We landed on the moon. Yes? Like the overthrow of Mosaddeq, or the manufacture of the Gulf of Tonkin incident, it was a stunning example of Mid-century American ingenuity that can make one feel small/humbled just contemplating it. Here is a way to prove that it happened using non-fancy Newtonian physics.
Exhibit A in this proof is footage taken by Lunar Module Pilot Charlie Duke of his Apollo 16 mission commander John Young tooling around the Descartes highlands in their lunar dune buggy. As can be seen in the video, below, the dune buggy occasionally passes Duke very nearly perpendicular to the camera—allowing one to slap on a 2D-coordinate grid and do some basic, undergraduate-level physics on the dust particles kicked up in the dune buggy's wake.
Writing for the Journal of American Physics, two scientists at the University of Colorado's Atmospheric and Space Physics lab, Hsiang-Wen Hsu and Mihály Horányi, compared the movement of the dust particles in the film against equations for the particles' trajectory in both terrestrial Earth gravity and lunar gravity.
Hsu and Horányi fixed the origin point of their graph to the buggy's fender and charted the dust's motion from the top of the cloud it produced, to make sure that the dust studied did not "intermix with grains coming off the surface with lower initial speeds." (Intermixing and collisions between the various bits of dust kicked up would add forces unaccounted for by the equations used.) The initial velocity of the moon dust (or regolith, as it is technically known) was calculated from the angular motion of the spoke on the front wheel.
To better visualize all this:
Hsu and Horányi found what you would expect, if you believe that American astronauts landed on the moon, and did not fake the lunar landing on a sound stage under the direction of auteur genius Stanley Kubrick. The acceleration due to gravity conveyed by the particle's motion ranged somewhere between 1.48 meters-per-second-squared and the established value for acceleration due to lunar gravity, 1.60 meters-per-second-squared. In other words, a value very far away from the acceleartion due to Earth's gravity, 9.8 meters-per-second-squared, a constant you were given on the first page of the quiz, so you wouldn't have to memorize it.
Here is Hsu and Horányi's charting of their measured particles' trajectories versus the physical equations:
If you would like to dig deeper and argue their findings the paper can purchased here.
While the evidence is pretty concrete, absolute certainty is not actually the province of real scientific inquiry. Given how brilliant Stanley Kubrick was as a filmmaker, it is entirely possible that he had this dust added in post-production using top-shelf practical effects.
It's like every time I watch 2001, or The Shining, or Eyes Wide Shut, I get something new out of it. It's mind boggling how good that guy was at making movies.
[image screencapture via footage by NASA; graphs via the Journal of American Physics]