Why do all objects fall at the same rate regardless of mass?

The gravitational force on an object near Earth is F = m × g, where m is its mass and g is the local acceleration due to gravity. Newton's second law says the resulting acceleration is a = F / m. Substituting, a = (m × g) / m = g, so the mass cancels and every object accelerates at g ≈ 9.81 m/s². A heavier object feels a bigger pull, but it also has proportionally more inertia, so the two effects exactly cancel.

At what rate does gravity accelerate objects toward the ground?

Near the surface of Earth, the acceleration due to gravity is about 9.81 m/s² (32.17 ft/s²), pointing straight down toward the centre of the Earth. After one second of free fall, an object is moving at roughly 9.81 m/s; after two seconds, about 19.6 m/s, and so on (in the absence of air resistance).

Why does a feather fall slower than a hammer on Earth but not on the Moon?

On Earth, a feather is slowed dramatically by air resistance because it has a large surface area and very little mass. On the Moon there is essentially no atmosphere, so there is no air resistance — gravity is the only force acting. In August 1971, Apollo 15 astronaut David Scott dropped a 1.32 kg hammer and a 0.03 kg falcon feather on the Moon's surface; they hit the ground at exactly the same instant.

Does gravity affect all objects the same way?

It accelerates them all at the same rate near Earth's surface (≈9.81 m/s²), yes — but the force depends on mass (F = mg), so heavier objects feel a larger force. They do not, however, fall any faster. This equivalence between gravitational mass and inertial mass is one of the most precisely tested principles in physics and is the cornerstone of Einstein's general theory of relativity.

How fast do objects fall on the Moon compared to Earth?

The Moon's surface gravity is about 1.62 m/s² — roughly one-sixth of Earth's 9.81 m/s². So an object dropped on the Moon falls about six times more slowly than on Earth. That is why astronauts move in those distinctive long, bouncy strides in the Apollo footage.

Why Do All Objects Fall Towards The Ground At The Same Rate, Regardless Of Their Weight?

Table of Contents (click to expand)

Universal Law Of Gravitation
Earth’s Gravitation
Weight And Mass

All objects fall at the same rate because the mass of the falling object cancels out: gravity pulls on it with a force F = m × g, but Newton’s second law (F = m × a) divides that force by the same mass to give the acceleration. The result is a = g ≈ 9.81 m/s² for everything in free fall, regardless of weight. Air resistance is what makes a feather fall slower than a brick in everyday life; in a vacuum, they hit the ground together — as Apollo 15 demonstrated on the Moon in 1971.

Universal Law Of Gravitation

Isaac Newton saw objects falling downwards after being suspended in the air all his life, but one fine day, in the year 1665 or 1666, he realized that there had to be a force causing the objects to fall downwards, instead of sideways or even upwards. He applied the same logic to an apple falling from a tree and used the example to devise his Universal Law of Gravitation^[1].

The law says that every pair of objects with mass pulls on each other with a force F = G · m₁m₂ / r², where m₁ and m₂ are the two masses, r is the distance between their centres, and G is the gravitational constant (about 6.674 × 10^-11 N·m²/kg²). The Earth tugs an apple downward, but by Newton’s third law the apple also tugs the Earth upward — it just has so little mass that the Earth’s motion in response is impossibly tiny.

Earth’s Gravitation

For an object near the Earth’s surface, the distance r in Newton’s formula is essentially Earth’s radius (the few extra metres of altitude make no measurable difference). Plug in Earth’s mass and radius, and the formula simplifies to F = m · g, where g = G · M_Earth / R_Earth² ≈ 9.81 m/s². That single number — the acceleration due to gravity — is the same whether you drop a coin, a brick, or a piano.

g is different for different planets, depending on their mass and radius. The Moon’s gravitational pull is about 1/6^th that of the Earth^[5], so any object’s weight on the Moon would be 1/6^th of what it weighs on Earth. Any object that falls towards the surface of the Moon will fall at about 1/6^th the rate that it would fall towards the surface of the Earth.

Weight And Mass

Here is the punchline. The gravitational force pulling an object down is F = mg, but Newton’s second law says that whatever force you apply to an object produces an acceleration a = F / m. So for a freely falling object near Earth, a = F / m = (m · g) / m = g. The mass cancels out. A bowling ball and a marble plunge with exactly the same acceleration of about 9.81 m/s², because the stronger pull on the bowling ball is exactly offset by its larger inertia.

Galileo is supposed to have first demonstrated this, allegedly by dropping two cannonballs of different weights from the Leaning Tower of Pisa in the late 1500s. The most spectacular re-run was performed live on the Moon: on August 2, 1971, Apollo 15 commander David Scott released a 1.32 kg geological hammer and a 0.03 kg falcon feather from the same height in front of a TV camera. In the Moon’s near-vacuum they hit the lunar dust at exactly the same instant — a textbook proof that, without air, every object falls at the same rate.

So why do a feather and a rubber ball fall to the ground at different times in everyday life? Well, a feather’s shape and extremely low mass make it especially susceptible to air resistance, the drag force the surrounding air exerts on anything pushing through it. Most everyday objects are dense enough that air resistance is negligible compared to gravity, so they all reach the ground at roughly the same time. Inside a vacuum chamber, even a feather and a bowling ball land together — exactly as Newton and Galileo would have predicted.

Since the force on a falling body from anything other than gravity (air drag aside) is negligible, the only acceleration affecting its motion is g = 9.8 m/s².

Therefore, their rate of falling towards the Earth’s surface is independent of their mass.

References (click to expand)