For my August 2017 diary, go here.

Diary — September 2017

John Baez

September 1, 2017

Launched 40 years ago, the Voyagers are our longest-lived and most distant spacecraft. Voyager 2 has reached the edge of the heliosphere, the realm where the solar wind and the Sun's magnetic field live. Voyager 1 has already left the heliosphere and entered interstellar space! A new movie, The Farthest, celebrates the Voyagers' journey toward the stars:

What has Voyager 1 been doing lately? I'll skip its amazing exploration of the Solar System....

Leaving the realm of planets

On February 14, 1990, Voyager 1 took the first ever 'family portrait' of the Solar System as seen from outside. This includes the famous image of planet Earth known as the Pale Blue Dot:

On February 17, 1998, Voyager 1 reached a distance of 69 AU from the Sun b 69 times farther from the Sun than we are. At this moment it overtook Pioneer 10 as the most distant spacecraft from Earth! Traveling at about 17 kilometers per second, it was moving away from the Sun faster than any other spacecraft. It still is.

That's 520 million kilometers per year — hard to comprehend. I find it easier to think about this way: it's 3.6 AU per year. That's really fast... but not if you're trying to reach other stars. It will take 20,000 years just to go one light-year.

Termination shock

As Voyager 1 headed for interstellar space, its instruments continued to study the Solar System. Scientists at the Johns Hopkins University said that Voyager 1 entered the termination shock in February 2003. This is a bit like a 'sonic boom', but in reverse: it's the place where the solar wind drops to below the speed of sound. Yes, sound can move through the solar wind, but only sound with extremely long wavelengths — nothing humans can hear.

Some other scientists expressed doubt about this, and the issue wasn't resolved until other data became available, since Voyager 1's solar-wind detector had stopped working in 1990. This failure meant that termination shock detection had to be inferred from the other instruments on board. We now think that Voyager 1 reached the termination shock on December 15, 2004 — at a distance of 94 AU from the Sun.

Heliosheath

In May 2005, a NASA press release said that Voyager 1 had reached the heliosheath. This is a bubble of stagnant solar wind, moving below the speed of sound. It's outside the termination shock but inside the heliopause, where the interstelllar wind crashes against the solar wind.

On March 31, 2006, amateur radio operators in Germany tracked and received radio waves from Voyager 1 using a 20-meter dish. They checked their data against data from the Deep Space Network station in Madrid, Spain and yes — it matched. This was the first amateur tracking of Voyager 1!

On December 13, 2010, the the Low Energy Charged Particle device aboard Voyager 1 showed that it passed the point where the solar wind flows away from the Sun. At this point the solar wind seems to turn sideways, due to the push of the interstellar wind. On this date, the spacecraft was approximately 17.3 billion kilometers from the Sun, or 116 AU.

In March 2011, Voyager 1 was commanded to change its orientation to measure the sideways motion of the solar wind. How? I don't know. Its solar wind detector was broken.

But anyway, a test roll done in February had confirmed the spacecraft's ability to maneuver and reorient itself. So, in March it rotated 70 degrees counterclockwise with respect to Earth to detect the solar wind. This was the first time the spacecraft had done any major maneuvering since the family portrait photograph of the planets was taken in 1990.

After the first roll the spacecraft had no problem in reorienting itself with Alpha Centauri, Voyager 1's guide star, and it resumed sending transmissions back to Earth.

On December 1, 2011, it was announced that Voyager 1 had detected the first Lyman-alpha radiation originating from the Milky Way galaxy. Lyman-alpha radiation had previously been detected from other galaxies, but because of interference from the Sun, the radiation from the Milky Way was not detectable.

Puzzle. What the heck is Lyman-alpha radiation?

On December 5, 2011, Voyager 1 saw that the Solar System's magnetic field had doubled in strength, basically because it was getting compressed by the pressure of the interstellar wind. Energetic particles originating in the Solar System declined by nearly half, while the detection of high-energy electrons from outside increased 100-fold. At this point Voyager 1 was 113 AU from the Sun.

