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by Joel Marks
“Over the course of a day, the earth spins once, or 360 degrees.” So pronounces The New York Times for August 26, 2005. Hardly news, you might say. But the asserted fact did have relevance to the news – which was that a team of geophysicists had found confirming evidence that the earth’s solid iron inner core rotates a tad faster than the rest of the planet: an extra 0.3 to 0.5 degrees per day, to be exact (more or less). This is possible because there is a molten outer core that allows the solid inner core to move somewhat independently of the layers above, including the surface where we live.
Unfortunately, the above background information provided by the Times reporter is incorrect, and possibly incoherent. “What?” you say. “What could be more obvious than that the earth turns once each day? Indeed, this is practically a tautology, or a geometric truism, since one rotation equals 360 degrees.” Nonetheless, it is wrong.
What exactly does it mean for a body to rotate 360 degrees in actual, physical space? You might suppose when a particular ‘spot’ on the surface – say Greenwich, England – returns to the same place. But what is this ‘same place’? Of course it doesn’t refer to the same location on the surface itself, for Greenwich never leaves that (putting aside for the time being the business of floating continents and such). So this ‘same place’ has to be determined relative to some other location or locations.
The convention, I believe, is to use the so-called ‘fixed stars’ as the reference point(s). Now I say “so-called” because nothing is fixed in the universe; everything is traveling somewhere, so far as anybody can tell. Not even the universe itself, is ‘fixed’. That’s why I called it a convention to use the stars as our reference point, because, when you get right down to it, motion itself is relative, as some fluffy-haired physicist once pointed out. Thus, not only the question of a full rotation is at base problematical, but so is any rotation at all; after all, you could take the earth itself as a fixed point. We do just that when we say that the moon orbits the earth for example; for otherwise we could just as well judge the earth and the moon to be a dual-planetary system orbiting the sun together in a kind of dance.
All right, then: The earth’s rotation is to be determined relative to the stars (other than the sun), which are so distant that for most practical purposes they can be conceived as immobile relative to one another and to us. In this way we can say that one rotation of the earth has taken place when there are two successive passages of Greenwich directly ‘beneath’ say, Betelgeuse. That’s how we know the earth has turned 360 degrees on its axis.
But now what about a day? How do we know when one day has elapsed? Heretofore, you, Dear Reader, like myself until I happened to think this through one evening many years ago, probably assumed that it’s the same thing as one rotation. But it is not. For the day is determined relative to our star, the sun, and not to the rest of them.
Imagine again Greenwich coursing around the earth’s axis. In sun-facing terms, a day is one noon to the next, and noon is whenever the sun is due south in Greenwich’s sky or, to use some technical terminology, is crossing the (Greenwich!) meridian. But is that not tantamount to Betelgeuse’s crossing the Greenwich meridian? No! The tie-breaker is that, in the meantime, the earth has also been moving around the sun.
Try to picture the consequence of this without a diagram. Plant yourself far above earth’s north pole and look straight ahead at the pole so that the whole northern hemisphere is directly in front of you (you are hovering over it in a prone position). Suppose Betelgeuse and the sun are aligned on exactly opposite sides of the earth, say with the sun ‘up’ (above your head) and Betelgeuse ‘down’ (below your feet, and the earth). And let’s put Greenwich on the side of the earth facing Betelgeuse, so that it is midnight there, and Midway Island on the other side of the world is at noon. (Grant me a little geographic license here since Midway is a little shy of 180 degrees longitude). Now imagine that the earth rotates 360 degrees, so that Greenwich is once again right beneath Betelgeuse. Will the sun be due south as seen from Midway island?
No! For the earth has also moved a little to the right and ‘up’in its orbit around the sun – approximately one degree, since there are (about) 365 days in the year. (Note that “one orbit” and “year” must also be defined, but I will leave that up to you.) Therefore the earth must rotate approximately one extra degree to bring Midway directly beneath the sun again, to noon. Upshot: The earth rotates approximately 361 degrees per day (and Betelgeuse shifts approximately one degree west each succeeding midnight).
One further surprising implication for our planet is that in the course of a 365-day year, the earth rotates 366 times. Note that this is completely distinct from the leap-year phenomenon. More generally, for any body orbiting a star, there is always one additional rotation for however many days there are in that body’s year. As a limiting case; if a planet rotated exactly once per revolution around its sun [‘year’], it would have no days since the sun would always be in the same place in its sky.
Now when I realized all of that, it felt like a stupendous astronomical discovery. And this brings me to the point of my telling you about this, aside from its intrinsic interest. As I argued in this column in Issue 33 (September/October 2001), philosophy has the same goal as science – namely, discovering what is true – and even has much the same methodology. But science always leaves plenty for philosophy to ponder, since there is one decisive difference between them: Science generates new data to test its hypotheses, whereas philosophy makes do with existing data, such as the ‘common knowledge’ of astronomy and geometry I just used to discover an extra rotation of the earth.
By the way: I noted that the Times reporter’s assertion might also be incoherent. That is because the very discovery he is reporting makes problematical what it even means to say that “the earth spins” since the earth is now seen to have independently rotating components.
© Joel Marks 2006
Joel Marks is an amateur astronomer and professor of philosophy at the University of New Haven. Other of his essays on astronomy can be found at http://skyskinny.blogspot.com/.