Category Archives: general relativity

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

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.

Continue reading

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

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 Sun goes round the Earth” are equally true, or equally false, or equally meaningless.

Here, for example, is this statement as written in Forbes by professor Richard Muller at the University of California, Berkeley.   It opens as follows: “According to the general theory of relativity, the Sun does orbit the Earth. And the Earth orbits the Sun.”  I invite you to read the rest of it; it’s not long.

What’s his point?  In Einstein’s theory of gravity (“general relativity”), time and three-dimensional space combine together to form a four-dimensional shape, called “space-time”, which is complex and curved.  And in general relativity, you can choose whatever coordinates you want on this space-time. 

So you are perfectly free to choose a set of coordinates, according to this point of view, in which the Earth is at the center of the solar system.  In these coordinates, the Earth does not move, and the Sun goes round the Earth.  The heliocentric picture of the planets and the Sun merely represents the simplest choice of coordinates; but there’s nothing wrong with choosing something else, as you like. 

This is very much like saying that to use latitude and longitude on the Earth is just a choice. I could use whatever coordinates I want.  The equator is special in the latitude-longitude system, since it lies at latitude=0; the poles are special too, at latitude +90 degrees and -90 degrees. But I could just as well choose a coordinate system in which the equator and poles don’t look special at all.

And so, after Einstein, the whole Copernican question — “is the solar system geocentric or heliocentric?” — is a complete red herring… much ado about nothing. As Muller argues in his article, “the revolution of Copernicus was actually a revolution in finding a simpler way to depict the motion, not a more correct way.

Well? Is this true? If not, why not? Comments are open.

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

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 just over a dozen steps, the basics of planetary astronomy; you can

But important unanswered questions remain.  Perhaps the most glaring is this: Does the Earth orbit the Sun, or is it the other way around?  Or do they orbit each other around a central point?  The Sun’s motion in the sky relative to the stars, which exhibits a yearly cycle, indicates (when combined with evidence that the stars are, on yearly time scales, fixed) that one of these three must be true, at least roughly.  But which one is it?

We saw that the Earth satisfies Kepler’s law for objects orbiting the Sun; meanwhile the Sun does not satisfy the similar law for objects orbiting the Earth.  This argues that Earth orbits the Sun due to the latter’s gravity, but the logic is circumstantial. Isn’t there something more direct, more obvious or intuitive, that we can appeal to? 

I won’t count high-precision telescopic observations that can reveal tiny effects, such as stellar aberration, stellar parallax, and Doppler shifts in light from other stars.  They’re great, but very tough for non-experts to verify. Isn’t there a simpler source of evidence for this very basic claim about nature — something we can personally check?

Your thoughts? Comments are open. [Be careful, when making suggestions, that you are not assuming that gravity is the dominant force between the Earth and the Sun. That’s something you have to prove. Are you sure there are no additional forces pinning the Earth in place, and/or keeping the Sun in motion around the Earth? What’s your evidence that they’re absent?]

From Kepler’s Law to Newton’s Gravity, Yourself — Part 2

Sometimes, when you’re doing physics, you have to make a wild guess, do a little calculating, and see how things turn out.

In a recent post, you were able to see how Kepler’s law for the planets’ motions (R3=T2 , where R the distance from a planet to the Sun in Earth-Sun distances, and T is the planet’s orbital time in Earth-years), leads to the conclusion that each planet is subject to an acceleration a toward the Sun, by an amount that follows an inverse square law

  • a = (2π)2 / R2

where acceleration is measured in Earth-Sun distances and in Earth-Years.

That is, a planet at the Earth’s distance from the Sun accelerates (2π)2 Earth-distances per Earth-year per Earth-year, which in more familiar units works out (as we saw earlier) to about 6 millimeters per second per second. That’s slow in human terms; a car with that acceleration would take more than an hour to go from stationary to highway speeds.

What about the Moon’s acceleration as it orbits the Earth?  Could it be given by exactly the same formula?  No, because Kepler’s law doesn’t work for the Moon and Earth.  We can see this with just a rough estimate. The time it takes the Moon to orbit the Earth is about a month, so T is roughly 1/12 Earth-years. If Kepler’s law were right, then R=T2/3 would be 1/5 of the Earth-Sun distance. But we convinced ourselves, using the relation between a first-quarter Moon and a half Moon, that the Moon-Earth distance is less than 1/10 othe Earth-Sun distance.  So Kepler’s formula doesn’t work for the Moon around the Earth.

A Guess

But perhaps objects that are orbiting the Earth satisfy a similar law,

  • R3=T2 for Earth-orbiting objects

except that now T should be measured not in years but in Moon-orbits (27.3 days, the period of the Moon’s orbit around the Earth) and R should be measured not in Earth-Sun distances but in Moon-Earth distances?  That was Newton’s guess, in fact.

Newton had a problem though: the only object he knew that orbits the Earth was the Moon.  How could he check if this law was true? We have an advantage, living in an age of artificial satellites, which we can use to check this Kepler-like law for Earth-orbiting objects, just the way Kepler checked it for the Sun-orbiting planets.  But, still there was something else Newton knew that Kepler didn’t. Galileo had determined that all objects for which air resistance is unimportant will accelerate downward at 32 feet (9.8 meters) per second per second (which is to say that, as each second ticks by, an object’s speed will increase by 32 feet [9.8 meters] per second.) So Newton suspected that if he converted the Kepler-like law for the Moon to an acceleration, as we did for the planets last time, he could relate the acceleration of the Moon as it orbits the Earth to the acceleration of ordinary falling objects in daily life.