Heliopause and beyond

In June 2012, NASA announced that the probe was detecting even more charged particles from interstellar space. This meant that it was getting close to the heliopause: the place where the gas of interstellar space crashes into the solar wind.

Voyager 1 actually crossed the heliopause in August 2012, although it took another year to confirm this. It was 121 AU from the Sun.

In about 300 years Voyager 1 will reach the Oort cloud, the region of frozen comets. It will take 30,000 years to pass through the Oort cloud. Though it is not heading towards any particular star, in about 40,000 years it will pass within 1.6 light-years of the star Gliese 445.

NASA says that

The Voyagers are destined — perhaps eternally — to wander the Milky Way.
That's an exaggeration. The Milky Way will not last forever. In just 3.85 billion years, before our Sun becomes a red giant, the Andromeda galaxy will collide with the Milky Way. In just 100 trillion years, all the stars in the Milky Way will burn out. And in just 10 quintillion years, the Milky Way will have disintegrated, with all stars either falling into black holes or being flung off into intergalactic space.

But still: the Voyagers' journeys are just beginning. Let's wish them a happy 40th birthday!

My story here is adapted from this Wikipedia article:

You can download PDFs of posters commemorating the Voyagers here:

September 10, 2017

On Friday, NASA will crash the Cassini spacecraft into Saturn! You can watch:

Go here to watch:

If you're impatient, watch this now:

If this doesn't make you shed a tear, you've got no heart. Since 2004, Cassini has been taking magnificent photos of Saturn, its moons, and its rings. It successfully sent the Huygens probe down to the methane oceans of Titan; it swooped past the steam plumes of the geysers on Enceladus, it discovered the huge hexagon on Saturn's north pole, and more!

But now it is running out of propellant and losing its ability to manuever. To prevent it from crashing into the moon Enceladus and perhaps infecting its ice-covered ocean, NASA wants Cassini to burn up and fall into Saturn. So in April 2017 they put it on an impact course: The Grand Finale.

They shot Cassini past Titan and used the giant moon's gravity to fling the spacecraft toward Saturn. Since then it's made 22 daring dives between the Saturn and its rings — one each week! I hope you saw this wonderful image from its latest plunge:

Over millennia, gravity organizes chunks of ice floating in space into amazingly delicate structures... mathematics in action!

Soon Cassini will fall into Saturn. Its final images will have been sent to us several hours before... but even as makes its fatal dive, it will be sending new data in real time. Its mass spectrometer will sample Saturn's atmosphere until Cassini loses contact and burns up like a meteor, finally becoming part of the planet it has been circling for years.

September 11, 2017

The dreamer awakens

After shooting past Pluto, the New Horizons spacecraft went to sleep. But on September 11 it woke up. It's preparing to visit something in the outskirts of the Solar System.

This thing is called 2014 MU69. It was discovered just 3 years ago. The picture shows what we saw as stars moved behind it in July... and a guess of its outline. It could be two things, or one shaped like a dumbbell.

What is it? It's called a cubewano. There are lots of them in the Kuiper Belt, but we don't know much about them... which is why we're taking a look.

Maybe cubewanos are made of ice, but in early July we took a good look at 2014 MU69 with the Hubble telescope, and we know it's red. That's actually not surprising. Lots of things out there are covered with reddish organic compounds called tholins. I wish I understood that better. But anyway, cubewanos could be balls of ice, or ice and rock, covered with tholins.

Back to New Horizons:

NASA's New Horizons spacecraft — which visited Pluto in July, 2015 — was placed in hibernation on April 7, 2017. The craft is set to be awoken today (September 11, 2017). In the meantime, the science and mission operations teams have been developing detailed command loads for New Horizon's next encounter, a nine-day flyby of the Kuiper Belt object 2014 MU69 on New Year's Day, 2019. Among other things, the mission has now set the flight plan and the distance for closest approach, aiming to come three times closer to MU69 than it famously flew past Pluto in 2015.

