This seems a straightforward question. However, it took a long time for astronomers to figure out the answer. Why the difficulty? Well, quite simply, the center of the galaxy is a long ways away, and it is not directly visible. In fact, since we are inside the galaxy, we don't even get a good view of what out galaxy looks like at all. So, where is the center of the galaxy, that how did we figure out its location?

The story begins even before the invention of the telescope. The Milky Way, that faint band of light wrapping all the way around the sky, is what our galaxy looks like from the inside. It completely circles the sky as a faint ring, so naturally it would seem that we are in the middle of the ring. With the invention of the telescope, astronomers found that the Milky Way was really composed of star and nebulae too dim to see individually with the eye. One of the earlier attempts to ascertain our position in the Milky Way dates to William Herschel, who in the late 18th Century counted stars in various directions in the sky. He found that wherever he looked in the Milky Way, he saw similar numbers of stars, but fewer looking out of the Milky Way. This led him to conclude that the Milky Way, the entire universe known at that time, was a large, somewhat flattened collection of stars, with the Sun not too far from its center. In the 1910's, Jacobus Kapteyn orchastrated a huge undertaking, using observations from more than 40 observatories, to map the galaxy. He, too, came up with a sort of fat pancake shape, with the Sun near its center. Unbeknownst to these astronomers, the space between the stars is not really empty, but is rather filled with a thin mixture of dust and gas called the interstellar medium, first shown to exist by Robert Trumpler in the 1930's. This interstellar medium interferes with our views of the galaxy, and it limits us to seeing only those portions of the galaxy comparatively near us. It is no wonder that we seem to be near the center of what we see!

The real break, though, came from the work of Henrietta Leavitt, who determined that a certain type of variable star, called Cepheid variables, pulsates at different rates depending upon how bright the star is. So, by measuring how quickly the star pulsates, you can determine how bright the star really is. By then measuring the star's apparent brightness, you can get an idea of the star's distance. The more distant the star, then the dimmer it appears. The astronomer Harlow Shapley used this method to determine the distance to globular star clusters. For some time, it had been known that more globular clusters were visible in the summer sky than in the winter sky. What Shapley found was that the globular clusters formed a huge, roughly spherical halo surrounding the galaxy. This was surprising, but not a shock. The real shock was that the center of this halo, which all reason said should be the center of the galaxy, was located tens of thousands of lightyears away from the Sun, roughly in the direction of the constellation Sagittarius. In fact, the center of the halo was beyond where most astronomers thought that the galaxy ended! Remember that at this time, most also felt that the Milky Way was the whole universe, so this was a startling finding that not only is the universe vastly larger than anyone had ever dreamed, but for the first time, we had evidence that the Sun was not anywhere near its center.

The saga continued a few years later when Karl Jansky was working to develop long distance radio communictions. He found that he kept picking up static that repeated each day. Eventually he homed in on the source of the static. It was coming from beyond the Earth, in the direction of Sagittarius --- in the direction where just a bit over a decade earlier the center of the galaxy had been determined to lie. This being the first celestial radio source located in the constellation Sagittarius, we call it Sagittarius A. (The second such source is called Sagittarius B, the third Sagittarius C, and so forth.) Later, radio surveys with greater resolution found that a portion of Sagittarius A is more compact and radio loud than other parts, and this is called Sagittarius A* (universally pronounced "Sagittarius A Star"). Measurements show that Sgr A* is located at the actual center of the galaxy.

Here we find some interesting things. Careful study of Sgr A* finds that it, too, has some structure. Part of it is moving away from us and part toward us. Knowing that the gas radiating the radio waves is moving around something due to the gravity of that something allows us to determine that the something at the center of the galaxy has a mass of many millions of times that of the Sun. While visual light does not penetrate the interstellar medium to the core of the galaxy, infrared light does, and we see that there are some stars near the center of the galaxy that are moving around some unseen body of millions of times the mass of the Sun. We can even determine from fluctuations in the radio waves that this body can't be any bigger than our Solar System. The only thing that we can come up with having that much mass in such a small volume, and still not be visible, is a black hole --- a very LARGE black hole. We call such a beast a supermassive black hole. Now you don't have to worry about it eating the rest of the galaxy. Black holes don't really do that. Everything else is safely far enough away that it just orbits. In fact, it doesn't really matter if you are orbiting a million mass black hole, a million stars, or even Avagadro's number of marshmallows. All that matters is the gravity. In fact, if you are just a few light years away, there is no way to tell what you are orbiting unless you look. So, the only time that you'd worry about falling into the black hole is if you were to be within a few hundred million miles of it. Anything farther, and you are just orbiting, and orbiting safely I might add.

Interestingly enough, we find what look to be supermassive black holes at the center of other galaxies, too. This raises an interesting question that we are still working on. Did the galaxy form where it did because of the gravity of the supermassive black hole, or did the supermassive black hole form as a byproduct of the formation of the galaxy. In recent years, the argument that the supermassive black hole formed because of the formation of the galaxy seems to be gaining more supporters than the argument that the black hole formed first. But, that is something that I may save for a later blog entry.

