Physics · gravitation

Galileo Drop Experiment

Race two falling objects, from a desk edge to a 300 m tower — with the free-fall equations shown beside the simulated result.
quadratic drag · RK4
Hammer vs Feather · Earth (air)

Objects

Environment

0.3 m to 300 m — logarithmic, so desk height and tower height are both reachable.

Recreate a real drop

Live drop

Earth (air) t = 0.00 s
speed
Result
Detail
The arithmetic

What the textbook says, and what actually happens

vacuum theory vs simulated fall

In a vacuum every object falls identically and two equations settle it. Add air and neither holds — but they remain the right starting point, and the gap between them and the simulation is the effect of drag.

Field notes

Why mass doesn't matter (until air does)

How it works

Gravity pulls equally; air pushes back unequally

Gravity accelerates every object at the same rate regardless of mass — that's the whole point of Galileo's (probably apocryphal) Pisa experiment and Apollo 15's very real one. What actually makes a feather fall slower than a hammer is air resistance, and air resistance depends on shape and mass in a way gravity doesn't: it scales with cross-sectional area, but the object's inertia (its resistance to being slowed down) scales with mass. A feather has enormous area for its tiny mass, so drag dominates almost immediately; a hammer has so much mass relative to its area that drag barely matters over a short drop.

Worked example

Drop a hammer and a feather together from 1.6 m in ordinary air and the hammer lands first, roughly 0.4 seconds sooner in this model. Remove the air — either on the Moon, like Apollo 15 actually did, or in an Earth vacuum chamber — and they land at exactly the same instant, down to the physics engine's numerical precision.

Did Galileo actually drop things off the Tower of Pisa?

Almost certainly not literally — it's a story told by his student Viviani, decades later, with no confirmation in Galileo's own writing. What's well documented is Galileo's careful reasoning (and rolling-ball experiments on inclined planes) that falling bodies accelerate independent of mass, which is the actual physics this tool demonstrates.

Was the Apollo 15 demonstration real?

Yes — Commander David Scott dropped a geology hammer and a falcon feather on live television on August 2, 1971, and they landed together, exactly as Galileo's physics predicted. It remains one of the most direct public demonstrations of the equivalence principle ever performed.

How long does it take to fall a given height?

In a vacuum, t = √(2h/g) — about 0.45 s from 1 m on Earth, 1.43 s from 10 m, 4.52 s from 100 m. Impact speed is v = √(2gh). Mass is in neither equation. With air, those times are a floor: the tool shows both so you can see what the drag actually costs.

Does a heavier object really fall faster?

Not because it is heavier. In a vacuum, no — a hammer and a feather land together. In air, a heavier object usually lands first, but the reason is its higher terminal velocity: more mass per unit of frontal area means drag takes longer to catch up with weight. Mass matters only through that ratio.

What is terminal velocity and when is it reached?

vt = √(2mg / ρCdA). An object approaches it asymptotically, so "reached" means close enough — around 95% within a few seconds for most everyday objects. The tool reports what fraction of terminal velocity each object has at impact, which tells you whether the drop was long enough for air to matter at all.

Why does drag depend on velocity squared?

Faster motion pushes more air out of the way per second and pushes it away faster — both effects scale with speed, so the combined drag force scales with speed squared. It's why terminal velocity exists at all: drag grows quadratically until it exactly cancels gravity.

Why does Mars only barely slow things down?

Mars's atmosphere is roughly 1.6% as dense as Earth's at the surface — present enough for dust storms, far too thin to meaningfully slow a dense object over a short drop. It's a genuine middle ground between Earth's air and the Moon's true vacuum.

Try the Apollo 15 preset first. On the airless Moon, a hammer and a feather hit the ground at exactly the same instant — Commander David Scott really did this in 1971.
Version history · 1 release
  1. v0.842026-07-28Galileo Drop: log height scale to 300 m, custom objects, free-fall equations shown; integrator made stable and honest

Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.