Hibernation reduced wear and tear on the spacecraft's electronics, lowered operations costs and freed up NASA Deep Space Network tracking and communication resources for other missions. But New Horizons mission activity didn't entirely stop during the hibernation period. While much of the craft is unpowered during hibernation, the onboard flight computer has continued to monitor system health and to broadcast a weekly beacon-status tone back to Earth. About once a month, the craft has sent home data on spacecraft health and safety. Onboard sequences sent in advance by mission controllers will eventually wake New Horizons to check out critical systems, gather new Kuiper Belt science data, and perform any necessary course corrections.

I don't know exactly why they woke it up just now. Can you find out?

And back to 2014 MU69:

Its orbital period is slightly more than 295 years and it has a low inclination and low eccentricity compared to other objects in the Kuiper belt. These orbital properties mean that it is a cold classical Kuiper belt object which is unlikely to have undergone significant perturbations. Observations in May and July 2015 as well as in July and October 2016 greatly reduced the uncertainties in the orbit. The updated orbit parameters are available in the MPC database.

2014 MU69 has a red spectrum, making it the smallest Kuiper belt object to have its color measured.

Between 25 June and 4 July 2017, the Hubble Space Telescope spent 24 orbits observing 2014 MU69, in an effort to determine its rotation period and further reduce the orbit uncertainty. First results show that the brightness of 2014 MU69 varies by less than 20 percent as it rotates. This places significant constraints on the axis ratio of 2014 MU69 to <1.14 assuming an equatorial view. Together with the fact that its shape has been shown to be very irregular, the small amplitude indicates that its pole is pointed towards Earth. This means that the timing of the New Horizons fly-by does not need to be adjusted to look at the "larger" axis of the object, simplifying the engineering of the fly-by significantly. The small amplitude makes it difficult to uniquely identify the rotation period at this time. Distant satellites of 2014 MU69 have been excluded to a depth of >29th magnitude.

Stay tuned! Make sure you wake up in 2019 and read what happens when New Horizons flies past this cubewano.

The first quote is from here:

The second is from here:

For more on cubewanos, go here:

September 14, 2017

It's beautiful!

This is a hellbender — a salamander, and the biggest amphibian in North America. Some people call them 'snot otters'. They're up to 2 feet long, they're slimy, and they look a bit like turds. But I think they're beautiful, a marvel of nature! They've lived on Earth for 65 million years. We've been here for only about 2 million.

Who will last longer? The hellbender is threatened — but some people are helping it out! They're cleaning up streams and repopulating them with hellbenders. Check out this fun video:

Hellbenders live in many eastern states of the USA, and are especially common in Missouri, Pennsylvania, and Tennessee — but mining and other human activities have silted up many of the fast-moving streams that they like. Already by 1981, hellbenders were extinct or endangered in Illinois, Indiana, Iowa, and Maryland, decreasing in Arkansas and Kentucky, and generally threatened.

So, restoring hellbenders must go hand in hand with restoring streams. But that's a good thing in itself!

The hellbender is a 'habitat specialist': it's adapted to fill a specific niche within a very specific environment. They like streams with large, irregularly shaped rocks and swiftly moving water. They avoid wider, slow-moving waters with muddy banks or slab rock bottoms. They love to hide next to a big rock, where they can hunt crayfish and small fish. Unfortunately, this helps amphibian collectors easily find them - another reason for their decline.

They start out with gills, but when they're a year and a half old they lose these gills and develop toes on their front and hind feet. After this metamorphosis they can only absorb oxygen through the folds in their skin. And that's another problem: they can only live in fast-moving, oxygenated water! If they get stuck in slow-moving water, they can't breathe.

Now people are trying to help hellbenders by breeding them in zoos and releasing them in clean streams. They can survive out in the wild if they don't get the fungal disease that's wiping out amphibians around the world: the chytrid disease. We really need good biologists to tackle that disease!