I did answer the question in the title of this blog entry, though. The center of the Milky Way galaxy is located in the direction of the constellation Sagittarius, and in particular in the direction of a radio source that we call Sagittarius A*.  Oh, and since Sagittarius is a summer constellation (for those of us in the Northern Hemisphere), and it marks the center of the galaxy, and the halo of globular clusters is centered at the center of the galaxy, this is the reason that you see more globular clusters in the summer in the Northern Hemisphere (or in the winter in the Southern hemisphere).

-Astroprof

I just got back home last night from a conference, which is why I have been out of touch.  I took my laptop, but for some reason it wasn't connecting.  The last Windows update seems to have confused the networking ability, and so far I can't figure out how to fix it.  :(

This was a regional conference, and I really enjoyed it.  I gave a talk that was well received (much better received than I had thought that it would be).  A number of people were talking to me about it afterwards, and some even complimented me on a talk that I gave a year ago, and that they had been using some of the things that I said at that time.  Well, it is nice to be noticed!  Also, I had been feeling a bit stressed and worn out before the meeting, and I feel better now.  OK, I am stressed because I am behind on grading, and I need to prepare for this next week's lectures, and I am very tired after the meeting.  It is amazing how tired you can get at one of these things.  Of course, for those of you who don't know about physics and astronomy conferences, this one had days that started at 9am and lasted until 9pm.  I have been at some that went until 10pm or even 12am (of course the ones going until midnight were the astronomy conferences, so they were scheduled when astronomers are naturally awake!).

This was a regional conference.  North America is divided into a dozen or so different regions by many of the professional organizations, and this was a joint meeting of three organizations whose regions overlapped.  There are regional meetings, national meetings, and international meetings.  Each conference has a different sort of emphasis and theme.  So, you really need to go to all of them that you can.  Of the meetings that I go to, the regional conferences tend to have a bit more of an educational focus (about two thirds research and one third physics and astronomy education).  There are more papers presented on pedagogy and so forth.  The international meetings are all research, and the national meetings has a few sessions on education.  The sort of research presented is different, too.  At the regional meetings, it is appropriate to talk about research underway and your preliminary findings.  Here, you get feedback that gives you ideas how to proceed.  You also give final results of research projects that you gave preliminary talks on at the last meeting.  At the national meeting, nobody cares what research you are doing, they want to know what you  did, so you present the finished project, along with your conclusions.  At regional meetings, there are a lot of graduate students presenting their research and the results of experiments and observations that they are doing that will eventually be put together to form their dissertation.  At the national meetings, you get the final result, and many graduate students are basically presenting the conclusions that they arrived at in their doctoral dissertations.  At the international meetings, you tend to see more papers that are broader in scope, summarizing years of research that had resulted in many published papers.  Often you will see work presented that have several publications.  At the national meetings, often the work presented is the same as in a paper just accepted for publication (and often the authors will have copies of the paper to give to anyone interested).  At the regional meeting, you will see work that is not quite ready for publication, or is going to be part of a published paper.  Now, this is all generalizations, mind you.  Sometimes someone presents pretty important stuff at the regional meeting before going on to present it at a national or international meeting (after all it is good practice, and at the regional meeting you'll often get feedback that will be helpful in preparing the later presentation). 

Another reason that you go to the conferences is to network with others.  You present your work, and that keeps you and what you are doing in the minds of others in the field.  You find out what others are working on.  This is useful because it opens the door to collaboration on projects.  After all, some research is pretty involved, and you can produce a better body of knowledge if different people work on different aspects of it, and some research is difficult, so two or more people working on the same project makes it go quicker and better.  Also, you get to interact with other faculty at other institutions.  Often you are the only one at your home institution working on precisely your area of expertise, and so this allows you to talk to others.

Frequently, you get ideas from other people's talks, too.  Or, they may present something and you decide to do some work to either support their work or to refute it.  That is how science is done.  In graduate school, I had an advisor who said that what you do in the laboratory is not really science until you've shared it with others.  The whole idea is to get another set of eyes on the work (eyes that are not biased).  So, your findings may be interesting, but that is all they are until others have independently reproduced your work.  Then, it is accepted as correct.  Presenting papers at meetings, or seeing presentations, is one way to transmit information.  There is no way that a presentation at a meeting can be complete.  That is what the publication is for.  However, there are a lot of physics and astronomy journals, and the shear volume of work published is mind boggling.  No one can keep it all straight.  These publications are also expensive, and most libraries can not afford to get all of them.  So, if someone does work that is closely related to your work, and you would really benefit from reading their papers, you might not even know that they have published until you go to a meeting, because they might publish in a journal that you don't read.  Now you know, so you can go read that paper in that journal.  Even if your library doesn't have the journal, you can get it from other library.  In our field there is a major online database of preprints that you can get the paper online, too, if it is there.  And, as I said, many people bring copies with them.

So, there you have it.  That is why we go to these conferences.  Granted it is more complicted than that, but this gives you an idea.  Those of my readers that are fellow academics already know this, but those of you that are not might wonder why there are so many professional conferences all the time.  I think that our administrators wonder at that, too.  Since conferences are a major part of the job, then you'd think that our insitutions would pay for them, right?  Well, most do have a travel budget for just this purpose.  However, the travel budget only goes so far, and if you are active in your field, you will quickly use up your travel allowance.  The rest of the costs are on you.  Now, if you are lucky enough to have your work supported by a grant, then some of that money can be used for travel, but even that is limited.  Most of us eventually foot some of the travel expenses ourselves  This is another reason for the type of papers presented at the national and international meetings being different from those at local meetings.  It is simply more expensive to go to those meetings, so you need to report of completed work there, and you expect to hear about completed work.  Also, you are more likely to be grant subsidized to travel to those meetings.

