Bad Astronomy
The entire universe in blog form

March 15 2015 7:30 AM

What Causes an Aurora?

I write a lot about aurorae, the lovely and eerie glowing lights at extreme latitudes caused when subatomic particles from the Sun are channeled down into the atmosphere by Earth’s magnetic field.

Whenever I do I always wind up having to write a brief explanation of how they work; that’s the responsibility of a science writer.

But my burden is now eased a bit thanks to this well-done video giving a solid overview:

What I like about the video is that it covers the basics without giving too much detail or worrying over distracting side issues. And I have all those covered in earlier posts! So, for your brainy pleasure, here is more detail on …

In fact, gathering all these links in one place will make my life a lot easier next time I post a gorgeous aurora time-lapse!

My thanks to David Miles, part of the Investigations of Cusp Irregularities sounding rocket program, who sent me some links about the ICI-4 rocket campaign, which led me to the video.

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March 14 2015 7:15 AM

Mars Mars The Martian

So I read the sci-fi book The Martian a while back, and I loved it. It’s hard sci-fi, an adventure tale with a lot of solid science and engineering in it. Despite being laden with technical stuff, it’s a page-turner, and I highly recommend it (especially since it’s being made into a movie with Matt Damon).

It seemed pretty accurate to me (I spot-checked some of the math, actually, because me = dork), but I’m not an expert in Martian geography. It turns out the terrain astronaut Mark Watney had to drive over on Mars is actually a little bit different than advertised.

I didn’t know this, but planetary geologist Alfred McEwen did! The folks with HiRISE (a camera on board NASA’s Mars Reconnaissance Orbiter) got him to describe the landscape there, and I’m honored they asked me to record an audio version of the article.

They also made a video using HiRISE images of the area in questions, and it’s very cool. It still blows me away that we can get images like this of Mars!

I imagine the movie of the book will make extensive use of HiRISE images. If they stick close to the book’s story, this’ll be a great movie. I can’t wait!

(N.B. The title of this post makes sense when you realize the second word is a verb.)


March 13 2015 11:30 AM

Crash Course Astronomy Episode 9: The Solar System

OK, over the past eight episodes of Crash Course Astronomy we’ve covered a lot of basics: What you can see, how you can see it, and how some basic forces sculpt what’s out there.

So. What’s out there?

Turns out, you don’t have to go far to find wonders: May I please introduce you to our local neighborhood, the solar system?

I wrote this to give you a taste of what’s what, knowing that the next few episodes will dive into detail on each planet, the asteroids, comets, and more.

I also wrestled with how much to say about Pluto, and in the end just used it here as a means to talk about how we define things and what we mean by “planet.” I get lots of email about this whenever I write about it. People agree, they disagree, they suggest ways we can manufacture a definition. I hope I covered that in this episode, but if you have more questions, I suggest reading this earlier post. And this one.

I’ve also written about geocentrism and heliocentrism before; as a coordinate system (like, observing stars from a telescope on Earth) geocentrism is fine, but if you want to send probes to other planets, it’s best to switch to the heliocentric frame. And from a philosophical standpoint, capital-G Geocentrism is simply wrong.

One thing I wanted to cover but didn’t have time was, where does the solar system end? This gets a little confusing—I’ve written about this too—because again it’s a matter of definition, and that will always get you into trouble. The Universe doesn’t really care about our definitions.

Our best bet is to keep our eyes and our minds open. Let the cosmos tell us how to categorize things. Don’t be too rigid, and do let things exist in the gray areas. You’ll find a lot more subtlety and wonder that way.

March 13 2015 7:00 AM

8 Things About Pi for Pi Day

Happy π Day!

Saturday is March 14, or, as it’s written in the U.S., 3/14. That makes it Pi Day, because the mathematical constant π is roughly equal to 3.14. Nerds celebrate this date every year, because, well, we’re nerds. Duh.

But this year’s π Day is special: It’s the year 2015, so the date is 3/14/15, giving us two more decimal places of the famous constant. In fact, if you celebrate it at 9:26:53 today, you get π to nine decimals: 3.141592653. Since the next digit is a 5, you can even round up and celebrate π Day for an extra second. Woohoo!

