This is a video I mentioned a while ago as a potential project for video analysis. Why? Because it's on the moon and that makes it have a double cool factor.
Dust on the Moon
I love this video, not just because it is in HD, but because it shows someone driving in a car on the moon. The MOON. On top of that, the dust that is kicked up by the wheels is really cool.
Let me start with a car on Earth that leaves a trail of dust.
This dust from the Earth car really doesn't look like the moon dust at all. Not only is the color different, but the moon buggy shoots dust up off the ground but it falls right back down. Why? Well, the real question is "why doesn't dust on Earth fall down?" Here is a diagram of one dust particle near the surface of the Earth.
The yellow balls represent dust particles and the blue balls represent the air (yes, I know it is actually more complicated than this). If you look at the one dust particle near the middle, there is just one force on it: the gravitational force. This gravitational force causes a change in momentum for the dust particle. If it was all by itself, this dust particle would be just like projectile motion since it would have a constant vertical acceleration. However, it's not alone. There are other particles moving around that will collide with the dust particle. These air (and even dust) collisions will keep the dust off the ground for a longer time than if it were just a plain old projectile.
This is why a car can leave a dust trail that stays around for a while.
What about on the moon? On the moon, there is still a gravitational force even though the gravitational field is smaller than on the surface of the Earth. However, on the moon there is no air. This means that there are no other particles for the dust to collide with to keep it off the ground. Ok, the dust could collide with other dust but this isn't a big deal. The moon dust is all mostly moving in the same direction so that the number of collisions would be small.
On the moon, the dust is just like a projectile motion. It goes up and it comes right down. There are no dust trails left by the lunar rover.
Video Analysis of Moon Dust
Now I am going to try to determine the acceleration of moon dust. This might not be simple, but I am going to try. One of the first things I always look for with a video is something I can use to get the scale. In this case, I am going to use the wheelbase of the lunar rover. According to the Wikipedia page on the Lunar Rover, the distance from front to rear axles is 2.3 meters.
This isn't the easiest video to analyze. Surely, you couldn't do it with Apollo era computers. Those things only had 64 kilobytes of memory. Well, here are some tips. First, I of course used Tracker Video Analysis - it's free.
- Use calibration point pairs. These allow you to mark two points in the video and track their motion. From this, Tracker will rescale and adjust the coordinate system.
- Tracker has video filters. I used the brightness filter to change the brightness levels to make the dust stand out a little more. Just play with these a little bit and see how it looks.
- Find the best part of the video. I picked a time around 1:30 when the car was perpendicular to the camera and you could see some dust.
Now for the data. I tried to mark the top of a dust plume, but even that is tough (and that might not be the location of just one dust particle anyway). Here is the vertical and horizontal position of this dust.
In the horizontal direction, the dust has a constant velocity of around 1.1 m/s. For projectile motion, this something you need to look for. If the only force on the dust is the gravitational force in the vertical direction, then there would be no change in motion in the x-direction. So, that's good.
In the vertical direction, Tracker Video gives a fit coefficient of -1.069 m/s2 in front of the t2 term. This is not the acceleration. Let me write down the quadratic fit equation along with the kinematic equation for constant vertical acceleration.
So, you can see that the value of 01.069 m/s2 isn't the vertical acceleration. It is half the vertical acceleration. This would mean the acceleration of moon dust would have a value of -2.14 m/s2. This would also be the measurement of the gravitational field on the moon. Since the only force on the dust is m*g, the vertical part of Newton's second law would be:
I would also change the units of the gravitational field. This gives a gravitational field on the surface of the moon with a value of 2.14 N/kg which isn't correct. The accepted moon g value is 1.6 N/kg. So, it's off - but it isn't THAT far off. Really, I am sort of surprised it is even this close. I could probably find a better view of dust and get a better estimate, but I am happy.
Speed of the Lunar Rover
Since I already calibrated the video, here is an extra plot of the motion of the Lunar Rover.
This shows it having a near constant horizontal speed of around 2.8 m/s (6.3 mph). The cool thing is to compare the horizontal speed of the dust with the speed of the rover. If the rover is going at 2.8 m/s then the linear speed at the edge of the wheel would have a speed of 2.8 m/s (with respect to the rover). What was the horizontal speed of the dust? It was about 1 m/s in the opposite direction. Just imagine if the rover wheel slipped on the dust. It would be spinning and kick up some dust. Would it make that dust go faster than 2.8 m/s? Probably not. Just to check, 1 m/s is less than 2.8 m/s - so, that is what we would expect.
Could You Fake This Video?
How can you make a post about the Apollo missions without also bringing up Moon landing conspiracy theories? So, does this video provide evidence that the moon landings were real or fake? Let's just say that humans didn't go to the moon and instead made a fake video of the rover. How could you do this? Here are some ideas. Oh, and this is before we had computers that were fast enough to make realistic CGI of the rover.
- Obviously we would have to make this in a studio.
- How would you get the dust to move correctly? I guess you would have to pump all the air out of the studio.
- But what about the apparent gravitational field? Even if you pumped the air out, the dust will have too great of an acceleration. I guess if you are going to pump out the air, you might as well build an anti-gravity device to reduce the gravitational field. Oh, or you could put the studio inside the vomit comet (plane that flies to make an apparent reduced gravitational field).
These ideas are fine. But what about something else? What if I recorded a video and then slowed it down to make just look like the moon? Let's say that there is an object dropped from rest on Earth (in the studio). How long would this take to fall? If we assume it started from rest, then I can write:
Here, aE is the vertical acceleration on Earth. But how long should this take in our fake moon video? If I want the object to fall the same distance but with a moon acceleration (am)? Since the distances are the same, I can write:
That means that each frame in the fake video would have to be 2.47 times as long as the studio video. Let's work backwards. If this was the case, how fast would the rover have to be going in the airless studio? Right now, the video is in 24 frames per second. If I change this to 24*2.47 = 59 frames per second, it should have the a dust acceleration of around 9.8 m/s2.
Here is what that looks like.
That just looks crazy. The craziest part is the camera shake. I guess you could make a fake camera shake. I mean, what the hell - you have already pumped the air out of studio, why not take it one more step and make a camera shaker. Here is what I would do. I would have some record video (ok - it would be film) while holding the camera. Measure the motion of the camera and then build a machine to reproduce this motion but faster. Should be easy. If they could send a man to the moon, they could build a fake camera shaker. Oh wait...
Ok. There is another way to make a fake moon video. What if I don't adjust the frame rate? There is still a way I can make the acceleration of objects look like they are on the moon - change the distance scale. Let me go back to my falling object kinematic equation (I am dropping the Δ in front of the time variable because I am lazy).
So, I have a distance measured in the "Earth" scale and the "moon" scale. Let me solve for the time in the Earth scale and substitute that into the moon scale equation.
This says that if I have a small model that is (1.6/9.8) = 0.16 times the size of the real thing, it will take the same amount of time to fall. All you need to do is to build a scale model of the moon at 16% scale. In this scale, the lunar rover would have wheelbase of just 37 cm and an astronaut would be about 30 cm tall.
Yes. This does introduce a new problem. How do you get your model astronauts to move? They would have to be little remote controlled astronauts. Again, this would be pretty tough to do with 1970's technology.
What am I saying? Hopefully, you don't think I am saying this:
No.
