Galileo's Gravitational Free Fall — 3D Lab Simulation
All bodies accelerate identically under gravity in vacuum
Theoretical Foundation & Historical Context
Overturning 2,000 years of Aristotelian physics, Galileo proved that in the absence of aerodynamic drag, all objects fall with identical gravitational acceleration regardless of their mass.
Law: Law of Free Fall & Universal Gravitational Acceleration | Scientist: Galileo Galilei | Year: 1589
Key Learning Objectives & Competencies
- ✓ Demonstrate empirically that all objects experience identical gravitational acceleration (g ≈ 9.81 m/s²) in vacuum regardless of mass.
- ✓ Derive and apply constant acceleration kinematics: v(t) = gt and y(t) = 0.5·g·t².
- ✓ Analyze fluid drag dynamics and terminal velocity when falling through atmospheric gas.
Mathematical Formulations & Differential Equations
y(t) = ½ · g · t²
Fall duration: t = √(2h / g)
F_d = ½ · ρ · C_d · A · v²
Quadratic drag dependent on area and velocity
v_t = √( (2·m·g) / (ρ·C_d·A) )
Reached when drag exactly balances gravity
Physical Parameters & Units of Measurement
| Symbol | Physical Quantity | SI Unit | Default |
|---|---|---|---|
| g | Gravitational acceleration (m/s²) | — | — |
| ρ | Fluid density (kg/m³) | — | — |
| C_d | Drag coefficient | — | — |
| m | Mass of falling body (kg) | — | — |
Real-World & Industrial Engineering Applications
Orbital mechanics, spacecraft re-entry trajectory analysis, and planetary landing descent.
Parachute aerodynamic design and terminal velocity safety protocols for skydiving and cargo airdrop.
Geophysical gravimetry for mineral prospecting and underground aquifer mass detection.
3-Step Controlled Experimental Protocol
- Step 1: Baseline Setup — Initialize the simulation in standard conditions and observe undisturbed system dynamics.
- Step 2: Parameter Variation — Gradually modulate physical parameters using the control panel sliders.
- Step 3: Verification & Phase Space Analysis — Compare phase space trajectories and conservation metrics against analytical ODE solutions.
Frequently Asked Questions (FAQ)
Why do a hammer and a feather hit the ground together on the Moon?
The Moon lacks an atmosphere, creating a near-perfect vacuum. Without air resistance, only lunar gravity acts on both objects, imparting the exact same acceleration (g_moon ≈ 1.62 m/s²) as Apollo 15 astronaut David Scott demonstrated.
Does gravitational acceleration vary across different locations on Earth?
Yes, g varies from ~9.78 m/s² at the equator to ~9.83 m/s² at the poles due to Earth's equatorial bulge (centrifugal force from planetary rotation) and closer distance to Earth's center at the poles.
What defines the terminal velocity of a falling skydiver?
Terminal velocity occurs when the upward aerodynamic drag force equals the downward weight force (F_drag = mg), resulting in zero net acceleration and constant fall speed (~55 m/s in belly-to-earth posture).
Related Simulations & Experiments
Interactive Simulation: Interactive real-time 60 FPS WebGL simulation is active in your browser. Rotate, zoom, and inspect physical apparatus components with full camera freedom.