Drop a hammer and a feather at the same moment and the hammer wins, obviously. But that is the air cheating. Take the air away and something surprising happens: they fall together and land at the exact same instant. Toggle Air resistance off in the lab above, press Drop, and watch. That single toggle is the whole idea of this lesson: gravity gives every object the same acceleration, no matter its mass.
Everything falls at the same rate
In free fall, gravity is the only force acting, and every object speeds up at the same rate, the acceleration due to gravity, written g. On Earth g is about 9.8 m/s², which means a falling object gains about 9.8 metres per second of speed every second.
The rate is the same whether the object is a hammer or a feather. That feels wrong, because gravity pulls harder on the heavier object. Here is why the two effects cancel exactly:
- The gravitational force on an object is its weight, F = m × g.
- By Newton’s second law, its acceleration is a = F / m.
- Put them together: a = mg / m = g. The mass cancels.
A heavier object feels a bigger pull, but it also has proportionally more inertia to move, so it ends up with the same acceleration. That is why, with the air removed, the hammer and the feather stay side by side the whole way down.
What air resistance really does
So why does the feather lose in real life? Air resistance, not gravity. As an object moves through air, the air pushes back, and that drag force grows with speed. For a light, spread-out object like a feather the drag quickly balances its small weight, so it stops speeding up and drifts down at a slow, steady terminal velocity. A dense, compact hammer barely notices the air over a short drop, so it keeps accelerating at nearly g.
Turn Air resistance ON and drop again: the hammer plummets while the feather lags far behind. Gravity is giving both the same g. The only thing that changed is the air.
Terminal velocity is not a property of falling, it is a property of the falling object: it depends on mass, cross-section and shape, so there is no single number for it. A skydiver falling flat levels off at roughly 55 m/s, about 200 km/h, and considerably faster head-down with a smaller cross-section. A feather reaches its own terminal velocity almost at once, at whatever speed its particular size and orientation allow, which is why “the terminal velocity of a feather” has no one answer. A dense compact object like a hammer never gets near its terminal velocity over a short drop at all, which is exactly why it appears to obey gravity and the feather appears not to.
g is different on the Moon, Mars and Jupiter
g is not a universal constant, it is a property of the body you are standing on. A more massive, denser world pulls harder:
| Body | g (m/s²) | g (ft/s²) | Times Earth's | What that means |
|---|---|---|---|---|
| Moon | 1.6 | 5.25 | 0.163 | About a sixth of Earth's. A drop takes about 2.5 times as long. |
| Mars | 3.7 | 12.14 | 0.378 | A bit over a third. Fall times are about 1.6 times Earth's. |
| Earth | 9.8 | 32.15 | 1.000 | The number every school problem means by g. |
| Jupiter | 24.8 | 81.36 | 2.531 | Two and a half times Earth's, so a fall takes about 0.63 as long. |
Two numbers get quoted for Earth in feet and they are not the same. The classroom value g = 9.8 m/s² converts to 32.15 ft/s². The defined standard gravity, 9.80665 m/s², converts to 32.174 ft/s², which is where the familiar 32.2 ft/s² comes from. They differ by less than a tenth of a percent, so either is fine for schoolwork as long as you do not mix them inside one calculation.
Switch the Body in the lab and drop from the same height: the fall is slow and dreamlike on the Moon and snappy on Jupiter. The fall time changes because g changed, not because the objects changed.
How fast and how far: the free-fall equations
Starting from rest, free fall follows two simple relationships (with g the acceleration and t the time):
speed: v = g × t | distance fallen: h = ½ × g × t²
Speed grows steadily (linearly with time), but distance grows faster and faster (with the square of time), which is why a fall looks slow at first and then rushes at the end. Rearranging the distance equation gives the fall time and the landing speed from any height:
fall time: t = √(2h / g) | impact speed: v = √(2gh)
The lab shows the fall time and impact speed for the height and body you pick, straight from these equations. Here they are worked out for a range of heights and all four worlds:
| Drop height | Moon (s) | Mars (s) | Earth (s) | Jupiter (s) | Lands at (Earth) |
|---|---|---|---|---|---|
| 1 m | 1.12 | 0.74 | 0.45 | 0.28 | 4.43 m/s |
| 2 m | 1.58 | 1.04 | 0.64 | 0.40 | 6.26 m/s |
| 5 m | 2.50 | 1.64 | 1.01 | 0.64 | 9.90 m/s |
| 10 m | 3.54 | 2.32 | 1.43 | 0.90 | 14.00 m/s |
| 20 m | 5.00 | 3.29 | 2.02 | 1.27 | 19.80 m/s |
| 50 m | 7.91 | 5.20 | 3.19 | 2.01 | 31.30 m/s |
| 100 m | 11.18 | 7.35 | 4.52 | 2.84 | 44.27 m/s |
Read down the Earth column and the square root shows itself: ten times the height is not ten times the fall. A 1 m drop takes 0.45 s and a 100 m drop takes 4.52 s, only ten times longer for a hundred times the height, because t grows with √h. Four times the height is exactly twice the time.
If gravity is weaker, how much longer is the fall?
This is the question that arrives most often, usually about a planet and one of its moons, and it looks harder than it is because the height is often missing. It does not need one.
Start from t = √(2h/g) and write it for two worlds. The height is the same in both, so it cancels, and what is left is:
t₂ / t₁ = √(g₁ / g₂)
Fall time is inversely proportional to the square root of g. Quarter the gravity and the fall takes twice as long. Nine times weaker and it takes three times as long. So an object that takes 3 seconds to fall on a planet where g = 8 m/s² takes 3 × √(8 / 2) = 6 seconds on a moon where g = 2 m/s², dropped from the same height, and it does not matter in the slightest what that height was.
The same reasoning in the other direction gives the height rule above: on one world, t ∝ √h.
Mass and weight are not the same
This trips almost everyone. Mass (in kilograms) is how much matter you are made of, and it is the same everywhere. Weight (in newtons) is the gravitational force on that mass, weight = m × g, so it changes with g. On the Moon your mass is unchanged, but you weigh about one sixth as much, because the Moon’s g is about one sixth of Earth’s. Astronauts do not lose matter in space; the pull on them changes.
Three traps worth knowing
- “Heavier things fall faster.” Only in air, and only because of drag. In a vacuum every mass falls at g. The air-off drop proves it.
- “A falling object speeds up forever.” Without air it gains g every second until it lands. With air, a real object levels off at its terminal velocity once drag balances its weight, which is why skydivers and feathers reach a steady speed.
- “g is a force” or “g is the same everywhere.” g is an acceleration (m/s²), and it is a property of the world you are on: 1.6 on the Moon, 24.8 on Jupiter.
Keep exploring
See where a = F / m comes from in Newton’s laws of motion, put weight into a calculation with the F = ma calculator (the “Free fall (weight)” preset uses weight = m × g), and watch how a steadily growing speed becomes a curved distance graph in motion graphs.