Music of the spheres

I’m teaching about the Copernican revolution in my first-year seminar these days. Before getting to Copernicus, we’re taking a look at what people thought about the motions of the planets at earlier times. We’re particularly focusing on the ancient Greeks, since that’s largely what Copernicus and pals were responding to.

Most astronomy textbooks talk about the Ptolemaic system, with its epicyles, deferents, and the like. But before there was Ptolemy, people like Eudoxus came up with pretty good, detailed models to explain planetary motion based on the idea that all of the heavenly bodies were attached to nested, concentric spheres. This “homocentric sphere” picture was very important, largely because it’s the one Aristotle championed.

To explain the complicated motions of the planets in this model, you need to use multiple spheres, all rotating about different axes at different rates. You’d think there’d be nice animations out there on the Web somewhere to show how this all worked, but I couldn’t find any, so I made my own:

More images and detailed explanations here.

Kepler stuff

About the Kepler mission’s announcement last week of tons of extrasolar planets:

1. A local Richmond TV station had me on the news to talk about the announcement. (The fact that they asked me primarily goes to show that astrophysicists are not exactly thick on the ground in Richmond.) I can’t stand to look at myself on video, but if you want to see it, go ahead.

2. Via Sean Carroll, some cool visualizations of the Kepler data, showing number of planets by size,  distance from star, temperature.

3. Sean says

A back-of-the-envelope calculation implies that there might be a million or so "Earth-like" planets in our Milky Way galaxy.

I’d go much higher than that. Kepler looked at about 150,000 stars and found five Earth-like planets (meaning roughly Earth-sized and in the habitable zone where liquid water could exist).  If you imagine that they had 100% efficiency — that is, that they found all the Earth-like planets there are in the sample — then one in 30,000 stars would have an Earth-like planet. Multiply by 100 billion stars in the galaxy, and you get about 3 million Earths.

But here’s the thing: Kepler’s efficiency can’t be more than about 1% or so. The mission works by looking for eclipses, which occur when the planet passes directly in front of the star as seen from Earth. That means that it only has a chance of detecting a planet if the geometry is fortuitously aligned. The probability of such an alignment occurring depends on the size of the star and of the planet’s orbit (in fact, it’s just the ratio of the two). For the actual Earth and Sun, the probability works out to 1%. Many of Kepler’s planets are closer in and have higher probabilities, but at best the geometrical alignment can only occur a few percent of the time on average.

Even with the right geometry, they don’t have a 100% chance of finding a planet, of course. Once you fold in all sources of inefficiency, I’d be very surprised if they have a better than 1% chance of finding any given Earth-like planet. I wouldn’t be surprised if it’s more like 0.1%

Just to be clear, that’s not a criticism of Kepler. It’s just an acknowledgment that this is a hard task they’ve set themselves!

So my back-of-the-envelope estimate is hundreds of millions, if not billions, of Earth-like planets in the Galaxy.

Zodiac silliness

Haven’t blogged much for a while.  Busy.

Apparently some astrological silliness has been making the rounds of some news sites and twitterers lately.  In case you’re wondering, Bad Astronomy has everything you need to know:

I'll note this silliness has extended well beyond Twitter; the prestigious scientific journal OK!* says that “Taylor Swift's the New 13th Sign Ophiuchus!” and goes on to say that even if the astrological signs change, “horoscope readings reportedly shouldn't be affected.”
Phew! I'll agree with them on that. After all€¦

Black hole questions

 Who knew that, a dozen years after I wrote something trying to explain a bit about black holes, people would still be reading it?  I get questions from time to time from readers, and I’m happy to try to answer them.  As long as I’m writing answers anyway, I’ll go ahead and post them here in case anyone else is interested.

This batch is from a high school student named Brandon Thrush.

 1. I have a good idea of what the event horizon is, but I do not know what you mean when you say that it is actually moving outward at the speed of light; does this mean that the whole entire black hole is moving at the
speed of light?

This is a very subtle and potentially confusing idea.

Suppose that you dropped a flashlight into the black hole, and at the exact moment it crossed the horizon, it emitted a photon (that is, a little burst of light) in a direction straight out, away from the black hole.  That photon would be stuck on the horizon, never falling into the black hole but never getting further away either.  Now, one of the main ideas of relativity is that light always travels at the same speed (the speed of light, naturally!) no matter how it’s measured or by whom.  So that photon is, by definition, traveling at the speed of light, and yet
it’s staying right on the horizon.  The logical conclusion is that the horizon is moving at the speed of light.

You might say that this is just a silly word game: Why do I say the horizon is moving outwards, rather than saying that the photon is sitting still?  The answer is just that the idea that the speed of light is always
the same (which means that photons never sit still) is so powerful and useful that physicists hate to give it up.  We’d rather say that the horizon is moving at the speed of light — even though it never gets anywhere!  — than give up on that idea.

