One of our readers, Michael Luxem, wrote a fact-check comment in response to the blog post, Arizona Cataclysm, that stated, *“**It is difficult to imagine something only 160 feet in diameter—about the length of three semi-tractor trailers—having that much destructive power. F = ma.”*

I pulled the statistics for this blog post from numerous web sources including Wikipedia, but I must admit I didn’t math-check the material, so after Michael’s challenge, it was research time. My worry at this point is not the revelation of incorrect facts, but that many of the links and pathways burrowed me into explosion and bomb impact studies, potentially resulting in the arrival of black Suburbans and the infamous Men in Black from Homeland Security. Read on and see…

In the formula: Force = Mass × Acceleration, it should be noted that weight and mass are different. The mass of an object is the amount of matter in the object, whereas weight is the measure of the amount of force exerted on the object within a gravitational field, or how hard gravity pulls on it. For example, the weight of a person varies on Earth compared to the moon. A one-kilogram mass placed on a bench presses down on the bench with almost 10 kg of force.

One newton is the force needed to accelerate one kilogram of mass at the rate of one meter per second squared. Force (one newton) = mass (one kilogram) × acceleration (one meter per second squared).

The meteor described in the blog was approximately 160 feet in diameter. Assuming it was a perfect cube, which it wasn’t, the dimensions of that cube would have been 160 feet long, by 160 feet wide, by 160 feet deep, for a total of 4,096,000 cubic feet. You might be surprised to note that one cubic foot, 12 inches by 12 inches by 12 inches of iron—of which the meteor was comprised—weighs 491 pounds! Hollywood dulls our senses to reality when we see bank robbers break into a vault and carry out gold bars under their arms. A one-cubic-foot bar, again the same dimensions as our iron bar above, would weigh 1,206 pounds! Yes, gold has more mass than iron. Oh, if only meteors were made of gold! The gold ingots stored in Fort Knox weigh 36.5 pounds each, not such an easy feat to slip out of the vault…but I’m getting away from topic here.

It’s simple to calculate the mass of our meteor by multiplying its total cubic feet by the weight of one cubic foot—491 pounds—to arrive at 4,095,999 pounds. Converted to tons, we get 2,047, which is significantly off from the 300,000 tons claimed by one of my reference websites, and consequently changes the impact force on Planet Earth, as we shall see shortly. Nevertheless, this is no insignificant puppy. A fully loaded semi-tractor rig is approximately 80,000 pounds. The mass of our meteor entering Earth’s atmosphere was 51 times that, at an accelerated force monumentally greater than a semi’s highway speed.

Now, let’s make sure all our units described follow the metric (SI) nomenclature.

Mass: 1,859,728 Kg

Acceleration: 12,964 m/s

Force: 44,837,137,865,368 newtons (4.48 × 10^{16})

I discovered an online TNT calculator and did some rough math to determine meteor force impact which could take me, as I mentioned above, into black Suburban influence, and came up with an explosive force of around 10 megatons of TNT. As a reference, the World War II nuclear explosion over Nagasaki was 20 kilotons. When you see the size of the Arizona impact crater, this all becomes clear.

Another force calculation which helped me understand the immense size of the impact crater was by calculating Kinetic Energy = KE, the formula is written as: KE = m(mass) × v(velocity)² ÷ 2.

1,859,728 kg × 12,964 m/sec² ÷ 2 = 1.56 × 10^{14 }J (Joules)

A Joule is: the SI unit of work or energy, equal to the work done by a force of one newton when its point of application moves one meter in the direction of action of the force, equivalent to one 3,600th of a watt hour.

It is estimated that before atmospheric entry the meteor had the energy of 5.36 × 10^{16}, approximately 12.8 megatons of TNT.

In January 2018, an estimated six-foot-wide meteor exploded in the atmosphere above Michigan with the power of 10 tons of TNT, it was said. I didn’t do the math proof. Here is the YouTube video.

- Purdue University constructed a rough app called “Impact Earth,” in which you can extract hypothetical meteor impact data and watch a simulated video of your design.
- For some detailed and complex impact mechanics calculations researched by the US Geological Survey, here is a fascinating link dating to 1928.

Thanks, friend Michael, for pushing me to spend the day (and into the night) researching some of the minutia of that famous monumental Arizona meteor impact, and as a consequence, frying my brain cells. I hope I got the calculations right. You might want to double check them (smile). The challenge is that there is a vast amount of conflicting information out there, much of it weakly researched. Add mine to that list. If you don’t hear from me soon, after a day’s plumbing the depths of explosive impact science, you know where to start looking.

Mikey

Your bookmark photos to your #s, the tanker snake and the car load of “protectors,” indicate you are in a different portal in American society.

Elon Musk lists a rogue asteroid as one of the three, existential threats to humanity on Earth. There is a probability distribution, a “Poisson distribution,” that can occasionally, fairly accurately, predict a super freak, black swan event such a mega-asteroid.

https://en.m.wikipedia.org/wiki/Poisson_distribution

In your idle moments, if such exist, can you tell me more about the joule, or at least its connection to Babylonian mathematics. Those dudes rocked in astronomy…5k years ago. Their calculations were done in multiples of 60 (360 degrees in a circle, 60 seconds in a minute, etc.). The joule had 3,600 units associated with it. Poisson would say it’s possibly a strong coincidence.

Saludos, Maestro.

Pancho Tequila

Timothy Harlow

Whatever the exact mass and force that was not a pretty day for whomever was around. I was at the crater when I was kid. Your original post photos bring back memories.

I did a little checking on your math. The meteor was likely more spherical, so the correct formuala for volume would be V = 4/3πr^3. I think you might have missed a couple of decimals as I came closer to the mass in your original post.

But, that’s beside the point. Cool post and a wonderful place; I need to go back.

Happy travels,

Tim Harlow

Justin

I learned something today! Mass vs. Weight.

What’s tomorrow’s lesson?

Ben Macri

Keep tuned in for the surprise…

Michael Luxem

Ben: You are a research gorilla! And a smart one at that. Thanks for burning the midnight oil to clarify the stats in your blog.

By the way, it was not my intention to submit a fact-check challenge regarding the data reported. My response was more a reflection of my ignorance about the destructive power of meteors impacting the earth. Stats or not, I will now be scanning the night skies for any fireballs headed my way. Thanks for an instructive article.

Ben Macri

😉