One thing 2017 has going for it is a total solar eclipse. Such eclipses are relatively common, but they often occur in hard to reach areas where not many people live. But the eclipse this Fall will wander across the central US, making it highly accessible. Such solar eclipses are only possible thanks to the favorable orbital geometries of the Sun, Moon and Earth, but its those same geometries that mean such total solar eclipses will eventually come to an end. 

Total eclipses are only possible because the Moon has about the same apparent size as the Sun. The diameter of the Sun is about 400 times larger than the diameter of the Moon, while Moon is about 389 times closer to the Earth than the Sun. So it is possible for the Moon to completely cover the Sun when they line up the right way. It doesn’t happen every month because the Moon’s orbit is tilted a few degrees from the orbital plane of Earth, so sometimes the Moon passes a bit above or below the Sun, and casts no shadow on the Earth.

An annular eclipse showing the “ring of fire.” Credit: Kevin Baird

But even when things line up perfectly, there isn’t always a total eclipse. The Moon’s orbit around the Earth isn’t perfectly circular. Likewise, the Earth’s orbit around the Sun isn’t perfectly circular either. So the apparent sizes of the Sun and Moon vary slightly, and this means sometimes the Moon can appear slightly smaller than the Sun during a solar eclipse. When this happens, it is an annular (ring) eclipse, since a thin outer ring of the Sun can still be seen.

In our present era, both total and annular eclipses can occur. But because of the tidal forces between the Earth and Moon, the Moon is gradually moving farther away from Earth. In the distant past, the Moon was closer, so annular eclipses weren’t possible. As the Moon continues to recede from Earth, total eclipses will only occur when the Moon is at a particularly close point in its orbit (perigee), while the Sun is near its most distant (aphelion). Over millions of years, annular eclipses will become the norm, and total eclipses will become increasingly rare.

So when will the last total eclipse occur? We can’t pin down an exact date, but we can get a basic estimate. The Moon currently moves away from the Earth at a rate of 3.8 centimeters per year. In the past that rate was slower, at about 2.2 centimeters a year. If we use about 3 centimeters per year as an average, then we can simply estimate how long it will take for the Moon’s apparent size at perigee to be the same size as the Sun’s apparent size at aphelion. It comes out to be about a billion years. Of course on that time scale other factors come into play. The Sun is gradually getting hotter, and expanding slowly as a result, which would shorten the time until the last total eclipse. But the Earth is also slowly moving away from the Sun as our star radiates energy and mass. Subtle gravitational effects between the Earth and other planets can also shift Earth’s orbit slightly, as well as the Moons. All of this can come into play. But if we only want a rough estimate, we can safely say that in about a billion years the days of total eclipses will come to an end.

One more reason to see one while you can.

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A day on Earth is longer than it used to be. The increase is tiny. Over the span of a hundred years the Earth’s day will increase by only a few milliseconds. It’s only been in the past few decades that we’ve been able to measure Earth with enough precision to see this effect directly. Using atomic clocks and ultra-precise measurements of distant quasars, we can measure the length of a day to within nanoseconds. Our measurements are so precise that we can observe various fluctuations in the length of a day due to things like earthquakes. Those fluctuations make it a challenge to answer another question. How has Earth’s rotation changed over longer periods of time?  

Variation of the length of a day in recent years. Credit: Wikipedia.

Part of the reason Earth’s days are getting longer is due to the gravitational pull of the Moon on our oceans. The tides slosh against the Earth, gradually slowing its rotation. Over millions of years this means Earth’s day was hour shorter than it is now, thus there were more days in a year than today. We see this effect in the geological record, which tells us an Earth day was about 22 hours long 620 million years ago. Trying to measure the length of a day between the recent and geological era, however, is difficult. Hundreds of years ago clocks weren’t accurate enough to measure this variation, and the length of a day was fixed to its rotation, making any such comparison impossible. But recent work has found a way to study Earth’s changing days.

