Of Particular Significance

Tag: sun

I hope that a number of you will be able to see the total solar eclipse next Monday, April 8th. I have written about my adventures taking in a similar eclipse in 1999, an event which had a profound impact on me. Perhaps my experience might give you some things to think about that go well beyond the mere scientific.

Meanwhile, for those who can only see a partial solar eclipse that day, there’s still something really cool (and very poorly appreciated!) that you can do that cannot be done on an ordinary day! Namely, you can easily estimate the size of the Moon, and then quickly go on to estimate how far away it is. This is daylight astronomy at its best!

Side note for those in the Boston area: I’m speaking about my new book at Harvard on Wednesday April 3rd.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON April 1, 2024

(This is the fourth post in a series, though it can be read independently; here are post #1 , post #2 , and post #3.)

For many years, I thought that measuring the distance to the Sun was quite difficult for a non-astronomer. I had the impression that it requires precision measurements, often involving telescopes or information from satellites, and that it was only easy to obtain a minimum distance and a maximum distance that were still quite far apart, as I explained in my last post.

But it’s not true. As I’ll explain today, it turns out that anyone can estimate the distance to the Sun, at night, with nothing more than the naked eye, basic reasoning, and… meteors.

Just from the fact that a long meteor crosses the sky in a few seconds, you can infer that the Earth-Sun distance is something like 100 million miles (km). If the Sun were only 10 million miles (km) away, the meteors would lazily drift among the stars, only a bit faster than the motions of the space station and other satellites, which take minutes to cross the sky. Meanwhile, if the Sun were a billion miles (km) away, then meteors would flash across the sky in a fraction of a second.

With a little more work and knowledge, you can use meteors to make an estimate of the Sun’s distance that’s well within a factor of 2 of the truth. It’s not even that hard to get a precise measurement that’s good to 10% or so.

It may seem odd that one can use such little specks of dust in the Earth’s atmosphere to determine, without a telescope, how far it is to the Sun. But in fact the method is simple. It’s so simple that it must have been pointed out two centuries ago. Curiously, though, I’ve never seen it written down anywhere. It seems to be little-known, even to scientists.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 23, 2024

(This is the third post in a series, though it can be read independently; here are post #1 and post #2; and post #4 blows this one out of the water, so don’t miss it!)

Measuring the distance to the Sun is challenging, for reasons explained in my last post. Long ago, the Greek thinker Aristarchus proposed a geometric method, which involves estimating the Moon’s sunlit fraction on a certain date. Unfortunately, because the Sun is so far away, his approach isn’t powerful enough; Aristarchus himself underestimated the distance. [This last remained true for later astronomers before the 17th century, though they got closer to the truth, presumably by using more precise methods than you or I could easily apply. I doubt anyone truly found a maximum possible distance to the Sun just using geometry.] The best we can do, using Aristarchus’ method and our naked eyes, is determine a minimum possible distance to the Sun: a few million miles.

Figure 1: A simple application of Aristarchus’ method tells us that the minimum distance to the Sun is a few million miles (km), ruling out the red region. But the entire green region is still allowed.

Today we’ll see how to obtain a maximum distance to the Sun, using an approach suggested in the previous post: by measuring speeds. Specifically, we’ll make use of a speed that the ancient astronomers weren’t aware of: the speed of light, also known as the cosmic speed limit c. That’s 186,000 miles (300,000 km) per second, or 5.9 trillion miles (9.5 trillion km) per year. We’ll find the Sun’s distance is less than 12 billion miles… still much larger than its true distance, but a significant improvement on our starting point!

Figure 2: By the end of this post, we’ll know a maximum possible distance for the Sun, too.
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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 19, 2024

A couple of years ago I wrote a series of posts (see below) showing how anyone, with a little work, can verify the main facts about the Earth, Moon, Sun and planets. This kind of “Check-It-Yourself” astronomy isn’t necessary, of course, if you trust the scientists who write science textbooks. But it’s good to know you don’t have to trust them, because you can check it on your own, without special equipment.

The ability to “do it yourself” is what makes science, as a belief system, most robust than most other belief systems, past and present. It also explains why there aren’t widely used but competing scientific doctrines that fundamentally disagree about the basics of, say, the Sun and its planets. Although science, like religion, is captured in texts and teachings that have been around for generations, one doesn’t need to have faith in those books, at least when it comes to facts about how the world works nowadays. The books may be from the past, but most of what they describe can be independently verified now. In many cases, this can be done by ordinary people without special training, as long as they have some guidance as to how to do it. The purpose of the “Check-It-Yourself-Astronomy” series is to provide that guidance.

