In 1991, I went to Teotihuacán, Mexico, to watch a total solar eclipse from the Pyramids of the Sun and the Moon. Alas, thick clouds moved in during the morning. At the time of totality, it just got really dark. I didn’t see a hole in the sky surrounded by a shimmering corona or any other eclipse phenomena: Baily’s beads, the diamond ring. I was crushed.
This year, I’m planning to go to Plattsburgh, N.Y., near the Canadian border, to watch the April 8 eclipse from a city beach on the western shore of Lake Champlain. If the clouds come in again … I don’t even want to think about it.
Astronomy is unlike economics in that astronomers can tell us with great accuracy what will happen in the heavens not just weeks from now, but hundreds of years from now. Eclipse-watching, on the other hand, is very much like economics in that it’s vulnerable to all kinds of uncontrollable effects. Like clouds. And traffic jams. And exorbitant rates or no vacancies in hotels and motels in the path of the eclipse, lending a new meaning to the term “blackout period.”
When the moon fully blocks the sun, the sky darkens, the temperature falls, birds roost for the night, and some stars pop out. “People laugh, cry, stare dumbfounded, jump up and down,” Peter Tyson, editor in chief of Sky & Telescope magazine, wrote in a special issue this year. “The hair on the back of your neck rises, and goose bumps cover your arms,” Kate Russo, who says she has witnessed 13 solar eclipses on six continents, wrote in the same issue.
I’m hoping for some of that craziness next month in Plattsburgh. In the meantime I’ve been thinking about eclipses in a more mechanical way.
One counterintuitive aspect of an eclipse is that the shadow cast by the moon starts in the west and travels east, even though the moon itself crosses the sky in the opposite direction, from east to west. This eclipse, for example, will travel northeast from Mexico through the United States to Canada. (Note: not “is likely to,” but “will.” That’s astronomy!)
I think most people would have a hard time explaining why an eclipse goes against the one-way traffic of the heavens — not just contra the moon but also contra the sun, the stars and the other planets.
Here’s the explanation. If you could look down on Earth from far above the North Pole, you would see what looks like a ball turning counterclockwise. What appears to an earthbound observer like the sun, the moon, the stars and the planets moving clockwise across the sky is really the Earth turning counterclockwise while those other heavenly bodies are fixed (the sun, the stars) or moving slowly (the moon, the planets).
Another key eclipse fact is that the moon actually revolves around the Earth in the same direction that the Earth is spinning. We don’t see it that way from Earth. It takes longer for the moon to go around the Earth than for the Earth to rotate on its axis, so the moon constantly falls behind from an Earth observer’s perspective. As a result it seems to be going clockwise, from east to west, like the sun and other bodies. That’s the opposite of its true direction.
In an eclipse, the moon’s true direction is revealed. The shadow that the moon casts moves rapidly across the Earth’s surface from west to east as the moon passes in front of the sun.
The reason people get confused about the eclipse’s direction of travel is that they’re mixing up two different concepts of velocity. One is angular velocity, or how much of the horizon, in degrees, an object transits in a given amount of time. The Earth is the clear winner in angular velocity. It rotates 360 degrees in a day, while the moon takes nearly a month to cover the same 360 degrees.
In terms of linear velocity, though, the moon is the clear winner. It has much farther to go in covering those 360 degrees. In its monthly circuit, the moon travels through space roughly twice as fast as a given spot on the Earth’s surface travels (though they’re going the same direction).
Linear velocity, not angular velocity, is what matters in an eclipse. The moon’s advantage in linear velocity versus the Earth’s surface will cause its shadow to zip across North America on April 8. In those few hours, the moon will complete only a tiny fraction of its orbit; its angular movement will be small. But its linear movement will be sufficient to paint an eclipse across the continent.
I realize that this explanation is going to leave a lot of readers in the dark, so to speak. This is confusing stuff and the newsletter format doesn’t allow me to demonstrate with oranges, basketballs and bare lightbulbs.
I hope I at least conveyed a sense of how cool this stuff is. Just thinking about eclipses can be mind-bending, even without seeing one. On the other hand, thought experiments go only so far. Like millions of other people, I really want to feel those goose bumps when the eclipse comes next month. Here’s hoping for clear skies on April 8.
Outlook: Antonio Gabriel, Michalis Rousakis and Pedro Diaz
Personal income in the United States probably grew by half a percent in February “on the back of robust gains in payrolls,” Antonio Gabriel, Michalis Rousakis and Pedro Diaz of BofA Securities, a unit of Bank of America, wrote in a note to clients on Sunday. Personal spending before adjusting for inflation also probably grew a “solid” half a percent, “driven by a sharp increase in auto sales,” they wrote. The Bureau of Economic Analysis is scheduled to release the official data on Friday.
Quote of the Day
“In economic theory, as in Harry Potter, the Emperor’s New Clothes or the tales of King Solomon, we amuse ourselves in imaginary worlds. Economic theory spins tales and calls them models. An economic model is also somewhere between fantasy and reality. Models can be denounced for being simplistic and unrealistic, but modeling is essential because it is the only method we have of clarifying concepts, evaluating assumptions, verifying conclusions and acquiring insights that will serve us when we return from the model to real life.”
— Ariel Rubinstein, “Economic Fables” (2012)