Why is π special? Most of us learn it because it’s the ratio of a circle’s circumference to its diameter. That’s pretty handy in geometry, but it goes much, much further than that. π appears in mathematical formulae all over the place, even where you might not expect it to. For some reason it appears to be woven into the very fabric of the Universe, popping up every time you look deeper into mathematics and physics.

In honor of this ubiquitous number, here are 8 (or 2π if you round down) facts about it you may or may not know. If you already know them, congrats! You’re a nerd. If not, then yay! You learned something. I can’t think of a better way to celebrate π Day than that.

A Year of π

Did you know there are different kinds of years? I won’t go into details (you can read all about them here, and I do mean all about them), but for our calendar we use what’s called a tropical year, which is 31,556,941 seconds long.

By coincidence, that is very close to π x 10 million! In fact, it’s off by less than half a percent. So if you need to know how many seconds there are in a year—which happens surprisingly often in my career— π x 10 million is a handy number to remember.

Legal π

There’s something of an urban legend that in 1897, Indiana tried to legislate the value of π to be exactly 3. That’s not precisely true. What happened was that an amateur mathematician had been working on a method to square the circle—to construct a square with the same area as a circle of given radius, using only a straightedge and a compass—and thought he found a solution (he hadn’t; there isn’t one). He submitted it to the Indiana Legislature, but it wasn’t ratified. His work didn’t even really say that π = 3; any value he found for π was incidental. But over the years, the story got warped, and now people think Indiana has that law in its books.

Anyway, there are other stories involved, like a joke story about Alabama redefining π, or the Bible stating it’s equal to 3. I find stories like this amusing. π is what it is, and humans trying to redefine it are, to coin an apropos phrase, trying to square the circle.

M and Ms
Approximating the shape of an M&M as an oblate spheroid, the volume of chocolate in it is 4/3 π a2 b, where a is the long radius and b the short one.

Photo by AmitP on Flickr

Pyramid π

When I was a kid, there was a huge industry in “ancient mysteries.” There still is, sadly—because I mean made-up mysteries, not real ones. Aliens didn’t help Hannibal cross the Alps, there’s no black hole in the Bermuda Triangle (the Bermuda Triangle doesn’t even exist), and the Egyptians didn’t really know about π.

Yeah, I’ve read quite a few breathless websites claiming they did. It’s even, they say, built into the pyramids! Well, one pyramid. Well, kinda. Basically, if you measure the circumference of the base of the Great Pyramid of Khufu and divide it by the height, you get a close approximation of 2π.

The thing is, that’s true! But it almost certainly wasn’t on purpose. It’s more likely to do with the slope of the wall chosen by the builders, which would drive the relationship between circumference and height. Also, many other pyramids (which had similar slopes) don’t have that same ratio, making it less likely to be mysterious ancient knowledge, and more a case of cherry-picking.

Mmmmm, cherry π picking.

π in Your i

Leonhard Euler was one of the greatest mathematicians of all time. He found a very weird relationship, called an identity, that goes like this: eiπ + 1 = 0. It’s a special case of a more generalized formula, but it’s true. e is the base of the natural logarithm, and i is the square root of -1, called an imaginary number (I’ll note it exists, in the sense that it has meaning in math, so the term “imaginary” is misleading).

This one simple formula has five of the most basic numbers in all of math in it, and they have this relatively simple relationship. Why is π in there? Well, the general equation has sines and cosines in it, and those have to do with circles, which is all about π! But the way it works out is still simple and elegant and beautiful. Also a bit mind-twisty. Actually, it’s a lot mind-twisty. But there you go.

20 πs

Another fun coincidence: eπ π = 19.999099979. That’s really close to 20! I don’t think there’s any deeper meaning in that, though xkcd found a use for it. Hover your mouse over that cartoon and you’ll get another one, too.

2 pie are round.

Photo by Amitp on Flickr

Stubbing Your τ

Some people don’t like π. Or, to be more accurate, they think there’s a better number to use: τ, the Greek letter tau, which is equal to 2π. The reasoning behind this has to do with making equations simpler and more elegant, which is fine, but in the end I find it a bit of a wash. Replacing π with τ doesn’t really help you in the long run, and π is good enough. It’s a lot of fuss over what boils down to what seems like pedantry to me. And if we switch to τ we can’t make pie jokes! So that’s probably enough reason not to make the switch.