Anyway, for those of you who wonder at why faculty are always flitting around going to conferences, this is why.  It isn't all fun and games.  Of course, for many academics, learning is fun, so ...

-Astroprof

Well, another spring break is coming to an end.  For those of us in academia using semesters, spring break is a regular March event.  The idea has even gone to the public schools here in this area.  They celebrate spring break, too, also with a week off in March.  But what good does it do?  OK, I'll admit that I really enjoyed having a week off.  I did a lot of yard work, house maintenance, word working (building a small cabinet), etc, that I normally don't have time to do.  I planned to do some astronomy, and to prepare for an upcoming conference, and grade papers, and prepare lectures, but I didn't.  Not until this weekend, that is.  Now, I am back to the routine.  Well, that is not any different than a regular weekend, other than that I had a week off.  I didn't travel anywhere, though that would have been fun.  Of course, for the next month, I'll be running all over Texas, but that will be work related.  I just caught up with things around the house.  Being single, things tend to add up.  It is hard for one person to keep up with it all.  That is particularly true for someone who is serious about being a college professor.  The job is more than just working 40 hours per week.  You never really stop being a professor.  The mind is always working.  You are always reading things that relate to the field.  Not everything is done at the office, and that means that you can work around the clock if you are not careful.  Again, being single, there isn't anyone else around to tell me to take it easy, I have to remember it for myself (and I sometimes forget).  Also, with no one else to spend time with, I might as well work ... after all, I actually like what I do.  It isn't just a job to me.

So, back to spring break.  What purpose did it serve?  A vacation?  Perhaps.  But is a week off in the middle of the semester the best thing?  The students are going to come back Monday, and most of them will be even worse off than normal.  It takes some discipline to spend these last two days of the break working on academic things like I am doing in order to put as much work in as I would on a normal weekend  (Not that I slacked off and just sat around all break, I worked on lots of things, just not college stuff.).  Most of the students won't even put in the normal amount of work that they would in a weekend.  So, they will be less prepared for class Monday than they ordinarily would.  Worse, they also won't have been thinking about their courses for a week, so they will have forgotten things.  OK, some worked over break.  But you all know that most did not.  Even those that really planned to put it off like I did until this weekend.  The difference is that I can do that with less bad results than they can. 

So, what purpose does spring break have?  Academically, a week long break doesn't really help.  The rest is nice, but a four day weekend would work as well for a rest, and it would be short enough that people would be less inclined to put things off until "later in the week" like they do with a nine day break (a week and a weekend).  The argument that the break is needed in order to provide a rest to promote learning is bogus at best.  We don't have a break in the Fall semester other than Thursday through Sunday for Thanksgiving.  The students learn just fine from the end of August through the end of November without a break.  In fact, the four day break near the end of the semester allows us to catch our breath before the final push for the end.  So, why the break in March?  Well, the real reason is that the tourism industry has pushed for it.  They want all those college kids to go somewhere and spend money.   In fact, with public schools off now, then there is money being spent all over the place, since it is now families travelling, not just college students.  Of course, if the travel and tourism industry were smart, they would lobby to change spring break into a series of smaller breaks spread out over the semester.  After all, would it not be a better business model to spread out the income (and the work) throughout the season rather than bunching it up?  Then, you would have steady income.  Also there would be security there, in that a week of bad weather at an inopportune time would not wreck the bottom line.  Also, you would get the same income using lower capacity and less staff, rather than having to have capacity for the peak periods, and perhaps extra staff then, as well.  Hmm.  Just a thought.  I will admit ignorance to how the travel and tourism industry really works. 

And, of course, I did enjoy the time off.  But, I would have enjoyed a series of smaller breaks just as well.  At any rate, spring break is over now, and it is now time for me to be hard at work getting ready for another week teaching, grading papers, and so forth.  I really need to get my presentation ready for the conference.  I know pretty much what I am going to say, though, and I've got a preliminary outline, so it is mainly just a matter of getting the visuals for the presentation done and putting it all on a flash memory stick to carry there.  I'll probably burn a copy to a CD, too, just in case.   The easiest thing is to do whatever the person right in front of me does, and since I don't know if they are using a CD or flash memory, I'll carry both.  I need to grade papers, but it was nice not to be getting any new ones this past week.  I do feel bad, though, about taking a complete break.  I didn't write or do any research for a week.  Bad Astroprof.  What sort of example am I setting for my students?  Bad, bad, bad. 

-Astroprof

A couple days ago, a NASA press release gave some of the preliminary findings from the Stardust spacecraft. For those that don't know, Stardust was launched in 1999, flew past Comet Wild 2 in early January 2004, and then returned to Earth this past January, bringing samples of the comet. Actually, what it brought back were samples of dust in the vinicity of the comet. Presumably these dust grains were ejected by jets of sublimating gasses erupting from the comet nucleus when heated by the Sun.