At this point, it’s customary to mention the quote from Lewis Carroll’s Through the Looking Glass, in which the Red Queen says something like “Here it takes all the running you can do just to stay in the same place.
If you want to get anywhere, you’ll have to go a great deal faster than that!”

2. When you give examples of two black holes, one smaller than the other, you say that in the smaller black hole you would be torn apart before you even reach the horizon, but in the larger one, you would not be torn apart until after you reach the horizon.  How can this be?

The reason is that the thing that tears you up is the “tidal force,” which has to do with the difference in the strength of the gravitational pull between one end of you and the other end.  If every atom in your body is
being pulled on (and hence accelerated) by gravity in the same way, you won’t feel any ill effects, but if one part of you is being pulled more strongly than the other, you will.  For a large black hole, the scale of everything is so big that there’s no real difference between the pull on your head and the pull on your feet: both are huge, but they’re essentially the same.  For a smaller black hole, each of those pulls is smaller, but they’re different, and that’s what matters.

3. When a black hole is formed, it is because of a dying star, but does the star suddenly collapse under its own gravitational force and what is left is its gravitational force field, called the black hole, or does the star gradually collapse into its own force field?

I think I like the first way of saying it better. Certainly “suddenly” is better than “gradually”: although the leadup to the final collapse is gradual, once the final collapse gets started, it’s very quick.

There’s another obligatory literary reference here, by the way: “Gradually and then suddenly” is the way Hemingway describes going bankrupt in The Sun Also Rises.
The big idea is that, before it collapses, a star exists in an equilibrium, in which the pressure caused by the star’s particles (nuclei and electrons) balances the pull of gravity.  When a black hole forms, the reason is that that balance couldn’t be sustained, and gravity won.  The particles get pulled in closer and closer to the center.  After that process is complete, all that an outside observer can detect is the gravitational field (which we often prefer to call the “curvature of spacetime.”)

4. When the star is collapsing into the center, what happens to the particles while reaching the center?  What is their fate?

Once they get very near the center, we have to admit that we just don’t know.  Everything we say about what happens to particles inside the horizon of a black hole is based on theory, not observation, since we never see the interior.  But at first (that is, immediately after crossing the horizon) we can have pretty high confidence in our descriptions of the process: the physical conditions at first are very similar to situations we see in other places, so we think we understand them.  But near the center, the densities and temperatures get very high, eventually passing out of the range where we think we understand the physics.

So here’s what we can say: during the collapse, the particles that are falling in towards the center get compressed to higher and higher densities and higher and higher temperatures until, at some point, …. we don’t really know.

5. When a large black hole, such as a stellar-mass black hole, constantly grows, does the gravitational field extend farther and farther?  If so, would not the black hole eventually consume everything in the universe?

The first rule to remember is that a black hole of a certain mass has just the same gravitational pull as any other object of that mass.  So, for instance, a black hole the mass of the Sun attracts outside objects just as much as the Sun does, and no more.

Now, it’s true that as a black hole sucks in more stuff, its mass grows, and so does its gravitational pull.  But after the black hole has gotten all of the stuff near to it, it stops adding new matter at any significant rate, and so it stays pretty much the same after that.

In principle, every black hole in the universe is slowly adding more mass and hence pulling more strongly, but it’s important to emphasize the word “slowly.”  A typical black hole, after it’s had some time to clean out its immediate surroundings, grows at such a slow rate that even over the lifetime of the Universe we wouldn’t expect its mass to grow very much.

6. You refer to a large black hole as a “stellar-mass” black hole, but what are the different names given to the different sizes of black holes?  What are they from the smallest to the largest?

I have to admit that I’m not up-to-date on the subject of classification of black holes.  The last time I paid much attention to the subject, two main categories of black holes were thought to exist:

  1. Black holes that formed from the collapse of stars.  These typically have masses of about 10 times the mass of the Sun (plus or minus quite a bit).
  2. Black holes at the centers of galaxies.  A typical mass for these is  a million times the mass of the Sun.  The conventional wisdom seems to be that most large galaxies have one of these, and that they formed along with the galaxy itself.

When I talk about stellar-mass black holes, I mean the first category.  The other kind are most often called supermassive black holes.

It’s perfectly possible for black holes to exist with other masses. People have talked seriously about the possibility of microscopic black holes, for instance. But the black hole candidates that people have found in the
sky mostly fall into those two categories.  (I think that some black hole candidates have been found with masses in between the two categories — say around a thousand times the mass of the Sun — but I don’t know much
about that.)

Planck launch pictures

Ken Ganga, a member of the Planck satellite collaboration, has some nice pictures of the launch on his blog.  (Not exactly breaking news, but I just found out about these pictures.)  There’s also a story about a potentially fatal problem with the satellite that was caught just barely before launch.

