earth

How to Tell that the Earth Spins

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Continuing with the supplementary material for the book, from its Chapter 2. This is in reference to Galileo’s principle of relativity, a central pillar of modern science. This principle states that perfectly steady motion in a straight line is indistinguishable from no motion at all, and thus cannot be felt. This is why we don’t feel our rapid motion around the Earth and Sun; over minutes, that motion is almost steady and straight. I wrote

  • . . . Our planet rotates and roams the heavens, but our motion is nearly steady. That makes it nearly undetectable, thanks to Galileo’s principle.

To this I added a brief endnote, since the spin of the Earth can be detected, with some difficulty.

  • As pointed out by the nineteenth-century French physicist Léon Foucault, the Earth’s rotation, the least steady of our motions, is reflected in the motion of a tall pendulum. Many science museums around the world have such a “Foucault pendulum” on exhibit.

But for those who would want to know more, here’s some information about how to measure the Earth’s spin.

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Beyond the Book (and What the Greeks Knew About the Earth)

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Since the upcoming book is basically done, it’s time for me to launch the next phase of the project — the supplementary material, which will be placed here, on this website.

Any science book has to leave out many details of the subjects it covers, and omit many important topics. While my book has endnotes that help flesh out the main text, I know that some readers will want even more information. That’s what I’ll be building here over the coming months. I’ll continue to develop this material even after the book is published, as additional readers explore it. For a time, then, this will be a living, growing extension to the written text.

As I create this supplementary material, I’ll first post it on this blog, looking for your feedback in terms of its clarity and accuracy, and hoping to get a sense from you as to whether there are other questions that I ought to address. Let’s try this out today with a first example; I look forward to your comments.

In Chapter 2 of the book, I have written

  • Over two thousand years ago, Greek thinkers became experts in geometry and found clever tricks for estimating the Earth’s shape and size.

This sentence then refers to an endnote, in which I state

  • The shadow that the Earth casts on the Moon during a lunar eclipse is always disk-shaped, no matter the time of day, which can be true only for a spherical planet. Earth’s size is revealed by comparing the lengths of shadows of two identical objects, separated by a known north-south distance, measured at noon on the same day.*

Obviously this is very terse, and I’m sure some readers will want an explanation of the endnote. Here’s the explanation that I’ll post on this website:

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Coordinate Independence, Kepler, and Planetary Orbits

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Could you, merely by changing coordinates, argue that the Sun gravitationally orbits the Earth?  And could Einstein’s theory of gravity, which works equally well in all coordinate systems, allow you to do that?  

Despite some claims to the contrary — that all Copernicus really did was choose better coordinates than the ancient Greek astronomers — the answer is: No Way. 

How badly does the Sun’s path, nearly circular in Earth-centered (geocentric) coordinates, violate the Earth’s version of Kepler’s law?  (Kepler’s third law is the relation T=R3/2 between the period T of a gravitational orbit and the distance R, which is half the long axis of the ellipse that the orbit forms.)   Since the Moon takes about a month to orbit the Earth, and the Sun is about 400 = 202 times further from Earth than the Moon, the period of the Sun would be 4003/2 = 8000 times longer than the Moon’s, i.e. about 600 years, not 1 year. 

But is this statement coordinate-independent? Can it serve to prove, even in Einstein’s theory, that the Earth orbits the Sun and the Sun does not orbit the Earth? Yes, it is, and yes, it does. That’s what I claimed last time, and will argue more carefully today.

Of course the question of “Does X orbit Y?” is already complicated in Newtonian gravity.  There are many situations in which the question could be ambiguous (as when X and Y have almost equal mass), or when they form part of a cluster of large mass made from many objects of small mass (as with stars within a galaxy.)  But this kind of ambiguity is not what’s in question here.  Professor Muller of the University of California Berkeley claimed that what is uncomplicated in Newtonian gravity is ambiguous in Einsteinian gravity.  And we’ll see now that this is false.

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Even in Einstein’s General Relativity, the Earth Orbits the Sun (& the Sun Does Not Orbit the Earth)

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Back before we encountered Professor Richard Muller’s claim that “According to [Einstein’s] general theory of relativity, the Sun does orbit the Earth. And the Earth orbits the Sun,” I was creating a series of do-it-yourself astronomy posts. (A list of the links is here.) Along the way, we rediscovered for ourselves one of the key laws of the planets: Kepler’s third law, which relates the time T it takes for a planet to orbit the Sun to its distance R from the Sun. Because we’ll be referring to this law and its variants so often, let me call it the “T|R law”. [For elliptical orbits, the correct choice of R is half the longest distance across the ellipse.] From this law we figured out how much acceleration is created by the Sun’s gravity, and concluded that it varies as 1/R2.