As I have said in a couple of previous posts, comets are believed to be relics of the formation of the Solar System. They formed in the outermost parts of the Solar System, where they have remained in a state of near suspended animation only a few degrees above absolute zero until something disturbed them to make they fall in closer to the Sun. In such a cold state, they are believed to have been very little altered in the last few billion years since their formation. So, studying comets helps us to understand the formation of the Solar System.

The press statement had several interesting comments. One that drew my attention as sort of strange was that olivine was found in the some of the dust grains, and olivine was not expected in comets. Huh? I am not a comet scientists, but I would not have been surprised one little bit to find olivine. This is one of the most common minerals that we know of. Not only is it very common in Earth rocks, particulary basalt and gabbro type rocks, but it is also found in meteorites, moon rocks, and on Mars. Olivine spectral signatures have also been found in the dust disks around young stars. These disks exend quite a long way from the stars, far enough out for comets to form, so it would not be a surprise for such comets to have olivine in them. Furthermore, some comet tails have shown the spectrum of olivine. So, how would it get into the comet's tail if it weren't in the comet. I must be missing something here. I hate these press statements because they leave out so much information. I then have to wait until something gets published in a journal (or I ask someone, if I know someone working on the project, which I don't in this case).

The other interesting statement was that some of the minerals in the dust grains are consistent only with high temperature formation. Thus, these dust grains must have formed near the Sun, and then somehow been incorporated into the comet. Now, this is a little different. Comets are supposed to form in the outer parts of the Solar System, where it was cold. So how did the high temperature minerals get there? There are a couple of possibilities. We know that protostars often have bipolar jets shooting out from their accretion disks along the polar axes. These jets would originate near the inner edge of the accretion disk, where it is quite warm. We have observed the jets shooting vast distances from protostars --- much farther than comets form, in fact. So, these jets could deposit material into the Oort cloud to be incorporated into comet formation. So, is Wild 2 an Oort cloud comet instead of a Kuiper beld comet? Hmm. Another scenario is that the T Tauri wind of the early protosun may have pushed the minerals out into the outer Solar System. A late protostar actually sheds a considerable amount of mass in a stream of material from the protostar. Some of the earliest (and most) studied such protostars were of the same type as the star T Tauri, so we call them T Tauri stars, and this stream of matter is the T Tauri wind. The T Tauri wind is in part responsible for the dispersal of the accretion disk of a protostar in the first place. So, it would not be completely unexpected that the T Tauri wind should push dust grains from the inner Solar System out to the edges, where they could be incorporated into comet. So, we need to modify our model of comet formation somewhat. Rather than totally ruining our ideas about using comets as a probe of the formation of the Solar System, this makes them even more valuable. Comets, if this is true, would store in deep freeze not just information about the outer Solar System, but rather about the whole Solar System!

Now, I losely use the term "comets" in the plural form. So far, we only have samples of one comet. Several spacecraft have now visited comets: Giotto, Deep Space One, Stardust, and Deep Impact. Each body seems to be different. So, comets may be as diverse as planets. We really have lot left to learn, and one sample from one comet is nowhere near enough. It is just the starting point.

When I first began teaching astronomy, comets were an interesting thing to end the semester with. Not much was known about them, and they were sort of a footnote in Solar System studies. However, comet studies have come a long way. The last decade has seen more information come to light about comets than had been known in all of astronomy history to that point. They are no longer footnotes. For the last few years, I have moved comets to a place of prominence in my class. I think that the more we learn, the more important that they will turn out to be.

-Astroprof

A couple days ago, in my post on Enceladus, I mentioned the rotation of Mercury as having a 3:2 spin-orbit coupling.  I thought that I might say more on the subject. 

Spin orbit coupling occurs when tidal forces on a planet or moon cause either speed up or slow down the rotation to match the orbital period.  The usual case is 1:1 spin-orbit coupling, such as Earth's Moon.  Tidal forces between Earth and the Moon work on both bodies to slow the rotation to match the orbit.  The Earth is bigger, so its work is done first.  The Moon, however, is still acting on Earth gradually slowing its rotation rate.  Fossil records indicate that millions of years ago, there were about 400 days in a year.  That isn't because the year was longer.  Instead, the days were shorter, so the Earth turned more in the course of a year.  Without the effects of the Moon, Earth might have a day only a five or six hours long.

As early as the 19th Century, physicists understood tidal dynamics enough to explain the 1:1 spin-orbit coupling of the Moon, and to even predict that tidal forces are also causing the Moon to recede from the Earth.  Reflectors left on the Moon by the Apollo astronauts, together with a powerful laser at McDonald Observatory in west Texas, showed that the Moon recedes from the Earth an average of almost 4 centimeters per year.  It was also entirely conceivable that a planet orbiting close to the Sun would experience similar forces as a moon around a planet.  So, it was not at all a surprise when the astronomer Giovanni Shiaparelli declared that Mercury had a 1:1 spin-orbit coupling to the Sun (not quite correct, as we shall see).