People are also creating artificial structures for hellbenders to hide in:

Read more about hellbenders at National Geographic, where this picture came from:

The hellbender's real name is Cryptobranchus alleganiensis, and it has two subspecies: the Eastern hellbender Cryptobranchus alleganiensis alleganiensis, and the Ozark hellbender Cryptobranchus alleganiensis bishopi. It's the only species in its genus, and its family contains the only two salamanders that are even larger: the Japanese and Chinese giant salamanders.

September 17, 2017

Mars is full of mysterious, intriguing landscapes. The south pole of Mars is covered with 'dry ice': frozen carbon dioxide. There's a lot of Swiss cheese terrain, where this layer of ice is full of holes. But the big pit in this picture is something else! It could be an impact crater.

This observation from NASA's Mars Reconnaissance Orbiter show it is late summer in the Southern hemisphere, so the Sun is low in the sky and subtle topography is accentuated in orbital images.

We see many shallow pits in the bright residual cap of carbon dioxide ice (also called 'Swiss cheese terrain'). There is also a deeper, circular formation that penetrates through the ice and dust. This might be an impact crater or it could be a collapse pit.

What causes the Swiss cheese terrain? The holes in the Swiss cheese are usually a few hundred meters across and 8 meters deep, with a flat base and steep sides. Here the holes seem to go all the way to the ground, but often they just go down to a layer of water ice.

We can learn how these holes form by actually watching them form. They start as small cracks. Once they have a steep wall at least 10 centimeters tall and at least 5 meters long, they start growing fast.

Remember, this is near the south pole, so at some times of year the Sun goes around very near the horizon. So, the walls of these holes catch more sunlight than the flat bottom. The holes grow as the dry ice in the walls evaporates.

This doesn't answer a bigger puzzle:

Puzzle. If the holes keep growing, why isn't all the dry ice gone by now?

The picture, and the quote, is from here:

In my version of this picture, north is to the left. You can see the Sun is shining from that direction. The full, unshrunken version of this picture is magnificently detailed: 50 centimeters per pixel!

For more on Swiss cheese:

Also see the comments on my G+ post.

September 23, 2017

The 8-fold rosette

Islam forbids alcohol — but, except for the more extreme sects, it allows the subtler intoxication of geometry. The 8-fold rosette, found on many a tiled wall, comes alive as you scan from top to bottom in this picture by Joumana Medlej. Learn to draw it here:

You can do it with a ruler and compass!

First draw a grid of squares. Then inscribe a circle in each square. Then divide each circle in 16 equal parts.

It already gets fun at this stage! It's easy to find the 4 points at the top, bottom, left and right of each circle, because that's where it touches the square. It's also easy to construct 4 more: just use your ruler to draw diagonal lines between opposite corners of the square.

At that point you've divided your circle into 8 equals parts. How do you get 16?

If you remember your high-school geometry you can bisect angles with a ruler and compass, so you can do it that way.

But Joumana Medlej does a different way, which is more efficient and less messy. I'm betting this is the traditional method. Can you guess it? If not, take a look at his website.

I had trouble understanding why her method works... until I used a calculator to check that $$ \tan(\pi/8) = 0.41421356237 \dots $$ which confirmed my guess that $$ \tan(\pi/8) = \sqrt{2} - 1 $$ a fact I'd never known.

How is this relevant?

When you divide a circle into 16 parts, it's like slicing a pie into slices with angles of \(\pi/8\). You can do this if you can draw a line whose slope is \(\tan(\pi/8)\). But it's easy to draw a line of slope \( \sqrt{2} - 1 \) if you happen to have a grid of squares, a compass and a ruler.

Okay, now figure out how &mddash; or see how Joumana Medlej does it! And there's more to drawing the 8-fold rosette that just this — it's fun to see the whole process.

