Free fall

In 1971 an astronaut dropped a hammer and a feather on the Moon, and they hit the ground together.

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A ball thrown straight up at 15 m/s. Launch it, switch the world to the Moon or Mars and launch again: the kept paths show how much higher it goes where g is smaller.

Everything falls with the same acceleration

Drop a coin and a sheet of paper together and the coin wins easily. For about two thousand years many people took this as proof that heavier things fall faster. Galileo argued the opposite: without air in the way, all objects fall with the same acceleration. Crumple the paper into a tight ball and drop it with the coin again. They now land almost together, because the crumpled paper meets far less air resistance. The weight did not change; the air did.

Motion under gravity alone is called free fall. Near Earth’s surface the acceleration of free fall is about 9.8 m/s², written g. The value changes a little from place to place, from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. Scientists have agreed on a standard value, g_n = 9.80665 m/s² exactly, which NIST lists among its reference constants. This course rounds it to 9.81 m/s².

BackgroundAt the end of the last moonwalk of Apollo 15, on 2 August 1971, Commander David Scott held a geology hammer in one hand and a falcon feather in the other, in front of the television camera. NASA’s report gives the numbers: a 1.32 kg aluminium hammer and a 0.03 kg feather, released together from about 1.6 m. With almost no air on the Moon, they fell side by side and struck the dust at the same moment. Mission controller Joe Allen later noted that the result was reassuring, since the crew’s trip home depended on the same theory.

How far and how fast

Free fall is steady acceleration, so the equations from the acceleration lesson apply with a = g. Dropped from rest, an object’s speed after t seconds is v = g t, and the distance fallen is d = ½ g t². After 1 s it has fallen 4.9 m and moves at 9.8 m/s. After 2 s it has fallen 19.6 m, four times as far. After 3 s, 44.1 m and 29.4 m/s. Turning the equation round gives the time to fall a height h: t = √(2h ÷ g). The hammer’s 1.6 m drop took √(2 × 1.6 ÷ 1.62) ≈ 1.4 s on the Moon. On Earth the same drop takes about 0.57 s.

A dropped ball every 0.1 s. The gaps grow because the speed grows by 0.981 m/s in each interval.

Throwing upward

A ball thrown straight up is also in free fall from the moment it leaves your hand. On the way up it slows by 9.81 m/s every second; at the top its velocity is zero for an instant; on the way down it speeds up again. The acceleration is 9.81 m/s² downward the whole time, including at the top. Thrown at 15 m/s, it takes 15 ÷ 9.81 ≈ 1.5 s to reach the top, rises 15² ÷ (2 × 9.81) ≈ 11.5 m, and comes back down to your hand at 15 m/s. In the lab above, the same throw rises about 69 m on the Moon and about 30 m on Mars.

Free-fall numbers also explain a reaction-time game. Hold a ruler just above a friend’s open fingers, let go without warning, and see where they catch it. If the ruler drops 20 cm before they grab it, the time was √(2 × 0.20 ÷ 9.81) ≈ 0.20 s. The ruler turns a distance you can read into a time too short to measure with a stopwatch, the same trick Galileo used with his slow ramp.

1603: Galileo times balls rolling down an inclined plane (approximate date).
1638: Two New Sciences publishes the law of falling bodies.
1687: Newton’s Principia explains falling with a force of gravity.
1971: Apollo 15: hammer and feather land together on the Moon.

Key points

Without air, all objects fall with the same acceleration g.
g ≈ 9.81 m/s² on Earth, 1.62 on the Moon, 3.71 on Mars.
From rest: v = g t, d = ½ g t², t = √(2h ÷ g).
A thrown ball accelerates downward even at the top.

A stone is dropped from rest. How far has it fallen after 2 s, in metres? (g = 9.81)
Same stone: speed after 3 s in m/s?
How long does a fall of 20 m take on Earth, in seconds? (two decimals)
The Apollo 15 hammer fell about 1.6 m with g = 1.62 m/s². How many seconds? (one decimal)
Why did the feather and hammer land together on the Moon?
- The Moon’s gravity is weak
- There is almost no air to slow the feather
- The hammer was light
A ball is thrown straight up. At the top of its path its acceleration is…
- zero
- 9.81 m/s² downward
- 9.81 m/s² upward
A ball is thrown up at 15 m/s on Earth. How high does it rise, in metres? (one decimal)
The same throw on the Moon (g = 1.62): height in metres? (one decimal)
In the strobe picture, why are the gaps between balls growing?
- The ball gets heavier
- The ball goes faster each interval
- The camera slows down
What is the standard acceleration of gravity g_n, in m/s², as listed by NIST?

Sources for this course (12)

OpenStax College Physics 2e, chapters 2 (Kinematics)
3.4 (Projectile motion)
5.2 (Drag forces) (openstax.org/books/college-physics-2e)
NIST CODATA standard acceleration of gravity g_n = 9.80665 m/s² exact (physics.nist.gov/cgi-bin/cuu/Value?gn)
NASA Moon Fact Sheet (surface gravity 1.62 m/s², nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html)
NASA Mars Fact Sheet (3.69 m/s² equator, 3.73 m/s² pole, surface air density about 0.016 kg/m³, nssdc.gsfc.nasa.gov/planetary/factsheet/marsfact.html)
NASA, The Apollo 15 Hammer-Feather Drop (science.nasa.gov/resource/the-apollo-15-hammer-feather-drop, quoting NASA SP-289)
Galileo, Two New Sciences (1638)
inclined-plane account via PBS LearningMedia/NOVA "Galileo's Inclined Plane"
long-jump take-off angle about 21°: Linthorne, Guzman and Bridgett, Journal of Sports Sciences 23(7)
2005, and Linthorne, Biomechanics of the long jump
OpenStax College Physics 2e 17.2 (sound 343 m/s at 20 °C).

Checked: 2026-10-17