Galileo's Revolutionary Insight
Before Galileo Galilei (1564–1642), it was widely believed (following Aristotle) that heavier objects fall faster than lighter ones. Galileo, reportedly through experiments at the Leaning Tower of Pisa, demonstrated that in the absence of air resistance, all objects fall at the same rate regardless of their mass. This was a profound departure from 2,000 years of accepted wisdom and laid the groundwork for Newtonian mechanics.
Newton's Law of Gravitation
Isaac Newton formalized free fall with his law of universal gravitation: the force on any object near Earth's surface is F = mg, where m is mass and g is gravitational acceleration (≈9.807 m/s² at sea level). Because acceleration = F/m = mg/m = g, the acceleration is independent of mass. This is why a feather and a hammer fall at the same rate in a vacuum — famously demonstrated by Apollo 15 astronaut David Scott on the Moon in 1971.
The Equations of Motion
Free fall follows the SUVAT kinematic equations with constant acceleration g. The three most useful for free fall are: (1) v = u + gt, which gives velocity at any time t; (2) h = ut + ½gt², which gives height fallen; and (3) v² = u² + 2gh, which directly relates velocity to height without needing time. When initial velocity u = 0, these simplify to v = gt and h = ½gt².
Air Resistance and Terminal Velocity
Real-world free fall includes air resistance (drag force), which is proportional to velocity squared: F_drag = ½ρC_dAv², where ρ is air density (1.225 kg/m³ at sea level), C_d is the drag coefficient, A is cross-sectional area, and v is velocity. Terminal velocity occurs when drag equals gravitational force: v_t = √(2mg / ρC_dA). A typical skydiver in spread-eagle position (C_d ≈ 1.0, A ≈ 0.7 m²) reaches terminal velocity of about 55 m/s (195 km/h). In a head-down dive position, this increases to ~90 m/s (320 km/h).
Gravity on Other Worlds
Gravitational acceleration varies across the solar system. On the Moon (g = 1.62 m/s²), objects fall about 2.46 times slower than on Earth — a fall from 1 meter takes 1.11 seconds instead of 0.45. Mars (g = 3.72 m/s²) sits between the two. Jupiter, despite being a gas giant with no solid surface, has a surface gravity of 24.79 m/s² — 2.53 times Earth's. At the Sun's surface (g = 274 m/s²), a 1-meter fall takes just 0.085 seconds and reaches 23.3 m/s.
Projectile Motion
When an object is launched horizontally, its motion can be decomposed into independent horizontal (constant velocity) and vertical (free fall) components. The time of flight is determined entirely by the vertical component: t = √(2h/g) for horizontal launch. The horizontal range is then simply R = v_h × t. When launched at an angle θ, the initial velocity splits into v_x = v·cos(θ) and v_y = v·sin(θ), and the flight time comes from solving h + v_y·t − ½g·t² = 0. This independence of horizontal and vertical motion explains why a bullet fired horizontally hits the ground at the same time as one dropped from the same height.