Mercury is very close to the Sun in the sky, so it is always very hard to see.  Mercury's the most elliptical of the major planets (Pluto's is slightly more, but Pluto isn't really major!).  The best time to observe Mercury is when it is at its farthest from the Sun, a point in the orbit called its aphelion.  Since Mercury's orbit is 88 days long, this happens about every three months.  So, Schiaparelli observed Mercury, and he believed that he saw vague fuzzy markings on it (an amazing observation, given his equipment!).  The next time Mercury was at aphelion, though, it was lined up with the Sun as seen from Earth, so he had to wait until the next aphelion after that.  He then was able to observe Mercury again, but seen from the opposite side of the Sun as before.  Then, the next aphelion, Mercury was again hidden in the glare of the Sun, but Shiaparelli was able to see the aphelion after that one.  He was now seeing the planet from the same vantage point as before.  Two aphelia later, he again saw the planet.  He kept this up for several years until the alignments were not so ideal.  His observations seemed to show the same fuzzy patches each time that he looked at Mercury from the same vantage point.  He was seeing Mercury exactly two orbits later, and it seemed to have the same side lit up.  So, from knowing that the Moon had a 1:1 spin-orbit coupling, he just assumed that so did Mercury.  After all, if every time that you look you see the same side lit, what else would you expect?  You'd just assume that it was spinning at the same rate as its orbit, so it would always keep one side towards the Sun.

This was the standard model for Mercury.  Even when I went to school, textbooks said that Mercury always kept the same side towards the Sun (pre-college textbooks are notoriously out of date when it comes to the latest scientific news).   The big shock, though, came in 1965 when astronomers using the powerful radio transmitter at the Arecibo radio telescope bounced radar signals off of Mercury.  The radar bounced back, but Doppler shifted.  A Doppler shift is a change in frequency of a wave reflected off of a moving object.  As Mercury rotated, one side was approaching us, and the other was receding.  This resulted in a Doppler shift on each side, but in opposite directions.  Analyzing the spread of the Doppler shifts, astronomers were able to accurately measure the rotational rate of the planet.  I often have my students do an exercise where they analyze this data to measure the rotational rate of Mercury.  What was found, though, in 1965 was that Mercury did not rotate in 88 days as everyone expected.  Instead, it rotated in a bit over 58.6 days.  This was exactly 2/3 of the orbital period.  Mercury has a 3:2 spin-orbit coupling.  So, that means that Mercury rotates exactly 3 times every two orbits. So, Shiaparelli was correct in thinking that he was always seeing the same side of the planet.  He was looking every two orbits.  He simply came to a wrong, though perfectly understandable, conclusion from his observations. 

So, how does this sort of strange 3:2 coupling occur?  Well, it is simple.  Mercury's orbit is very elliptical.  It's aphelion (farthest from the Sun) is almost 50% farther than its perihelion (closest to the Sun).  Thus, the tidal forces that would lock the planet are far stronger at perihelion than at aphelion.  So, what has happened is that the Sun has locked the perihelion rotational rate to very near the orbital rate.  However, elliptical orbits speed up and slow down, moving fastest at perihelion.  So, Mercury is locked to the faster portion of its orbit.  This also means that the aphelion is going to have the same side illuminated every second orbit.  It is just dumb luck that Earth's orbit is such that we only get to get a good view of Mercury every two Mercury orbits!

Anyway, another piece of astronomy history trivia.

-Astroprof

Well, this week is spring break for me.  Now, that doesn't mean that I will just sit around all week with nothing to do!  I have a LOT planned for the week.  I've already started.  The students seem to think that spring break is a break for the faculty.  Well, it isn't.  It is really a time to catch up.

This weekend, I put week killer and fertilizer on the lawn, pruned trees, ant poison on the yard, termite poison around the foundation and fence, carpenter ant poison on the fence, replaced part of the fence eaten by termites and carpenter ants, and made measurements of the other parts of the fence that I need to buy the materials for to replace.  I need to paint, too.  Oh, and I did my income tax this weekend, and I just electronically filed it.  (I can do astrophysics, but this stupid tax stuff drives me nuts.  I don't know why I put it off, since I am getting a nice refund, thanks to mortgage interest, property tax deduction, and lots of medical expenses this past year.).  Also, I am going to a conference in a bit over a week, and I need to prepare the paper that I am presenting.  That is on top of writing, preparing lectures for the next few weeks, developing new lab materials, and the rest of the professor stuff that I do.  Oh, and I really need to spend a day cleaning my office.  I am getting a new computer in a couple weeks, and I need a place to put it!  (It won't go where the old one is.).  Of course, that means backing up all my files this week.  I am also taking a group of students on a three day field trip in early April, so there is work to do for that, as well.  Gah.  I think that I need a month long spring break to do all of this!!!!

Anyway, that has been most of yesterday and today's work, so I have not had time to think astronomical things to blog about.  I'll do more of that soon, though.  I had a great post on light pressure and how light can have momentum, but I am having trouble with MSN Spaces and getting it into here.  I tried to put a few simple equations, and it is giving me issues.  Hmm.  How can I have a science blog without a few equations now and then?  There's got to be a way to do this. 

-Astroprof

Enceladus.  Mmm.  Mexican food.  Oh, wait.  Back on topic.  This is the usual response to thinking about this moon of Saturn.  I teach evening classes a lot, and we are often covering the Saturn system at 8pm or so, with hardly anyone in the class (myself included) having had supper yet.