Slices of π

(This one’s mathy. If you’re a mathophobe, you might want to skip this, and if you’re an etymologist, don’t complain about the word mathophobe.)

So π turns up in lots of math equations. Part of that has to do with trigonometry, as I mentioned above; circles, sines, and cosines show up a lot. That means there are lots of ways to calculate π. You just have to manipulate the equation so you get π on one side, and all the messy formulae on the other. That kind of stuff has been around a long time, and if you’re curious, a Web search will keep you busy a while.

But I just found out about a new method—well, new to me—and it’s cool. It’s described by Evelyn Lamb at the Roots of Unity math blog. It has to do with what are called “continued fractions,” where you have a fraction inside another fraction. These are weird and a bit chewy to get your head around, but let me show you how this works. Here’s the fraction:

continued fraction pi
It's not as bad as it looks, I promise.

Photo by Evelyn Lamb

Yegads, I know. But we can break it down step by step, look at each part of the fraction and ignore the remainder until the next step.

So we start with the first part, which is 3. OK, good. That’s easy enough.

The next part is 1/7. That’s equal to 0.142857142857… If we cut the continuing fraction off there and add 3 to it, we’re already close to π: 3.142857…

The next part is 1/15. If we cut the fraction off there, then it’s 3 + 1/(7 + 1/15). That’s the same as 3 + 1/(106/15) = 3 + 15/106 = 3.1415094… which is a bit closer still.

If you keep doing that, following the fraction down, you get ever closer to π. As an armchair math nerd, this makes me smile. What’s interesting as well is that it converges quickly. After just two steps we’re already accurate to the fourth decimal! As Lamb points out, this makes it easier to memorize π if that’s your thing. In the case above, remembering three numbers (3, 7, 15) gets you to five digit accuracy. Doing the fraction means memorizing fewer numbers! Nifty.

The point? There’s more than one way to bake a π.

Universal π

Famous people born on π Day include astronauts Gene Cernan (1934) and Frank Borman (1928), and astronomer Giovanni Schiaparelli (1835).

But also, one Albert Einstein was born on March 14 in 1879. His equations for general relativity are still used today to describe the physical nature of the Universe, replacing Newton’s physics. This eventually led to what’s called the Friedmann equation, which describes the dynamics of the structure of space time:

Friedmann equation
Yes, this will be on the test.

Photo from Wikipedia

Note the presence of π! Yes, it actually plays into the very fabric of space and time themselves! So no kidding, π is an important number. Carl Sagan uses this idea quite a bit in his fantastic novel Contact, too. The movie is great as well.

You might want to dismiss π Day as just a bit of silliness, but honestly, if there is a number we should pay our respects to, it’s π. It’s everywhere, and it’s not hard to make the case that our modern civilization depends on it (look around you; how many machined parts are circles, spheres, cylinders … and it pops up in equations governing electronics, too).

So have a happy π Day! And if you do celebrate it, make sure it’s with …

… a close circle of friends.

P.S. If you’re still not satiated with mathy days, have a look at my Mole Day article. I also wrote about Pi Day in 2013.

*Correction, March 13, 2015, at 13:45 UTC: This post originally misstated that eiππ= 19.999099979. The correct equation is eππ = 19.999099979.

March 12 2015 1:00 PM

Another Ocean in Space: Jupiter’s Moon Ganymede

Hot on the heels of the announcement that hydrothermal vents have been found on Saturn’s moon Enceladus, we get another watery alien world announcement: Indirect evidence has been found for a salty ocean under the surface of Jupiter’s moon Ganymede!

Ganymede is a huge moon, bigger than Mercury, and edging in on Mars-sized territory (Ganymede is 5,270 kilometers in diameter; Mercury is 4,880 and Mars 6,780). Its density is low, meaning it probably is a mixture of rock and ice—that’s common for moons in the outer planets. In the 1990s, the Galileo spacecraft flew past the moon several times, and careful measurements of its magnetic field indicated it might have an ocean of liquid water deep under its surface.