As I showed, nothing more than pre-university geometry, trigonometry, and algebra, along with some star-gazing and a distant friend or two, is required to

However this list is missing something important. From these methods, one can only obtain the ratios of planetary sizes to each other and to the Sun’s size, and the ratios of distances between planets and the Sun. Yet I did not explain how to measure the distance from the Earth to the Sun, or the distance from the Sun to any of the other planets, or the sizes of the other planets. It’s difficult to learn these things without sophisticated equipment and extremely precise measurements; the easiest things to measure about the planets and the Sun — their locations, motions and sizes — aren’t sufficient. (I’ll explain why they’re not sufficient in my next post.)

But shouldn’t there be a way around this problem?

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 16, 2024

The Moon has a four-week cycle; it is full every four weeks (actually every 29.5 days). But ocean tides exhibit a two-week cycle; they are large one week and then smaller the next.

Specifically, as in Fig. 1 below, ocean tides are stronger (“spring tides”) around New Moon and Full Moon than they are at First Quarter Moon and Last Quarter Moon (“neap tides”). The pattern is seen, roughly at least, all around the world (though the details are not simple, as they depend on the shape of the coastline and other factors.)

Figure 1: Tides in Anchorage, Alaska, USA, during October 2023; the blue line shows how the water rises and falls about twice a day (note the vertical columns are each two days wide!) The pattern of strong and weak tides on alternate weeks is clearly visible. New Moon occurred on October 14 and Full Moon on October 28th, just before the peak tides.

What’s behind this pattern? And what does it tell us about the Sun and Moon that we wouldn’t otherwise easily know? Perhaps surprisingly, it tells us that the average mass density of the Sun — its mass divided by its volume — is only a little smaller than the average mass density of the Moon. Here’s why.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 12, 2024

The fusing of small atomic nuclei into larger ones, with the associated release of particles carrying a lot of motion-energy, is the mechanism that powers the Sun’s furnace, and that of other stars. This was first suspected in the 1920’s, and confirmed in the 1930s.

Nuclear fission (the breaking of larger atomic nuclei into smaller pieces) was discovered in the 1930s, and used to generate energy in 1942. Work on fission in settings both uncontrolled (i.e. bombs) and controlled (ie. power plants) proceeded rapidly; bombs unfortunately were quickly designed and built during World War II, while useful power plants were already operating by 1951. Meanwhile work on fusion also proceeded rapidly; in the uncontrolled setting, the first bomb using fusion (triggered by a fission bomb!) was already made in 1951, and in a flash of a decade, huge numbers of hydrogen bombs filled the arsenals of superpowers large and small. But controlled fusion for power plants… Ah.

Had it been as easy to control fusion as it was to control fission, we’d have fusion plants everywhere; fossil fuels would be consigned only to certain forms of transportation, and the climate crisis would be far less serious than it is right now. But unfortunately, it has been 70 years of mostly bad news — tragic news, really, for the planet.

But finally we have a little glimmer of hope. On December 5th, somebody finally managed, without using a bomb, to get more fusion-generated energy out of an object than the energy they had to put into it.

[UPDATE: Not really. Though this was a success and a milestone, it wasn’t nearly as good as advertised. Yes, more energy came out of the fusing material than was put into the fusing material. But it took far more energy to make the necessary laser light in the first place — 300 megajoules of energy off the electricity grid, compared to a gain from the fusing material of about 1 megajoule. So overall it was still a big net loss, even though locally, at the fusing material, it was a net gain. See this link, in particular the third figure, which shows that the largest energy cost was electricity from the grid to run the lasers. In short, well, it’s still a good day for fusion, but we are even further from power plants than we were led to believe today.]

Poster Child for Particle Physics

In the Sun and similar stars, fusion proceeds through several processes in which protons (the nuclei of the simplest form of hydrogen) are converted to neutrons and combine with other protons to form mainly helium nuclei (two protons and two neutrons). Other important nuclei are deuterium D (a version of hydrogen with a proton and neutron stuck together), tritium T (another version with a proton plus two neutrons — which is unstable, typically lasting about 12 years), and Helium-3 (two protons plus one neutron.)