 

On a more serious, note, though, Seeking Solace had asked for clarification on a news story that she had heard about Enceladus.  I got similar requests from students, and other non-astronomy faculty.  I missed the actual TV report (that teaching night classes, again), but from all the questions, they must have pretty well botched it.  What usually happens is that the report is filled with partial truths and incomplete facts.  Part of this is ignorance of the reporters, and part is producers cutting material in order to have more time for commercials.  Sadly, a major part is also the difficulty that research scientists often have communicating their subject to the general public.  Hmm.  That might be a good blog topic for me to tackle later on.  In a field so dependent upon public money, we really should, everyone of us, become experts at communicating to the public.

 

I hadn’t planned on doing a blog about Enceladus until all the confusion began.  So, here goes.

 

Enceladus is one of the medium sized moons of Saturn.  It was discovered by William Herschel in 1789.  While medium sized in the Saturnian system, Enceladus quite a bit smaller than our Moon, Titan (Saturn’s largest moon), the four major moons of Jupiter, or many other bodies in the Solar System.  Its size, coupled with a fairly close orbit to Saturn, makes Enceladus difficult to study from Earth.  We really knew very little about it until Voyager I passed Saturn in 1980 and Voyager II in 1981.  These spacecraft showed a rather strange body, portions of which appeared to have grooves or ridges, and other portions seemed to be heavily cratered.  The Voyagers also found a very, until then unknown, ring around Saturn that seemed to be associated with Enceladus.  In keeping with convention, this ring being the fifth discovered around Saturn was named the E Ring (the previous four rings being named A, B, C, and D Rings).  Furthermore, Enceladus is one of the brightest bodies in the Solar System, reflecting most of the sunlight that falls on it.  Speculation was that perhaps some sort of ice volcanism may be the source of these strange observations. 

 

There the story sat for a long time.  Saturn is VERY far from Earth, so observations from here simply could not answer the questions.  Now, the Cassini spacecraft has been studying Saturn up close for somewhat over a year now.  Several flybys of the moon Enceladus were planned for the mission, and these flybys have not disappointed us.  Finally, we caught what appears to be an ice geyser in progress.  This spews water out at high velocity, perhaps coating the moon with a fine “snow”, and even sending ice particles upwards in excess of Enceladus’ escape velocity, thus providing the material for the E Ring.  The problem, though, is now to explain how an ice geyser can exist on Enceladus. 

 

The way that a geyser works is for liquid under pressure to suddenly have the pressure released, causing the liquid to boil.  The pressure of the gas from the boiling liquid then ejects gas and boiling liquid through whatever orifice allowed the pressure to be released.  You get a geyser.  Now, to a little physics.  The boiling and freezing temperatures of a liquid, such as water, are not set in stone.  We are taught that water boils at 100C and freezes at 0C.  That is only true, though, for pure water at standard atmospheric pressure.  The higher the pressure, the higher the boiling point, and conversely lower pressure results in a lower boiling point.  You can raise the boiling point in a pot of boiling water by keeping the lid on the pot.  In your car’s radiator, the boiling point is raised by having the coolant system under pressure.  If you open the radiator while hot, you suddenly reduce pressure and that can make the radiator suddenly boil over (as a geyser of hot steam and boiling water all over you, if you are not careful).  Lowering pressure lowers the boiling temperature.  So, for example, in high altitude cities, water boils at a lower temperature.  Thus, cooking directions are different at high altitudes than for low altitudes.  As the pressure continues to drop, so does the boiling temperature.  At low enough pressure, the boiling point of water is below normal human body temperature.  Hence, your blood would boil at sufficiently high altitudes.  At very low pressure, the boiling point of water is actually as low as the freezing temperature.  For this and lower pressures, water is never a liquid --- it is only a solid or a gas.  Carbon dioxide exists in this way at normal Earth atmospheric pressure --- it is only a solid (dry ice) or a gas.  To be liquid, carbon dioxide must be placed under higher pressure.  Mars has this problem with water.  On the surface of Mars, the atmospheric pressure is so low that water is only a solid or a gas, not liquid.  Enceladus has no atmospheric pressure, so water on or near its surface can exist only as a solid or a gas.  If liquid water were to work its way up to near the surface, then the pressure would be low enough for it to boil.  The pressure from the boiling water might then break through the surface, and you get a geyser.  The temperature is so cold there, though, that the gas would almost instantly crystallize into tiny ice crystals.

 

So, that is how you get an ice geyser.  But it does not answer a deeper question.  How do you get the liquid water in the first place?  Saturn and its moons get nearly 1% of the sunlight that Earth gets.  This means that it is COLD there.  The surface temperature is likely colder than -180C.  Water can’t be liquid below 0C can it?  Well, pure water at atmospheric pressure can not.  However, water expands when it freezes.  So, kept under pressure, you can lower the freezing point.  One of the reasons that ice skates work is that the blades concentrate your weight on a small area, creating high pressure, melting a tiny layer of ice.  So, the skates really are sliding on a layer of water that is lubricating the interface between the ice and the skates.  However, at low enough temperatures, this would not work, and the skates would drag on the ice.  Could pressure be keeping water liquid on Enceladus?  No, not by itself.  Without some source of heat other than the Sun, Enceladus would be far too cold.

