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Free Fall on Earth and the Moon Explained
Drop a hammer and a feather together. On Earth the hammer lands first, but only because of the air. Without air, all objects fall with the same acceleration g, whatever their mass. Astronaut David Scott showed this on the Moon in 1971, dropping a hammer and a falcon feather that landed at the same moment.
Why mass doesn't matter
A heavier object is pulled harder by gravity (its weight W = mg is bigger), but it is also harder to speed up (a = F/m). The two effects cancel exactly: a = mg/m = g.
Free-fall equations
Released from rest, taking downward as positive and ignoring air: v = gt, s = ½gt², and the time to fall a height h is t = √(2h/g). On Earth g = 9.81 m/s²; on the Moon g = 1.62 m/s², about six times weaker.
Mass vs weight
Mass (kg) is the amount of matter and is the same everywhere. Weight (N) is the force of gravity, W = mg, and changes from place to place. A 60 kg person weighs about 589 N on Earth but only about 97 N on the Moon.
Projectile motion
A ball launched horizontally at speed u keeps that horizontal speed (no air), while it falls vertically exactly like a dropped ball. The two motions are independent: x = ut and y = ½gt². That's why a ball fired sideways and one dropped from the same height land at the same time.
Worked example
A stone falls 20 m. On Earth: t = √(2 × 20 / 9.81) ≈ 2.0 s. On the Moon: t = √(2 × 20 / 1.62) ≈ 5.0 s, about 2.5 times longer (not 6 times, because t ∝ 1/√g).
Frequently asked questions
Do heavier objects fall faster?
Not in a vacuum. All objects have the same acceleration g. On Earth, air resistance slows light, wide objects like feathers much more than heavy, compact ones.
What is g on the Moon?
About 1.62 m/s², roughly one-sixth of Earth's 9.81 m/s².
What is the difference between mass and weight?
Mass is the amount of matter in kilograms and never changes. Weight is the gravitational force W = mg in newtons, and it depends on where you are.
How long does it take to fall 20 m?
Without air resistance, t = √(2h/g): about 2.0 s on Earth and about 5.0 s on the Moon.