It's easy to check that

$$ \tan(\pi/8) = \sqrt{2} - 1 $$ if you remember your half-angle formulas: $$ \sin(\theta/2) = \sqrt{\frac{1 - \cos \theta}{2}} $$ $$ \cos(\theta/2) = \sqrt{\frac{1 + \cos \theta}{2}} $$ From these it follows that $$ \tan(\theta/2) = \sqrt{\frac{1 - \cos \theta}{1 + \cos \theta}} $$ and a little algebra and trig give $$ \tan(\theta/2) = \frac{1 - \cos \theta}{\sin \theta} $$ which I suppose I should have remembered, but didn't. When you take \( \theta = \pi/4\) this gives $$ \begin{array}{ccl} \tan(\pi/8) &=& \displaystyle{ \frac{1 - \cos(\theta/4)}{\sin(\theta/4)} } \\ \\ &=& \displaystyle{ \frac{1 - \frac{1}{\sqrt{2}}} {\frac{1}{\sqrt{2}}} } \\ \\ &=& \sqrt{2} - 1 \end{array} $$ Puzzle. what's a more efficient way to see that \(\tan(\theta/8) = \sqrt{2} - 1\)?

Before we were distracted by the dazzling delights of modern mathematics, mathematicians knew Euclidean geometry inside and out in ways most of us can scarcely imagine now. Tiling patterns like the 8-fold rosette are a little taste of that bygone age.

Ken Smith gave a very nice answer to the puzzle on my G+ post. It boils down to a single picture, whose contemplation also leads to a proof that \(\sqrt{2}\) is irrational.

September 29, 2017

How to move the Sun

Suppose we wanted to move the Solar System. How could we do it?

Okay, first things first: why would we want to?

Well, our Sun will eventually become a red giant. In just about 1.1 billion years it will become 10% brighter — enough to boil the Earth's oceans and create a runaway greenhouse effect. If we could move the Earth farther from the Sun, that would buy us time. But it would be even cooler to carry the Earth to a brand new star. And to keep it from freezing en route, we could try to move the whole Solar System.

Of course this seems like a wacky idea. But a billion years ago, the whole concept of intelligent life was a wacky idea. Heck, back then they didn't even have the idea of an 'idea'. So a lot can happen in a billion years.

One way to move the Solar System is a Shkadov thruster. The Russian physicist Leonid Shkadov came up with this idea in 1987. Russian physicists have had some impressively bold thoughts, and this is a great example.

The idea is to build an enormous mirror or 'light sail'. If you did it right, the push of sunlight would balance the pull of gravity towards the Sun, so it wouldn't fall in and it wouldn't fly away.

With this mirror in place, more sunlight would shine out into space in one direction than another! This would push the Sun, which would drag the Solar System with it.

The acceleration would be very tiny. At best, after a million years the Sun would be moving at just 20 meters per second... and it would have moved 0.03 light-years. That's a respectable distance, but nowhere near the closest star.

But with a constant acceleration, the distance traveled grows as the square of the time (at least until special relativity kicks in). So, after a billion years, the speed would be 20 kilometers per second... and the Sun would have moved 34,000 light-years! That's a third the diameter of the Milky Way!

Of course, a billion years would be pushing it, since we're expecting the oceans to boil away just 100 million years after that. You don't want a last-minute rush to hand off the Earth to a new star! Luckily, we won't need to go nearly this far to reach a nice new star.

Building a Shkadov thruster won't be easy.

For starters, it will take a lot of material! Viorel Badescu, a physicist at the Polytechnic University of Bucharest in Romania, estimated the mirror would have to weigh 1/10,000th of the Earth's mass. That's 600,000,000,000,000,000 tonnes. The easiest way to get this stuff might be to mine the planet Mercury.

Hey, I've got an idea! Let's start with an easier project, as a kind of warmup. Let's stop global warming.

What really pisses me off about modern politics is that we're spending so much energy fighting about stupid stuff instead of thinking big.

For more on the Shkadov thruster:

The Shkadov thruster is just one kind of stellar engine. For others, try this:

Also try this:

Ah, those Eastern Europeans, with their big ideas and their disdain for little words like 'the'.

Also check out the discussion on my G+ post.

For my October 2017 diary, go here.


© 2017 John Baez
baez@math.removethis.ucr.andthis.edu

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