That wasn’t all. We also saw that objects that orbit the Earth — the Moon and the vast array of human-built satellites — satisfy their own T|R law, with the same general relationship. The only difference is that the acceleration created by the Earth’s gravity is less at the same distance than is the Sun’s. (We all secretly know that this is because the Earth has a smaller mass, though as avid do-it-yourselfers we admit we didn’t actually prove this yet.)

T|R laws are indeed found among any objects that (in the Newtonian sense) orbit a common planet. For example, this is true of the moons of Jupiter, as well as the rocks that make up Jupiter’s thin ring.

Along the way, we made a very important observation. We hadn’t (and still haven’t) succeeded in figuring out if the Earth goes round the Sun or the Sun goes round the Earth. But we did notice this:

This was all in a pre-Einsteinian context. But now Professor Muller comes along, and tells us Einstein’s conception of gravity implies that the Sun goes round the Earth just as much (or just as little) as the Earth goes round the Sun. And we have to decide whether to believe him.

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Earth Orbits the Sun, or Not? Why Coordinates Can’t Be Relevant to the Question.

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We’ve been having some fun recently with Sun-centered and Earth-centered coordinate systems, as related to a provocative claim by certain serious scientists, most recently Berkeley professor Richard Muller. They claim that in general relativity (Einstein’s theory of gravity, the same fantastic mathematical invention which predicted black holes and gravitational waves and gravitational lensing) the statement that “The Sun Orbits the Earth” is just as true as the statement that “The Earth Orbits the Sun”… or that perhaps both statements are equally meaningless.

But, uh… sorry. All this fun with coordinates was beside the point. The truth, falsehood, or meaninglessness of “the Earth orbits the Sun” will not be answered with a choice of coordinates. Coordinates are labels. In this context, they are simply ways of labeling points in space and time. Changing how you label a system changes only how you describe that system; it does not change anything physically meaningful about that system. So rather than focusing on coordinates and how they can make things appear, we should spend some time thinking about which things do not depend on our choice of coordinates.

And so our question really needs to be this: does the statement “The Earth Orbits the Sun (and not the other way round)” have coordinate-independent meaning, and if so, is it true?

Because we are dealing with the coordinate-independence of a four-dimensional spacetime, which is not the easiest thing to think about, it’s best to build some intuition by looking at a two-dimensional spatial shape first. Let’s look at what’s coordinate-independent and coordinate-dependent about the surface of the Earth.

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Is it Meaningful to Say that Earth Goes Round the Sun, or Not? (And Why Is This So Hard…?)

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Is the statement “The Sun Orbits the Earth” false? Not according to professor Richard Muller of the University of California, Berkeley, as I discussed yesterday. Muller argues that Einstein’s theory of general relativity implies that you can view the Sun as orbiting the Earth if you like, or that both the Sun and Earth orbit Venus, or a random point in space, or anything else for that matter. Meanwhile, every science textbook in our kids’ classrooms says that “The Earth Orbits the Sun“. But for all of our discussions yesterday on this subject, we did not yet collectively come to any conclusions as to whether Muller is right or wrong. And we can’t hope to find evidence that the Earth orbits the Sun if the reverse is equally true!

When we’re trying to figure out whether a confusing statement is really true or not, we have to speak precisely. Up to this stage, I haven’t been careful enough, and in this post, I’m going to try to improve upon that. There are a few small but significant points of clarification to make first. Then we’ll look in detail at what it means to “change coordinates” in such a way that would put the Sun in orbit around the Earth, instead of the other way round.

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Sun Around the Earth, or Earth Around the Sun?  Did Einstein Say “It’s all the same”?

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We’re all taught in school that the Earth goes round the Sun.  But if you look around on the internet, you will find websites that say something quite different. There you will find the argument that Einstein’s great insights imply otherwise — that in fact the statements “The Earth goes round the Sun” and “The … Read more

Earth Goes Around the Sun? What’s Your Best Evidence?

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It’s commonly taught in school that the Earth orbits the Sun. So what? The unique strength of science is that it’s more than mere received wisdom from the past, taught to us by our elders.  If some “fact” in science is really true, we can check it ourselves. Recently I’ve shown you how to verify, in … Read more

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