View source for Apollo 15 hammer and feather

During an [[Wikipedia:Extravehicular activity|EVA]] on [[Wikipedia:Apollo 15|Apollo 15]], astronaut [[Wikipedia:David Scott|David Scott]] performed a live hammer-and-feather drop test to confirm [[Wikipedia:Equations for a falling body|Galileo's idea]] that they should fall at the same rate.<ref>[https://science.nasa.gov/resource/the-apollo-15-hammer-feather-drop/ The Apollo 15 Hammer-Feather Drop] NASA (2018).</ref>

: Apollo 15 full EVA 3 footage: [https://youtu.be/ZjIxg-bjcdY?si=aj2uEffRE-i3A3an&t=8587 YouTube]
: Clip of the hammer and feather experiment: [https://commons.wikimedia.org/wiki/File:Apollo_15_feather_and_hammer_drop.ogv Wikimedia Commons]

This page is based on computations by [[MCToon]] on [https://mctoon.net/moon-landing/ 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.<ref>[https://www.pbslearningmedia.org/resource/nvmm-math-fallingbodies/galileos-falling-bodies/ Galileo's Falling Bodies] PBS LeaningMedia.</ref>

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:
# It was filmed in a vacuum
# 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===

{|class="wikitable"
|+ Data
| David Scott height || 1.83 m
|-
| Hammer + feather fall height || 1.2 m
|-
| Lunar gravity || 1.625 m/s<sup>2</sup>
|-
| Earth gravity || 9.8 m/s<sup>2</sup>
|-
| 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:

<math>x=ut+\frac{1}{2} at^2</math>
* <math>x</math> is vertical distance of the fall
* <math>u</math> is initial velocity

<math>u</math> is 0 m/s, so <math>ut</math> cancels:

<math>x=\frac{1}{2} at^2</math>

Solving for time, <math>t</math>:

<math>t = \sqrt{ \frac{2x}{a} }</math>

<math>t = \sqrt{ \frac{2(1.2)}{1.625} }</math> 

<math>t = 1.215 s</math>

Performing the same calculation assuming Earth gravity, we get:

{|class="wikitable"
|-
| 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:

<math>t=\frac{36}{29.97}</math>

<math>t=1.20 s</math>

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

<table class="wikitable">
<tr>
 <td> Measured value </td>
 <td style="background-color:#E6FFE6"> 1.20 s </td>
</tr>
<tr>
 <td> Lunar gravity prediction </td>
 <td style="background-color:#E6FFE6"> 1.215 s </td>
</tr> 
<tr>  
 <td> Earth gravity prediction </td>
 <td style="background-color:#FFE6E6"> 0.495 s </td>
</tr>
</table>

==References==

[[Category:Globe evidence]]
[[Category:Apollo evidence]]