Although our ancestors of centuries past didn’t have accurate clocks, they were good astronomers. They observed and documented astronomical events such as the occultation of bright stars by the Moon, as well as solar eclipses. The occurrence of these events depends critically on when and where you are. If, for example, an astronomer in one city sees the Moon pass in front of a star one night, an astronomer in a nearby city will only see the Moon pass close to the star. By comparing the observations of these astronomical events with the actual time of their event as calculated from the orbital motions of the Earth and Moon, we know exactly when and where they occurred. Fitting a history of observations together, we can get an average rate for the increase of a day. That turns out to be about 1.8 milliseconds per century.

There are two things that are interesting about this result. The first is that it’s pretty amazing to be able to determine this rate from historical documents. The observations span more than two and a half millennia, and are written in various languages and locations. Gathering them all together and verifying them is an amazing effort. The other is that this rate is actually less than the rate theorized from the tidal effects of our Moon (about 2.3 ms/century). This is likely due to changes in Earth’s overall shape. We know, for example, that the melting of ice since the last ice age (about 10,000 years ago) has released pressure at the Earth’s poles, allowing it to return to a more spherical shape. This would tend to shorten Earth’s days a bit. The combination of these two effects give us the historical rate we see.

Overall this work is a great demonstration of how history can speak to us. If we listen closely, we can even see the changes of time.

Paper: F. R. Stephenson, et al. Measurement of the Earth’s rotation: 720 BC to AD 2015. Proceedings of the Royal Society A. DOI: 10.1098/rspa.2016.0404 (2016)

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Yesterday I talked about how time can be symmetrical in physics. For example, a video of billiard balls colliding looks the same whether played forwards or backwards. This would seem to contradict our everyday experience that time flows ever onward in one direction. We can remember yesterday, but not tomorrow, and if we break our favorite coffee mug we can’t simply unbreak it. This unidirectional nature of events is called the arrow of time, and it’s a bit of a mystery.

In classical Newtonian physics, interactions between simple particles is perfectly time symmetric. Where the direction of time appears is through thermodynamics. For example, if you had a room full of air, with all the air molecules bouncing around, it is very unlikely that all the molecules would at one point clump together in one corner of the room. It’s theoretically possible that all the air molecules happen to have the right trajectory to reach the corner at about the same time, but it’s extremely unlikely. On the other hand, if you started with a pressurized container of air in the corner and then released the air, the molecules would almost certainly spread evenly throughout the room given a bit of time. If you think of these examples as time-reversed siblings of each other, you can see that both are possible, but one is far more probable than the other.

We can express this difference in probability in terms of entropy. The pressure, temperature and volume of the gas in the room is known as its state. Since these are determined by the positions and speeds of all the air molecules in the gas, which is collectively called the microstate of the gas (the state of all the microscopic particles). For a given state of the gas, there are lots of ways the atoms could be moving and bouncing around. As long as the average motion of all the atoms is about the same, then the pressure, temperature and volume of the gas will be the same. This means there are lots of equivalent microstates for a given state of the gas. The more microstates for a given state of the gas, the greater the entropy of the gas, and the more likely the gas will be found in that state. So the arrow of time can be stated as the direction of increasing entropy. This is often expressed as the second law of thermodynamics, which states that the entropy of a system can never decrease.

In quantum theory the arrow of time can be expressed in other ways. In the simple Copenhagen interpretation of quantum theory, a quantum object is in a probabilistic state defined by a wavefunction, which then collapses into a definite state when observed. This collapse of the wavefunction is not reversible, and thus there is a single direction to time. In many ways the Copenhagen interpretation is overly simplistic, but the idea holds in other interpretations as well. For example, quantum systems left to themselves become more entangled over time. So another way to express the arrow of time is to say that it is in the direction of increasing entanglement.

Of course none of this addresses our most direct experience of time’s arrow, which is that we seem to have a conscious experience of the unidirectional flow of time. It’s so deeply ingrained in our personal experience that we intuitively feel that events occur at a specific “now” even though relativity clearly disproves a cosmic present moment. Just why we have such a strong experience of the arrow of time isn’t clear.

But given time, we might be able to figure it out.