New observations of the moon using Hubble support this. Ganymede has a weak magnetic field, and, like on Earth, this generates an aurora—the glow created when high-speed subatomic particles slam into the extremely thin atmosphere. This glow is brightest in ultraviolet, and so astronomers used the Space Telescope Imaging Spectrograph (my old camera!) on Hubble to observe Ganymede. STIS is quite sensitive to UV and detected the aurora.

Now this part is a bit tricky: Jupiter has a powerful magnetic field as well, which interacts with Ganymede’s. As they do, the aurora changes position over time, moving up and down in latitude. However, the observations show that the aurorae do not change nearly as much as expected if Ganymede were solid. The best way to explain this is if the moon has a salty ocean under its surface. The ocean would have its own magnetic field and would resist the influence of Jupiter’s magnetic field, which in turn keeps the aurora steadier.

This ocean is probably located about 150 km deep under Ganymede’s surface and may extend another 100 km deeper. If so, then it contains more water than all the oceans on Earth! That’s astonishing.

Ganymede art
A lovely drawing of Ganymede and its aurora, with Jupiter in the background.

Drawing by NASA, ESA, and G. Bacon (STScI)

Speculation time: Interestingly, older observations indicate the presence of various salts (like magnesium sulfate) on the surface. So we have a salty ocean, and salt on the surface … that makes me wonder if the ocean is interacting with the surface in some way, maybe leaking up through cracks. Given how deep the ocean is that seems unlikely, but geez, given all these new and delightful discoveries I wouldn’t rule it out just yet.

Surface/subsurface interactions are important because the radiation from Jupiter can interact with the surface too, creating simple organic molecules. If those can get down into the water … well, like I said, this is all speculation. But it’s interesting.

And clearly an investigatory path we should follow. This is all very new, and so we’re taking our first steps of discovery here. With oceans under Enceladus and Jupiter’s moon Europa, as well as possibly under Saturn’s giant moon Titan as well, it seems that outer space is loaded with watery worlds. They may not be what we first expected, but hey, nature is smarter than we are. Science is all about learning what it’s trying to show us.

March 12 2015 7:00 AM

Evidence for Hydrothermal Vents on Saturn’s Moon Enceladus Hints at Conditions for Life

When we think about life in the solar system, we tend to look to Mars. But science has broadened our minds in recent times—science has a way of doing that—and many scientists are turning their attention to the outer solar system. There are moons made of ice there, and some have entire oceans of liquid water under their surfaces.

Saturn’s moon Enceladus is particularly interesting, with geysers of water spewing hundreds of kilometers into space from its south pole. And now it’s just gotten even more exciting: Two teams of scientists have found evidence of hydrothermal vent activity on the little moon!

We know there’s liquid water under the surface of Enceladus because of the geysers. The mighty gravity of Saturn squeezes and stresses the moon, and friction inside it heats it, causing the ice to melt. Cracks near the south pole (called sulci, singular: sulcus, a word I’m fond of) open and close as the moon is squeezed, and the huge pressure under the surface causes the water to erupt out.

Enceladus’ surface is covered in ice; the sulci can be seen as parallel “tiger stripes” at the bottom.

Photo by NASA/JPL/Space Science Institute

These geysers were discovered in Cassini spacecraft images. The probe actually flew through a plume and detected water, dust, and simple organic molecules, too.

But this is different than hydrothermal activity. The evidence comes in the form of teeny tiny bits of silicate material detected by Cassini as well. This stuff is in the volume of space around Saturn, and it consists of grains only a few nanometers across (a typical bacterium is 10x bigger for comparison). The most likely source of these grains is hydrothermal vents in Enceladus; hot water with dissolved minerals in it comes into contact with colder water, and the minerals precipitate out in the colder environment, forming the grains. These then are carried out and blasted into space by the geysers.

This fits well with what we know of Enceladus; the surface is frozen, there’s an ocean of water underneath, and then under that is probably a rocky core of material. That last would be the source of the minerals. The core itself is probably warmed by the same tidal friction from Saturn keeping the water liquid above it. Cracks form in the core/water boundary where hot material can come out: hydrothermal vents.

