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.

How it works

Gravity pulls equally; air pushes back unequally

The free-fall equations

In a vacuum h = ½gt², so t = √(2h/g) and v = √(2gh). Mass appears in neither: every object falls the same way.

Air pushes back unequally

Drag scales with cross-sectional area, inertia with mass. A feather has enormous area for its mass; a hammer has so much mass for its area that drag barely matters over a short drop.

Terminal velocity

Drag grows with v² until it cancels weight: vt = √(2mg / ρCdA). Falling further adds time, not speed.

The height decides

Over 1.6 m a ping-pong ball has barely felt the air; over 56 m it has long hit terminal velocity. Same objects, opposite impressions.

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, on the Moon like Apollo 15 or in a vacuum chamber, and they land at exactly the same instant. In a vacuum t = √(2h/g) gives the bars above, for any mass; with air those times are a floor, and the tool shows both so you can see what drag costs.
Field notes

Why mass doesn’t matter (until air does)

The equivalence principle

Gravitational acceleration does not depend on what an object is made of or how much it weighs: a consequence of gravitational and inertial mass being the same thing, tested to extraordinary precision by modern experiments, not just dropped hammers.

Ballistic coefficient and terminal velocity

The ratio of mass to (drag coefficient × area) decides how much air matters: a high ratio (dense, streamlined) barely notices air; a low one (light, spread out) is dominated by it at once. Terminal velocity is reached asymptotically: about 95% within a few seconds for most everyday objects. A feather is there almost instantly; a dense hammer from a short drop never gets close. The tool reports what fraction of terminal velocity each object has at impact.

A heavier object does not fall faster because it is heavier

In a vacuum a hammer and a feather land together. In air a heavier object usually lands first, but through its higher terminal velocity: more mass per unit of frontal area means drag takes longer to catch up. Drag goes as v² because faster motion pushes more air out of the way per second and pushes it away faster.

1971Apollo 15

Why the Moon is the perfect demo

No atmosphere means zero drag on anything at any speed: the Moon is a giant free vacuum chamber. Commander David Scott dropped a geology hammer and a falcon feather on live television on 2 August 1971 and they landed together. Mars’s atmosphere is roughly 1.6% as dense as Earth’s: present enough for dust storms, far too thin to slow a dense object over a short drop.

Did Galileo drop things off the Tower of Pisa?

Almost certainly not literally: it is a story told by his student Viviani decades later, with no confirmation in Galileo’s own writing. What is documented is his careful reasoning and rolling-ball experiments on inclined planes that falling bodies accelerate independently of mass.

Questions

What people ask

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.

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