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[av_video src=’http://vimeo.com/117815404′ format=’16-9′ width=’16’ height=’9′]

We think of light as being extraordinarily fast. It’s so fast that a beam of light could travel from New York to Los Angeles in about a hundredth of a second. If anything can be called fast, then that ultimate speed limit must surely qualify. And yet, on an astronomical scale, light is tediously slow. Our solar system is a mere speck in the vast scale of the cosmos, and yet light takes time to journey even that speck.

You can get a feel for slowness of light in the video, where the journey of light is shown in real time. From the instant it leaves the Sun’s surface, to just past Jupiter takes nearly three-quarters of an hour. A video showing the journey all the way to Pluto would take more than 5 hours. It would take about 18 hours to reach Voyager 1. All that time to take the smallest step into the universe.

As you watch this video (or part of it) keep in mind that this isn’t a representation of “rocket speed,” or any speed we can remotely achieve. It is the limit of all possible speeds. It is the expanding sphere of influence for anything we do. We are bound by that speed, as is everything else in the universe.

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Imagine you are traveling in a train.  If you were to walk down the aisle of the train, you would be moving at a walking pace relative to the other passengers, but someone watching the train go by would see you and all the other passengers race by at great speed.  In other words, your speed is relative.  It depends on what you are measuring it against.  Relative to another passenger your speed is slow, but relative to the ground your speed is fast.  That, in a nutshell, is relativity.

This concept of relativity dates back at least as far as Galileo (which is why it is sometimes called Galilean relativity).  Before Galileo’s time it may have been known, but it wasn’t a big deal because motion could always be measured relative to the fixed Earth.  But as we learned the Earth moves around the Sun, this raised an interesting philosophical puzzle.  Is there some great cosmic vantage point against which all speeds can be measured, or is it really the case that speed is always relative?  Is there such a thing as absolute speed?

In the mid-1800s, physicists came to understand that light was a wave.  At the time it was thought that all waves travel through a medium.  Sound waves travel through air, water waves travel through water, and so on.  That means there must be a medium through which light travels.  Physicists couldn’t observe this medium, but they called it the luminiferous (light-bearing) ether.  There soon began a hunt to observe the ether, because the ether was a way to measure absolute speed.

If you drop a pebble in a calm lake, you can see the ripples flow outward at a particular speed.  The ripples flow with the same speed in every direction.  But if you were moving in a boat and dropped a pebble into the water, the ripples would seem to move slower in the direction of the boat’s motion, and faster in the opposite direction.  Because of the boat’s motion the speed of the ripples would be different in different directions.  The same would be true with the ether.  Since the Earth must be moving through the ether, the speed of light must be different in different directions.

In 1887, Albert Michelson and Edward Morley performed an experiment to measure this difference in the speed of light.  But what they found was the speed of light was always the same.  No matter what direction light travelled, no matter how they oriented their experiment, the speed of light never changed.  This was not only surprising, it violated the principle of relativity.  After all, if you stand on a moving train and toss a ball, the speed of the ball relative to the ground is the speed of the ball plus the speed of the train, not just the speed of the ball.  Basically what Michelson and Morley found was that if your “ball” was light, the speed of your ball relative to the  train and the speed of the ball relative to the ground is the same.  It seemed the speed of light (and only the speed of light) is absolute, and this made no sense at all.

Then in 1905 Albert Einstein published a solution to the problem, known as special relativity.  He demonstrated that if the speed of light is absolute, then time must be relative, as given in the equation above.  It relates the different times of two observers, say you and me.  In this case, T’ is your time as you measure it, T is your time as I measure it, V is your speed relative to me, and C is the speed of light.  What it says is that your time appears slower to me than it does to you.  The faster you move relative to me, the slower your time appears to me.  This sounds insane.  How can time be relative?  It is, however, very real.

We can see how this works if we imagine a clock made with light.  Take two mirrors and place one above the other and facing each other, then bounce a pulse of light between them.  We can measure time by counting the number of times the light bounces off a mirror.  Each bounce is like the tick or tock of a mechanical clock.  If you could watch the pulse of light, you would see it move up and down between the mirrors at the speed of light.  Up and down at a constant rate.  Now suppose you took your clock on a fast moving train.  Standing in the aisle of the train, you would see the light pulse move up and down at the same rate as before.  Up and down at the speed of light.