Enceladus geyser
From a distance, and backlit by the Sun, the geysers are obvious.

Photo by NASA/JPL-Caltech/Space Science Institute

The second team of scientists were looking for the source of methane that’s been found in the plumes. These same hydrothermal vents are one likely source, bringing methane-laden compounds into Enceladus’ undersurface ocean, which again then spews them out in the geysers. They note it’s possible there is another, nonhydrothermal source, but given the other study finding silica, the idea of hot vents makes sense. It’s possible both ways are at work as well; but if true, that still means the hydrothermal vents are there.

So what’s the big deal? Well, understanding how geologic processes work on other worlds is exceedingly cool. But there’s a more immediate interest in this as well.

We see these vents in the ocean bottom on Earth, too. The water there is very hot, heated by tectonic processes inside Earth’s crust. It brings up minerals and nutrients, and life thrives there. A lot of the processes are the same as what’s imagined is happening on Enceladus; minerals are dissolved in hot water that spews up into the cold ocean, precipitating out. A lot of it is sulfur-based, but amazingly life exists there anyway. The environment is highly toxic to humans—huge pressure, boiling water near the vents, freezing a bit farther away, and loaded with icky chemicals—but as a scientist once said, “Life finds a way.”*

Are there giant alien tube worms filtering the waters of Enceladus for life-giving nutrients a billion kilometers from Earth? It’s a nice thought, and it’s possible. I wouldn’t say it’s likely just yet; we’re a long way from that. But this evidence for hydrothermal vents takes us a nice step closer to knowing. And that is a very exciting step indeed.

*Yes, I mean Ian Malcolm from Jurassic Park, and yes he was a terrible scientist who didn’t understand chaos theory at all, but it’s still a good line.

March 11 2015 7:30 AM

Unlike Temperatures, Climate Change Deniers Are Falling Fast

If you’re hoping to deny the reality of global warming, things aren’t looking so good for you right now. A couple of events are making it ever more clear that those vocal about it are in trouble. Deservedly.

The first big item is that solar physicist Wei-Hock “Willie” Soon appears to be firmly in the pocket of fossil fuel interests. He is not a climate scientist, but he’s published papers linking changes in the Sun’s output to Earth’s temperature, claiming that it’s the Sun heating us up, not human-generated carbon dioxide.

His claims about the science have been pretty thoroughly torn apart by climate scientists dating back as far as 2003 and have also been refuted on the Skeptical Science site as well. Despite the claims, the Sun’s output has marginally decreased in recent years, while temperatures on Earth go up.

Greenpeace obtained FOIA documents showing Soon received more than $1 million of funding from Big Oil over the past few years. A funding source isn’t necessarily damning, except for two things. One is that Soon neglected to mention his funding in nearly a dozen papers he’s published, and that is a huge, huge, no-no in science. If you have a potential conflict of interest, you report it.

The other is that given that his science has been refuted, coupled with his funding, his repeated claims that human CO2 pollution isn’t causing global warming are pretty suspicious. When you find out his funding has come from Exxon, the American Petroleum Institute, and the Koch brothers, well, yikes.

What I find funny is that groups like the Heartland Institute—remember them, when they likened climate scientists to ruthless dictators and serial killers?—are defending Soon, when they were screaming bloody murder over the ridiculous “Climategate” nontroversy. For denial groups like them it’s all about sowing doubt.

But this is where we are today. The science is in, it’s extremely clear, and the consensus among climate scientists is solid. If your political stance is based on nonsense, and you’re called out, all you can rely on is doubling down, making lots of noise over nothing, or making increasingly embarrassing stunts. You certainly can’t rely on reality, because you’ve long since left that behind.

It can’t help that the film Merchants of Doubt comes out this week. The documentary, based on the book by Naomi Oreskes, outlines the shenanigans pulled by climate change deniers over the years. Hopefully it will raise awareness about them and their tactics.

Is it hot in here, or is just the planet?

Photo by Shutterstock/Eunika Sopotnicka

Speaking of which, the second item causing deniers to sweat comes from Google. I recently wrote that the search engine is now using curated results when people search on vaccine-preventable diseases, to prevent the rampant spread of misinformation.