By the way, in addition to his Planck blog, Ken has a personal blog, mostly about funny things he’s found while living as an American expatriate in Paris.

If the Sun turned into a black hole

Some time back in the’90’s I wrote a document explaining some things about black holes.  To my amazement, people still read it, and they occasionally send me questions as a result.  I’m happy to answer these when I can, and as long as I’m answering them anyway, I might as well post them here.

The latest is from Chris Warring:

My friend and I are having a debate over the question “If the Sun turned into a black hole, what would happen to the Earth’s orbit?”

I quoted from your article  “What if the Sun *did* become a black hole for some reason? The Earth and the other planets would not get sucked into the black hole; they would keep on orbiting in exactly the same paths they follow right now….a black hole’s gravity is no stronger than that of any other object of the same mass.”

My friend argued that since astroids impact the Sun then they would also impact the black hole.  This would eventually increase the mass, increase the gravitational pull on the Earth, and place the Earth on a decaying orbit.

I have since read a little on Hawking Radiation, and that black holes evaporate.  I now wonder if the black hole that was our Sun would evaporate, losing gravitational effects on the Earth, and the Earth would end up drifting away from where our Sun use to be.

Here’s my answer:

First, let me say that all of the effects you mention are very small. They would alter the Earth’s orbit a little bit over very long times. When I wrote what I did about the Earth’s orbit, I wasn’t considering such tiny effects. But they’re fun to think about, so here goes.

It is true that, if the mass of the Sun (or black hole, whichever is at the center of the Solar System) goes up, then the Earth’s orbit will be affected. Specifically, it would move to a smaller orbit. And of course the reverse is true if the mass goes down.

First, let’s talk about what’s happening right now, and then consider what happens if the Sun turned into a black hole. Right now, things do crash into the Sun from time to time, increasing the mass of the Sun. On the other hand, there’s constant evaporation from the Sun’s atmosphere (as well as energy escaping in the form of sunlight, which translates into a mass loss via E = mc2). I’m pretty sure that the net effect right
now is that the Sun is gradually losing mass. Taken in isolation, this mass change would cause the Earth to drift gradually into a larger orbit.

That phrase “Taken in isolation” is important. There are other things that affect Earth’s orbit much more than this tiny mass loss rate. The main one is gravitational tugs from other planets, especially Jupiter. I
guess it must be true that the gradual mass loss of the Sun gradually makes all of the planets drift further out, although the details might be complicated.

There’s also the fact that the Earth is being bombarded by meteors. Those presumably slow the Earth down in its orbit. Taken in isolation, that effect would make the Earth spiral in towards the Sun.

I’ve never tried to work out the size of any of these effects. A lot is known about the effects of other planets’ gravitation on our orbit (the buzzword for this being Milankovich cycles). The other effects are much smaller.

Now, what would happen if the Sun became a black hole? Things like meteors would still get absorbed from time to time, but much less often than they do now. That may go against intuition, because we think of black holes as really good at sucking things in, but in fact the black hole has the same gravitational pull as the Sun on objects far away, and it’s a much smaller target, so fewer things actually hit it. So the rate
of mass increase due to stuff falling in will be less than it is now. On the other hand, stuff won’t be evaporating nearly as fast as it does now. (There would be Hawking radiation, but that’s incredibly small, much less than the rate at which atoms are boiling off the Sun now.) So the net effect would certainly be that the black hole would gradually go up in mass, whereas the Sun gradually goes down. The net result would be that the Earth would gradually get closer to the black hole.

But again, the key word is “gradually”: these are really really tiny effects. I’d bet that they’d be too small to have any noticeable effect even over the age of the Universe.

Will we find extraterrestrial life?

My friend Tim asked me this question:

What do you think are the chances that we’ll detect (not necessarily physically encounter, but detect) life on another planet by the end of the century?

I think the odds are quite good, actually.

First, here’s something that I’m pretty confident is true: Within a few decades, we will have figured out how to measure the chemical composition of the atmospheres of other planets.  We’re moving fast in that direction right now, and while it’s a hard technical problem, I don’t see any show-stopping reasons why we can’t do it.  Basically, you have to have telescopes with sharp enough resolution to see the planet separately from its star, and then you just do spectroscopy.

I’ll be very surprised if we haven’t done this to hundreds and hundreds of planets within the next few decades.  We’ll know what molecules are in the atmospheres of those planets.  That means that we’ll detect life if a couple of conditions are satisfied:

  1. Extraterrestrial life is not very rare.
  2. Extraterrestrial life leaves identifiable chemical signatures in the atmospheres of host planets.