Fusion is a fascinating process, because all four of the famous forces of nature are needed. [The fifth, the Higgs force, plays no role, though as is so often the case, the Higgs field is secretly crucial.] In a sense, it’s a poster child for our understanding of how the cosmos works. Consider sunshine:

  1. We need gravity to hold the Sun together, and to crush its center to the point that its temperature reaches well over ten million degrees.
  2. We need electromagnetism to produce the light that carries energy to the Sun’s surface and sunshine to Earth.
  3. We need the strong nuclear force to make protons and neutrons, and to combine them into other simple nuclei such as deuterium, tritium and helium.
  4. We need the weak nuclear force to convert the abundant protons into neutrons (along with a positron [i.e. an anti-electron] and a neutrino.)

How can we be sure this really happens inside the Sun? There are quite a few ways, but perhaps the most direct is that we observe the neutrinos, which (unlike everything else that’s made in the process) escape from the Sun’s core in vast numbers. Though very difficult to detect on Earth, they are occasionally observed. By now, studies of these neutrinos, as here by the Borexino experiment, are definitive. Everything checks out.

In the recent experiment on Earth, gravity’s role is a little more indirect — obviously we wouldn’t have a planet on which to live and laboratories in which to do experiments without it. But it’s electromagnetism which does the holding and crushing of the material. The role of the strong and weak nuclear forces is similar, though instead of starting with mostly protons, the method that made fusion this week uses the weak nuclear force long before the experiment to make the neutrons needed in deuterium and tritium. The actual moment of fusion involves the strong nuclear force, in which

  • D + T –> He + n

i.e. one deuterium nucleus plus one tritium nucleus (a total of two protons and three neutrons) are recombined to make one helium nucleus and one neutron, which come out with more motion-energy than the initial D and T nuclei start with.

The Promise of Endless Cheap Safe[r] Power?

The breakthrough this week? Finally, after decades of promises and disappointments, workers at a US lab, Lawrence Livermore Laboratory in California, working at the National Ignition Facility, have gotten significantly more energy out of fusion than they put in. How this works is described by the lab here. The steps are: make a pellet stocked with D and T; fire up a set of lasers and amplify them to enormous power; aim them into a chamber containing the pellet, heating the chamber to millions of degrees and causing it to emit X-rays (high-energy photons); the blast of X-rays blows off the outer layer of the pellet, which [action-reaction!] causes the inner core of the pellet to greatly compress; in the high temperature and density of the pellet’s core, fusion spontaneously begins and heats the rest of the pellet, causing even more fusion.

Not as easy as it sounds. For a long time they’ve been getting a dud, or just a little fusion. But finally, the energy from fusion has exceeded the energy of the initial lasers by a substantial amount — 50%.

This one momentary success is far from a power plant. But you can’t make a power plant without first making power. So December 5th, eighty years and three days after fission’s first good day, was a good day for fusion on Earth, maybe the first one ever.

If this strategy for making fusion will ever lead to a power plant, this process will have to repeated over and over very rapidly, with the high-energy particles that are created along the way being directed somewhere where they can heat water and turn a steam turbine, from which electric current can be created as it is in many power plants. Leaving aside the major technical challenges, one should understand that this does not come without radioactive pollution; the walls of the container vessel in which the nuclear reactions take place, and other materials inside, will become radioactive over time, and will have to be disposed of with care, as with any radioactive waste. But it’s still vastly safer than a fission power plant, such as are widespread today. Why?

First, the waste from a fission plant is suitable for making nuclear weapons; it has to be not only buried safely but also guarded. Waste from a fusion plant, though still radioactive, is not useful for that purpose.

Second, if a fission plant malfunctions, its nuclear chain-reaction can start running away, getting hotter and hotter until the fuel melts, breaks through the vessel that contains it, and contaminates ground, air and water. By contrast, if a fusion plant malfunctions, its nuclear reactions just… stop.

And third, mining for uranium is bad for the environment (and uranium itself can be turned into a fuel for nuclear weapons.) Mining for hydrogen involves taking some water and passing electric current through it. Admittedly it’s a bit more complicated than that to get the deuterium and especially the tritium you need — the tritium be obtained from lithium, which does require mining — but still, less digging giant holes into mountains and contaminating groundwater with heavy metals.

Meanwhile, both forms of nuclear power have the advantage that they don’t dump loads of carbon into the atmosphere, and avoid the kind of oil spills we saw this week in Kansas.

So even though we are a long way from having nuclear fusion as a power source, and even though there will be some nuclear waste to deal with, there are good reasons to note this day. Someday we might look back on it as the beginning of a transformed economy, a cleaner atmosphere, and a saved planet.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON December 13, 2022

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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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON June 1, 2022

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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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON May 24, 2022

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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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON May 5, 2022

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.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON May 4, 2022

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