July 9, 2014--Weight of the World

We needed some crushed rock to fill empty patches in one of our garden paths. I went to the contractor's yard where we bought some last year. I brought an empty five-gallon bucket since it comes loose and has to be shoveled into something to be able to transport it.

It was a hot morning and I took my time filling the pail. When topped out I attempted to lift it and slide it into the back of our station wagon. Last year it was difficult, this year nearly impossible.

"This weighs a ton," I grunted to Rona who was getting out of the car to help me hoist it.

"Not exactly," she said, always the literalist.

"It feels like one, but if it's not a ton, then how much does it weigh?" I gasped.

"Maybe 50 pounds."

"Could be," I said now soaked with sweat.

"Maine is pretty much solid rock," Rona noted. "I wonder how much the whole state of Maine weighs."

"I'm not sure we can find that out but I do remember some years ago when Googling that I stumbled on how much the entire Earth weighs."

"How much?"

"I don't remember the specifics but we can look it up when we get home."

Which we did.

"It's an amazing amount," I said. "I don't know how to translate it into a number, like x-gazillion, but the actual number is 13,170,000,000,000,000,000,000,000 pounds.

"How do they know? I mean determine that?"

"Good question. Let me see if I can find out."

"Making it particularly complicated," Rona added, "the Earth's not made of a single substance. I remember from high school Earth Science that there's the mantle, the molten core composed, I think, of iron and so forth."

I turned to Scientific America for guidance, believing it was my original source some years ago.

Sure enough, from March 2004, "How Can the Weight of Earth Be Determined?" which begins with a version of scientific metaphysics--like, what is weight anyway?

If you weigh yourself on a bathroom scale, the article noted, and you're 190 pounds, on the Moon, because of its smaller mass, you weigh only one-sixth of that. And then in deep space you'd weigh nothing at all. And for that matter, neither would Earth.

So where does that leave you? Actually nowhere useful because the issue is not how much the Earth (or you) weigh beyond our solar system but right here on, well, Earth.

So how do we figure out how much Earth weighs on Earth?

As you might imagine there are fancy, mathematical ways to do this (which I used to but no longer understand), or one can use that bathroom scale in an unorthodox manner.

Open the bathroom window, preferable one on at least the second floor, and throw the scale out of it. Count how long it takes to hit the sidewalk. Then measure the distance from the window to the street and with these figures you can compute the acceleration (g) of the scale. The answer you will get is 9.8. meters per second (s^-2)  Knowing this value of g for Earth's surface, along with the gravitational constant G and the 6,731-kilometer distance to Earth's center, you have enough information to calculate Earth's mass--it will be 6 x 10²⁴ kilograms.  Or, 13,170,000,000,000,000,000,000,000 pounds.

When I explained all this to Rona (I mean, attempted to), she rolled her eyes up in her head and said, "Can we just go to the quarry now and get the crushed rock we need? I mean . . ."