Continue reading

Celebrating 2/22/22 (or was it 22/2/22)?

I hope you all had a good Twosday. Based on what I saw on social media, yesterday was celebrated widely in many parts of the world that use Pope Gregory’s calendar. I had two sandwiches to in honor of the date, and two scoops of ice cream.

In the United States, the joy continues today, it being now 2/23/22. Though not quite as wonderful as 2/22/22 on Tuesday, it’s still another nicely symmetric number worthy of note. In fact we get a full week of this, including 2/24/22 tomorrow, 2/25/22 on Friday, and so on, concluding on 2/29/22 … uhh, (oops) I mean, 2/28/22, because 2022 is not a Leap Year. For some reason.

In other countries, where it is 23/2/22, the celebration is over for now … because without symmetry, where’s the love? Ah, but they’re just more patient. They’ll get their chance in a month, when it’s 22/3/22, a date that will go unnoticed in the USA but not in Europe.

But what, exactly, are we getting so jazzed about? After all, what is the significance of it being the 22nd or 23rd date of the second month of a year labelled 2022? Every single bit of this is arbitrary. Somebody, long ago, decided January would be the first month, making February month number 2; but it wasn’t that long ago that March was the first month, which is why September, October, November and December (7, 8, 9, and 10) have their names. It’s arbitrary that January has 31 days instead of 30; had it been given thirty, the day we call the “22nd” would have been the “23rd” of February, and our celebration would have been one day earlier. And 2022 is arbitrary two too. Other perfectly good calendars referred to yesterday by a completely different day, month and year.

This, my friends, is exactly what General Relativity (and the rest of modern physics) tells you not to do. This is about putting all of your energies and your focus on your coordinate system — on how you represent reality, instead of on reality itself. The coordinate system is arbitrary; what matters is what actually happens, not how you describe what happens using some particular way of measuring time, or space, or anything else. To get excited about the numbers that happen to appear on your measuring stick is to put surface ahead of substance, math ahead of physics, magic ahead of science. It’s as bad as getting excited about how a word is spelled, or even what word is used to represent an object; a rose by any other name.

But we humans are not designed to think this way, it seems. We cheer when we’ve driven a thousand miles, a milestone (hah) which combines the definition of mile (arbitrary) with the fascination with the number 1,000 (which only looks like an interesting number if you count with ten fingers, rather than 12 knuckles, as the Babylonians did, or eight tentacles, as certain intelligent sea creatures might do.) We get terribly excited about numbers such as 88, or 666, which similarly depend on our having chosen to count on our ten fingers. A war was ended on 11/11 at 11:00 (and one was started on 22/2/22 — coincidence?)

Celebrating birthdays is a little better. No matter what calendar you choose, or whether it even lasts a year (as, for example, in Bali), the Sun appears to move across the sky, relative to the distant stars, in a yearly cycle. When it comes back to where it was, a year has passed. If we define your age to be the number of solar cycles you’ve experienced, then that means something, no matter what calendar you prefer. Your birthday means something too as long as we define it not by the arbitrary calendar but by the position of the Sun on the day of your birth.

Similarly, the solstices that mark the days with the shortest daylight and shortest darkness, and the equinoxes that have days and nights equal in duration, are independent of how you count hours or minutes or seconds, or even days. It doesn’t matter if your day has 24 equal hours, or if you divide your daylight into 12 and your darkness into 12, as used to be the case. It doesn’t matter what time zones you may have arbitrarily chosen. If you want to mark days, you can use the time that the Sun is highest in the sky to define “noon”, and count noons. A year is just over 365 noons, no matter what your calendar. The time from solstice to solstice is about half that. But the date we call “December 25th” does not sit on a similarly fundamental foundation; it shifts when there’s a leap year, and sometimes it’s three days after the solstice and sometimes four. Many other holidays, driven by Moon cycles rather than a Sun cycle, are even less grounded in the cosmos.

Being too focused on coordinates can cause a lot of trouble. The flat maps that try to describe our spherical Earth make all sorts of things seem to be true that aren’t. They all make the shortest path between two points impossible to guess. Some wildly exaggerate Greenland’s size and minimize the entire African continent. Most of them make it difficult to imagine what travel over the north or south pole is like, because there’s a sort of “coordinate singularity” there — a single point is spread out over a whole line at the top of the map, and similarly at the bottom, which makes places that are in fact very close together seem very far apart.

A coordinate singularity of a more subtle type prevented scientists (Einstein among them) from realizing for decades that black holes, which were once called “frozen stars,” have an interior, and that you could potentially fall in. The coordinates originally in use made it seem as though time would stop for someone reaching the edge of the star. Bad coordinates can obscure reality.

Physics, and science more generally, pushes us to focus on what really happens — on events whose existence does not depend on how we describe them. It’s a lesson that we humans don’t easily learn. While it’s fine to find a little harmless and silly joy at non-events such as 22/2/22 or 2/22/22, that’s as far as it should go: anything that depends on your particular and arbitrary choice of coordinate system cannot have any fundamental meaning. It’s a lesson from Einstein himself, advising us on what not two do.