 

How else can you make water liquid at low temperatures?  Well, you can add impurities.  You do this with the coolant of your car.  Add antifreeze, and the freezing temperature of the water is lowered (also the boiling temperature is raised, but that is a different story).  What could act as antifreeze on Enceladus, though?  There has been speculation that ammonia might do the job.  Ammonia is known to be fairly common in the outer Solar System.  The clouds on Saturn, for example, are ammonia clouds.  The bright zones on Jupiter are ammonia clouds.  In sufficient concentrations, ammonia can act as an antifreeze, lowering the freezing temperature.  However, ammonia can only lower the freezing temperature to at best to a bit over -100C.  This is still too warm of a temperature for Enceladus, without some other source of heat.  Furthermore, a boiling mixture of ammonia and water would leave ammonia gas.  Analysis of the geyser plumes shows no ammonia so far, within detection limits of the Cassini spacecraft.  Thus, ammonia must be in such low concentration that at best it could only lower the freezing temperature by a few degrees.  So, the water must be at only slightly below 0C temperature.  This can only be accomplished by some heat source.  So, where does Enceladus get its heat?

 

Following the Voyager images of Enceladus, scientists began to suspect that perhaps tidal heating might be the heat source for the moon.  Many astronomers and planetary scientists were shocked to find very active volcanoes on Io, one of Jupiter’s moons.  Io is far too small to be geologically active, they thought.  However, Io turns out to be the most volcanically active body that we have observed in the Solar System.  It achieves this activity by tidal heating.  Orbital resonances between Io and the other major Jovian moons (Europa, Ganymende, and Callisto) regularly stretch and deform Io.  This stretching, then relaxing, then stretching, then relaxing has the effect of kneading the interior of the moon.  This produces the heat energy to keep Io’s interior molten.  Thus, Io is volcanically active.  Could something like this be at work with Enceladus?  Well, the same mechanism can not be at work.  Saturn really only has one moon of sufficient mass to do the job:  Titan.  However, Titan it too far away from Enceladus, and the two moons do not have an orbital resonance.  So, interactions with the other moons can’t be a source of heating.  However, Enceladus has an interesting relationship between its orbital period and its rotational period.  Enceladus has a 1:4 spin-orbit coupling.  That means that the moon rotates once per four orbits.  Spin-orbit coupling is nothing new.  Our own moon has a 1:1 spin-orbit coupling, so that it rotates one per orbit, thus keeping the same side towards Earth.  The planet Mercury has a 3:2 spin-orbit coupling, meaning that it rotates exactly 3 times per 2 orbits.  Thus, every orbit, it appears to have the opposite side towards the Sun.  Enceladus’ spin-orbit coupling, together with its fairly close orbit to Saturn, would result in varying tidal stresses.  These stresses would heat the interior of the moon, just as similar stresses heat Io’s interior.  However, computations show that the tidal stresses are simply not enough to warm the interior of the moon to the point that it would melt the ice.

 

So, what else can heat the moon?  The only way to determine the mass of a body in space is to see how gravity affects its motion, or how its gravity affects the motion of something else.  So, we have until now just guessed at the composition of Enceladus.  We know that the moons of the outer solar system are icy in nature, so we assumed a standard ratio of ice to rock for Enceladus.  However, the Cassini spacecraft’s orbit is slightly altered passing by Enceladus.  Analysis of Enceladus’ effect on the spacecraft allows for the determination of the moon’s mass.  We find that Enceladus is somewhat denser than we though.  That means that a larger portion of the moon is rock than we had assumed.  More rock also means more radioactive elements.  We know that energy released through radioactive decay is a significant source of heat in bodies such as Earth and the other rocky planets, asteroids, etc.  So, could the increased rock content of Enceladus result in more radioactive heating.  Yes!  However, calculations seem to indicate that it is not enough radioactive heating to account for a temperature sufficient to melt ice.

 

A further mystery is that only the southern portion of Enceladus seems to be warm.  These mechanisms would heat the moon more or less uniformly.  Why would only the southern portion of the moon be warm?  One speculation is that perhaps the ammonia antifreeze model might actually be at work in deeper layers of the moon, somehow carrying heat from the deeper interior to nearer the surface, but only in one area of the moon.  Again, we look to Mars to see hot spot plumes that create volcanic regions on the planet, leaving other portions of the planet almost completely untouched by tectonic activity.  Could a deep ammonia rich mantle be carrying heat to the south polar region?

 

Well, the answer might be a combination of all these factors.  Radioactive heating might add to the heat produced by tidal stresses.  Asymmetric transport of heat might concentrate it in the southern polar regions.  There is speculation that this might provide just enough thermal energy to keep water liquid several kilometers below the surface of the moon without adding ammonia to the water.  This water, under pressure, works its way to the surface, and erupts as ice geysers.  The only real catch seems to be that there is enough heat, perhaps, to keep liquid water liquid, but not enough to melt ice into liquid.  So, we still have a mystery as to how it got to be liquid in the first place. 

 

So, there you have the mystery of Enceladus.  Hopefully this answers some of the questions that people may have.  Of course, it may raise others ...