But as I watch you speed past, I see something slightly different.  I would also see the pulse move at the speed of light, but from my view the light can’t move straight up and down because it must also be moving along with you.  I would see the pulse move diagonally up then diagonally down, which is a slightly longer distance between each bounce.  That means it would take the light longer to travel from bounce to bounce.  So from my point of view the ticks and tocks of your clock are slower than the ticks and tocks as you see them.  Your clock appears to be running slow because of your motion relative to me.  The faster you move relative to me, the more your clock will slow down from my point of view.

You might think this effect only occurs because the clock relied on light to tell time, but this effect is real for everything.  If you have a GPS in your phone or car, you rely on relative time being true every time you use it.  A GPS determines your location by receiving signals from satellites orbiting the Earth.  Those satellites broadcast their time and location, which your GPS uses to determine your position, so it is vitally important that the satellites broadcast the proper time.  But the satellites are moving at high speed relative to you, which means their clocks run slightly slow.  To give you the accurate time the satellites have to account for that slowdown effect.  When your phone tells you where the nearest coffee shop is, it’s using special relativity to do it.

So how does all this relate to astrophysics?  It’s one of the ways we know the universe is expanding.  When we observe the light from distant galaxies, the light appears more red than we would expect.    The more distant the galaxies, the more their light is redshifted.  This effect is known as the Doppler effect, and it is due to the fact that the galaxy is moving away from us.  The galaxies are moving away from us because the universe is expanding.  But suppose over long periods of time light just naturally reddens?  How do we know astronomers are not being fooled?

Special relativity tells us we’re not.  We can observe supernovae in nearby and distant galaxies, and what we find is that when a supernova goes off in a distant galaxy it happens more slowly than a supernova in a closer galaxy.  The time of a distant supernova appears slower to us because the distant galaxy is moving away from us at a faster rate than the closer galaxy.

Strange as it is, special relativity works.  Time after time.

Tomorrow:  Flying kites in a thunderstorm leads us to a single elegant theory describing lightning, magnets and light.  Don’t try this at home, just stay tuned for Part 4.

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In our modern age, we measure time by clocks calibrated to an international standard.  With the exception of the occasional leap second, each day is exactly 24 hours long.  So you might figure that the time between noon on Monday and noon on Tuesday is likewise 24 hours, but things are not quite so simple.

If we consider “noon” to be the time at which the sun is highest in the sky (which we can measure by a sundial), rather than “when the clock reads 12,” then the time between successive noons is not quite 24 hours.  Relative to our clock, our sundial will seem to run a bit fast on some days, and a bit slow on others.  To relate sundial time to clock time, we therefore need a correction known as the equation of time.  I’ve plotted this equation in the figure below, and it shows the correction factor needed at various times of the year.

The reason for this correction is because of two factors.  The first is that Earth’s orbit is not quite a perfect circle but rather a slight ellipse.  For part of the year, it is a bit closer to the Sun than its average distance, and for part of the year it is a bit further away.  While the Earth rotates on its axis at essentially a constant rate, the Earth’s speed around the Sun is not constant.  Instead, it orbits a bit faster when it is closer to the sun and slower when farther away.  Because the Earth is orbiting the Sun, the Earth has to rotate about a degree more than 360 degrees to go from noon to noon.  On days when it moves faster, it has to rotate a bit more than that, and on days when it moves more slowly, it has to rotate a bit less.

The second factor is due to the tilt of the Earth’s axis.  Because of this tilt, the Sun appears higher in the sky during the Summer months and lower in the Winter months.  This means from one noon to the next, the Sun is a bit higher or a bit lower depending on the season.  That daily shift means the time at which the Sun is highest in the sky (noon) is a bit early or a bit late.

The combination of these two factors creates the equation of time you see above. It is the ebb and flow of the celestial clock as our home rounds the Sun.

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