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Moses-Hall: Pi in the sky: Celebrate the circle on Tuesday


Joy Hall


Sunday, March 12, 2017

There is something pi-ous about a circle.

Moon, Earth, banana cream: all around us, nature is rounded. This Pi Day, on 3.14, it is a time to roundly celebrate the circle.

The circumference of any pie is pi times the diameter.

At a fundamental level, though, roundness is an illusion. The flits and smears of molecules and atoms are wavy and unknowable at the fractional micro micro level. It is impossible to measure the exact length or circumference of anything, because of the weird vagueness of atomic shape. The finest details are an irreconcilable blur. Perhaps even space itself is chunky in a way that would preclude any perfectly smooth shape.

Earth’s roundness is smoothed even more: from far away, the tall mountain gaps and small whitecaps are worn smooth by distance. From the (equally round) Moon, the Earth looks a perfect sphere. Even as the sphericity gives way to finer details, the first guess at the shape is round, not square, not triangular. The reason for that is gravity.

Earth’s gravity pulls everything toward its center. Rocks, oceans, molasses in January — everything feels the pull. Liquids line up around the circumference of the largest objects. Four and a half billion years ago, a molten Earth oozed into a spherical shape, which it has retained while cooling and hardening on the outside. Molasses in January spreads 10,000 times less readily than water, holding hills and rills longer, and lava spreads a billion times less readily than that. And gravity doesn’t end there.

Oceans spread around to sea level, give or take waves and molecules. The mountain bumps and rugged chunks we see here in the weeds are a matter of perspective. Mount Everest itself, with an elevation of 29,000 feet, towers over the rest of Earth’s ripples and rhythms, but that 29,000 feet is just a speck compared to the overall Earth radius of 29 million feet — a bump of only 0.1 percent — flatter, in a sense, than the nooks and crannies of a pancake.

The biggest factor in taking Earth out of round comes from its spin, which fattens the equator by 26 miles via the same force that keeps you from falling out of the Loch Ness Monster at Busch Gardens.

Pie roundness, in New York State, sometimes came in banana cream. The Yankee version of banana pudding, it was a dish favored by Dad that I only remember Mom making once. That once, I pleaded to serve it. Mom hemmed. I begged. She hawed. “Please!” I gave her my best grade-school waitress look. She relented. I reached into the refrigerator.

I held it flat: pancake flat, level as the sea, consistent ever with gravity — but one tiny moment, an Everest later, it slipped from the pie pan, a banana aviator. It spun and twirled and circled its equator, then quick crash landed, on feet and ’frigerator. The custard was broken, left nothing but crater. Not the work of a waiter but a pastry terminator!

Maybe that’s why she never made another banana cream.

The shortfalls in Earth roundness, proportionally small though they are, have effects beyond the marble shape of our home, and reciprocate to the Moon. The twice-daily tides, arising from a three-foot front and rear gravity bulge of the ocean under the Moon that we spin through each day, not only sweep away castles of sand and bits of mainland, but also cause an occasional global leap-second.

All that tiding puts a strain on the Earth: it spins every 24 hours, yet the bulges of Moon tide hang, still, under the Moon. The relentless Earth spin drags those bulges ahead of the Moon, which are then pulled back toward the Moon’s gravity, dragging against the Earth. It’s a tiny push-me-pull-you effect, but the drag eventually slows the Earth such that at the end of a million years, our days are 14 seconds longer. In addition, the tidal bulge ahead of the Moon pushes it away, by 1.5 inches per year.

Earthquakes deform the surface, redistributing Earth’s massive crust, and the bounce-back of continents that were once held down by glaciers also changes the roundness. Both of these, like a tire that throws a weight, can wobble us off the 24-hr spin by a few micro-seconds one way or the other.

So it’s pi time.

And a lot of it is Moon pi.

Joy Moses-Hall teaches physics and astronomy at Pitt Community College. She has a PhD in oceanography and is the author of the novel Wretched Refuge.