Max Q
- Max Q: Dynamic pressure analysis
- 3D Path: Spatial trajectory visualization
The rocket experiences three main forces:
- Thrust: ( F_{thrust} = \dot{m} \cdot v_{exhaust} )
- Gravity: ( F_g = \frac{G M m}{r^2} )
- Drag: ( F_d = \frac{1}{2} \rho v^2 C_d A )
Runge-Kutta 4 provides 4th-order accuracy by sampling slopes at:
- Beginning of timestep (k1)
- Midpoint using k1 (k2)
- Midpoint using k2 (k3)
- End using k3 (k4)
Final estimate: weighted average with 1/6, 2/6, 2/6, 1/6 weights.
The simulation tracks 7 variables:
[Position_X, Position_Y, Position_Z, Velocity_X, Velocity_Y, Velocity_Z, Mass]
See EXPLANATION.md for detailed physics derivations.