It seems Google may be preparing to use this science-based method of ensuring evidence-based results into other arenas, including climate change. Right now, Google uses various methods to rank search engine results, including the number and “authority” of sites that link to other sites. But this method is easy to game, giving pseudo- or anti-science sites higher credence in Google’s results page. Researchers at Google have published a paper proposing instead using “knowledge-based trust,” where the facts of the site are compared to what is commonly known to be true among trusted sources. As New Scientist says, “Facts the web unanimously agrees on are considered a reasonable proxy for truth.” You can claim, for example, that the Earth if flat, and get links from popular sites about it, but in this new system you won’t get much Google love. As you shouldn’t.

I’ll note that this new methodology is somewhat worrisome, since it still relies in some ways on a notion that if a majority of authorities agree on something, people who disagree could be shut down. In the paper, the researchers discuss ways the algorithm would need to improve. But it’s still, in theory, possible to game the system.

But it is rather comical to me, in a schadenfreude kind of way. Google wants to base search results on expert scientific consensus? Yes, that very well should give climate change deniers an existential frisson of fear.

One could even say that, for them, there really is a chill in the air.

March 10 2015 1:00 PM

Icy Twin Craters on Mars

I’ve mentioned a few times here that I write a biweekly column for, a site that has lots of news and blogs dealing with space exploration (Sen stands for “Space Exploration Network”). The news articles are free, but the blogs are subscription only.

My latest article there is one I’ve been meaning to write for some time: What phenomenon sculpted this weird pair of craters, each with a central pit in it? It turns out the answer is … layered. is worth the subscription price. There are a lot of good writers there, including my friends Emily Lakdawalla, Chris Lintott, and many more. Go check it out!

March 10 2015 10:00 AM

Hear the Scirens Call to STEM

I’m really pleased to see so many people and organizations doing what they can to inspire young girls to take up STEM (science, technology, engineering, and math) paths in school. Women are still severely underrepresented in those fields. It’s a complicated situation—endemic sexism at the professional level, unconscious bias about teaching girls at the grade-school level, and everything in between—but one thing that I think will help is raising awareness and making sure there’s a positive, supportive atmosphere out there.

That’s why I’m very pleased that my good friends, the Scirens—Taryn O’Neill, Gia Mora, Christina Ochoa, and Tamara Krinskyhave created a short video in honor of International Women’s Day to help girls get into STEM.

The Scirens are four actresses who love science and are great science communicators. They do a lot of outreach, getting science out to the public in clever ways. They have Science Soirées, private but very informal get-togethers with a scientist speaker and a curious audience of people who are free to ask questions and spark conversations. Christina (as part of the Nerd Brigade) helps organize science Q&A sessions at the L.A. Natural History Museum as part of First Friday there (I was just at one last week and it was really great; lots of people attended and were clearly loving it). Gia has a one-woman cabaret act called “Einstein’s Girl,” an allegory of physics and love, and it’s really good (I saw it last year in Denver). And lots more.

Having role models is important. A lot of the time, kids don’t see people like themselves on TV, in movies, or online, and that is certainly true for girls when it comes to science. We’re doing a lot better with that now, but that doesn’t mean we can relax. We need to keep making sure this message gets out, and making it even more diverse and inclusive, so that anyone, everyone, can feel that they can choose to pursue a STEM career if they want to.

Realistically, that will take a long time and will involve a lot of work and broadening of our efforts. But we’re facing the right way, we’re moving in the right direction, and every time we make that path easier, we all win.

Update (Mar. 10 at 20:00 UTC): To be clear, the Scirens don't officially do the Q&A sessions at the LA Museum; Christina does that and she is part of both Scirens and the Nerd Brigade.

March 10 2015 7:00 AM

Green Europe

This may be a little early for St. Patrick’s Day, but that’s OK: Europe isn’t really going green. At least, not this green.

This astonishing image is from the European Space Agency Proba-V satellite, a small Earth-observing sat that monitors vegetation (that’s what the V is for in its name!) across the entire planet. This image is actually a composite of blue, red, near-infrared (just outside the color range our eyes can detect, where plants are highly reflective), and mid-infrared, so the colors aren’t what you’d really see if you were in space looking down.