Introduction

This simulation models the launch of the Saturn V rocket, the vehicle used during NASA's Apollo missions to the Moon. It visualizes the rocket's ascent, stage separation, and trajectory using simplified physics. The simulation tracks key parameters such as:

• Altitude (distance from Earth's surface)
• Velocity (total, horizontal, and vertical components)
• Pitch angle (gravity turn maneuver)
• Mass (including stage separation)
• Thrust and acceleration

Graphical elements include a dynamic canvas showing the rocket, Earth curvature, clouds, and stars, along with real-time charts for velocity, altitude, and pitch angle. Controls allow users to start, pause, reset, and adjust simulation speed.

Physics Model

• Stages: Three Saturn V stages with specified burn times, thrust, initial and final masses, and specific impulses (ISP).
• Gravity: Varies with altitude using the inverse square law.
• Drag: Simplified atmospheric drag is applied based on altitude-dependent air density.
• Gravity Turn: Pitch angle is adjusted to simulate the gravity turn maneuver for orbit insertion.
• Centripetal effects: Basic approximation included in vertical acceleration calculation.

Limitations

• Simplified Aerodynamics: Drag modeled with constant cross-sectional area and fixed coefficient; real aerodynamics are more complex.
• Gravity Turn Approximation: Simplified formula may cause unrealistic trajectories at high horizontal velocities.
• Stage Modeling: Constant thrust and mass flow; real engines vary slightly in throttle and timing.
• No Orbital Perturbations: Neglects Earth's rotation, Moon/Sun gravitation, and detailed orbital mechanics.
• Instantaneous Altitude: Shows altitude above Earth’s surface, not apoapsis or periapsis for interplanetary trajectories.
• No Fuel Slosh or Thermal Effects: Internal fuel dynamics, structural bending, and thermal stresses are not included.
• Retro-Focused Visualization: Canvas graphics prioritize visual effect over strict scientific accuracy.

Summary

This simulation provides a visually engaging, physics-informed approximation of the Saturn V launch, suitable for educational and demonstration purposes. While it captures the general behavior of multi-stage ascent and gravity turn maneuvers, it does not replace detailed orbital mechanics or NASA mission planning software.