Apollo 15 hammer and feather

During an EVA on Apollo 15, astronaut David Scott performed a live hammer-and-feather drop test to confirm Galileo's idea that they should fall at the same rate.

Apollo 15 full EVA 3 footage: YouTube

Clip of the hammer and feather experiment: Wikimedia Commons

This page is based on computations by MCToon on mctoon.net.

Background

Before Galileo, the popular idea was that heaver objects fall faster than lighter ones. Aristotle believed the rate of falling was proportional to the object's weight.

Galileo challenged the idea in the late 1500's, postulating that all objects fall at the same rate when disregarding air resistance. He is said to have demonstrated this by dropping two objects of the same material but different weights from the Tower of Pisa, showing that they do in fact hit the ground at the same time.

Newton would later mathematically prove why this is the case in his law of universal gravitational. Heaver objects have more mass, and therefore more gravitational force is exerted on them. At the same time, objects with greater mass have a greater resistance to acceleration (Newton's second law; the law of inertia). The additional gravitational force perfectly cancels out the additional inertia, resulting in an equal acceleration for all mass near the surface of Earth.

Analysis of Scott's test

By analysing the footage, we can conclude:

1. It was filmed in a vacuum
2. It was filmed in a location experiencing lunar gravity

And therefore we can conclude it was filmed on the moon.

1. Vacuum

Demonstrating 1. is straightforward. The hammer and feather fall at the same rate, which is only possible where there is no air resistance.

2. Lunar gravity

Data

David Scott height	1.83 m
Hammer + feather fall height	1.2 m
Lunar gravity	1.625 m/s2
Earth gravity	9.8 m/s2
Video frame rate	29.97 fps
No. frames to fall	36

We can use a kinematic equation to predict the time it should have taken for both objects to fall:

$x=ut+\frac{1}{2}a{t}^2$

• $x$ is vertical distance of the fall
• $u$ is initial velocity

$u$ is 0 m/s, so $ut$ cancels:

$x=\frac{1}{2}a{t}^2$

Solving for time, $t$:

$t=\sqrt{\frac{2x}{a}}$

$t=\sqrt{\frac{2(1.2)}{1.625}}$

$t=1.215s$

Performing the same calculation assuming Earth gravity, we get:

Lunar gravity	1.215 s
Earth gravity	0.495 s

Now to measure the time taken for the hammer and feather to fall, divide the number of frames by the frame rate:

$t=\frac{36}{29.97}$

$t=1.20s$

The prediction for lunar gravity matches the measured time taken to fall.

Measured value	1.20 s
Lunar gravity prediction	1.215 s
Earth gravity prediction	0.495 s