That’s as much as I can say with confidence.  From here on it’s guesswork.  Regarding #2, one important question is what would count as an identifiable signature.  People will naturally look at first for the chemicals that we find in our own atmosphere but that would not be there if there weren’t life.  I think that plain old oxygen (O2) is one of the main ones here: the oxygen would all be in other forms such as CO2 if it weren’t constantly replenished by biological processes.  I have no idea whether extraterrestrial life will be based on similar chemistry to ours, so maybe O2 won’t be the signature we’ll see.  But it does seem likely to me that, if a planet has life on it, there’ll be molecules in its atmosphere that you wouldn’t expect to see in a dead planet, and once we get good at doing spectroscopy, we’ll find them if they’re there.  So I’m not too worried about #2.

#1 is the one nobody knows about.  Is extraterrestrial life found on lots of planets, or is it a one-in-a-trillion shot?  Here, you just have to make your best guess.  Personally, I don’t think it’s likely to be incredibly rare, so once we’re mass-producing spectroscopy of other planets, we’ve got a good shot at finding it.  But that claim is based on no data — it’s a Bayesian prior probability — so feel free to disbelieve me.

I think this life is far more likely to be simple microbes than big intelligent things.  I doubt we’ll be hearing messages from ET any time soon.  That doesn’t mean that I think searches for intelligent life like SETI are a bad idea, though: they’re quite cheap compared to lots of scientific research, and the payoff if they succeed is so huge that I think it’s worth throwing a little bit of resources their way, despite the long odds.

Science and human space flight

President Obama’s commission to examine possible options for the future of human space flight is getting ready to issue its final report.  They are apparently discussing seven different possible options, some that involve going to Mars, and some that don’t.  There was an interesting report in Nature last week about a recent public meeting held to discuss the various options. (Thanks to my brother Andy for pointing this out.)

Of course, I’m most interested in the implications for science, so this caught my eye:

The panel plans to cost out the scenarios by next week, and also to assess the benefits of each for 12 key areas.

One of those areas is the potential to gain scientific knowledge from each strategy, says panel member and astrophysicist Christopher Chyba, of Princeton University in New Jersey.

To that end, yesterday’s meeting was mostly devoted to presentations from scientists representing four communities supported by NASA: Earth sciences, space-borne biological and physical science, astrophysics and planetary science.

So what did the scientists have to say? Well, according to Nature one of them didn’t have much of a case to make:

Anthony Janetos, representing Earth sciences, was hard-pressed to find an example. The director of the Joint Global Change Research Institute in College Park, Maryland, Janetos hedged when panel member and former astronaut Leroy Chiao asked if the thousands of pictures he took during shuttle flights were really all that useful. Janetos said they were “marginally” useful.

The others seem to have more sanguine views of the potential for getting science from human space flight.  The astronomer Marcia Rieke naturally and correctly pointed to the Hubble Space Telescope, which has been incredibly productive and has always depended on humans in space for support.  Planetary scientist Steven Squyres says there’d be a big scientific payoff from sending humans to Mars, comparing a human mission to the Spirit and Opportunity rovers:

He said that astronauts on Mars could do in a minute what his rovers averaged in a day, and pointed out that Spirit and Opportunity had covered less ground during their entire mission than Apollo astronauts in a lunar rover were able to travel in a day.

Of course, the fair comparison is between what humans could do and what a robotic mission could do if it had the same budget as a human mission (i.e., thousands of times what was spent on Spirit and Opportunity).  I doubt very much that the humans would win out in that comparison.

I doubt that you can ever justify sending humans into space on scientific grounds.  But that’s not and never has been the reason we send humans into space.  If we send humans to Mars, it’ll be for the intrinsic awesomeness of the achievement.  Personally, I don’t think that awesomeness is worth the price at the moment.  I think if we’re going to spend upwards of $1011 on engineering and R&D, it should be on a massive investment in energy technology for Earth.  If we do send humans to Mars, of course, I reserve the right to think it’s awesome and to be excited about it.

By the way, one of the Augustine panel’s seven options is particularly baffling to me:  “what the members called the "flexible path," which would avoid the "deep gravity wells" of the Moon and Mars, saving the time and cost of developing landers to carry astronauts to the surfaces of those bodies.”

A flyby of the moon might be followed by more distant trips to so-called Lagrange points, first to the location where the gravity of the Moon and the Earth gravity cancel each other out, then to where the gravity of the Earth and Sun cancel out. There could also be visits to asteroids or flybys of Mars leading to landings on one or both of the low-gravity moons of Deimos and Phobos.

This seems to me to have most of the disadvantages of human space flight but to cut way, way back on the advantages, i.e., both the scientific payoff and the intrinsic awesomeness.

New telescope

Our department just took delivery of a new 14″ telescope, to be used for classes, student projects, and public observing nights:


As you can see, it’s not in the  best possible observing location at the moment.  Plans are in motion to give it a permanent home on the roof of our building.

Thanks a lot to Dean Newcomb for buying us this!