 

-Astroprof

 

I thought that I’d say a few words about asteroids.  “Asteroid” is a layman’s term for a large chunk of rocky material orbiting the Sun.  The term that professional astronomers use is “Minor Planet.”  Smaller bodies are called “meteoroids,” though there is no defined distinction between what makes something a large meteoroid or a small asteroid.  I suppose that if it were coming right at you, you’d think most anything were an asteroid. 

 

Most asteroids are likely left over from the formation of the Solar System.  The great majority seem to have orbits that put them farther from the Sun than Mars, but closer than Jupiter.  This region of the Solar System we call the asteroid belt.  A popular misconception is that the asteroid belt is chock full of these bodies.  You can imagine spacecraft having to weave between them.  Well, it isn’t like that at all.  Rather, the asteroids are generally so far apart that most would not even be visible to the naked eye even if you were standing on another asteroid.  The asteroid belt is mostly empty space.  You can plot a spacecraft’s course right through the asteroid belt without even looking to see where know asteroids are located, and the chances are great that you’d never even pass near enough one to see it.  You’d have to be extraordinarily unlucky (or lucky, depending on what you wanted) to even encounter one.

 

When asteroids were first discovered, and for nearly a hundred or so years thereafter, there was speculation that they may have come from a missing planet that had broken up, blown up, or had some such catastrophe that made the planet into a field of asteroids.  Well, it isn’t so.  There never was a planet there.  Most asteroids were likely never any larger than they are now.  Most seem to be rubble piles, composed of aggregates of smaller pieces.  They never really had a chance to grow into a planet.  Jupiter, being so massive, prevented that.  Jupiter’s gravity would have kept the asteroids from accumulating into anything larger than they are today.  Now a few of the larger asteroids have some characteristics that are more planet-like than being just piles of stuff.  Some of the largest ones are spherical due to the effects of their gravity.  They also seem to be at least partially differentiated, with the heavier material sinking towards the interior.  A few of these may have run into one another, shattering each other into smaller bits, giving us the iron and stony-iron meteorites.  Most, though, likely stayed small.

 

A bit over a century ago, the astronomer Daniel Kirkwood noticed that he didn’t seem to find many asteroids whose orbital periods matched integer ratios of Jupiter’s orbital period.  For example, asteroids were not found with orbits having periods 1/2, 1/3, 3/8, 5/8, 3/7, etc of Jupiter’s orbital period.  We call these orbits deficient in asteroids the Kirkwood Gaps.  He reasoned that somehow Jupiter regularly pulling on these asteroids in the same places in their orbits must move them out of their orbits.  A little under two decades ago, Jack Wisdom calculated that asteroids placed in these locations would have orbits that became unstable.  In particular, he found that these orbits would become chaotic, with wildly varying eccentricities.  The asteroids would then have orbits that carried them far from the classic asteroid belt.  Many of these asteroids would then hit the inner planets.  Interestingly enough, this would not happen immediately, but a few hundred million years after the formation of the Solar System. 

 

Evidence from the Moon and other bodies without erosion to cover up the distant past seems to indicate that the Solar System experienced a period of heavy bombardment early in its history.  The textbook explanation for this period of heavy bombardment is that it resulted from the planets sweeping up material left over from the formation of the Solar System.  Evidence continues to mount, though, that there was a second, late bombardment period.  This late bombardment happened few hundred million years later, while the first heavy bombardment was still winding down.  This would seem to fit nicely with Wisdom’s findings. 

 

An interesting thing, though, about forming the Kirkwood Gaps by Wisdom’s method is that it also would predict that asteroids near those gaps would occasionally go nutty and start flying around with chaotically varying orbits.  This means that asteroids that are perfectly well behaved now might in the future be a danger to Earth.  By chaotic orbits, I don’t mean random.  Rather, chaos, as used here, is a specific mathematical term.  Instead of suggesting truly random behavior, it suggests deterministic behavior that is simply beyond our ability to calculate.  So, we can’t even tell which asteroids would go nuts, nor when they would do so.  Hmm.  This might also explain why the period of intense bombardment slackened off, but did not drop to zero.  There are still plenty of things out there that pose a potential hazard to Earth.  If you look at SpaceWeather.com, you’ll see a listing of recent near misses, and a count of how many potentially hazardous objects are known.  A few years ago, when I first had students looking at the site, the number was under 200.  Now it is over 750.

 

Well, we are OK if we find them all, right?  No.  As I said, some asteroids near the Kirkwood Gaps might become problematic with little advance warning.  And there is another problem.  Asteroids wander around even without Jupiter’s influence. 

 

There is something called the Yarkovsky effect that can also alter the path of an asteroid.  A lot of people don’t realize it, but light can push on things.  At the subatomic level, there is no real distinction between particles and waves.  Everything seems to have both particle and wave properties.  So, light, normally thought of in wave terms, can carry momentum, normally something associated with particles.  We know that light can push on things.  This has been measured.  In fact, this also forms a limit to how bright an object such as a massive star or the accretion disk of a black hole can be.  If the luminosity is too much, then the light itself simply blows the outer parts of the object off into space.  This limit in brightness is called the Eddington Limit, after Arthur Eddington, who described it about a half century ago.  Well, now we come to conservation of momentum.  If light carries momentum, then the object emitting the light must have momentum in the opposite direction.  In other words, if light from object X pushes on object Y, then object X is also pushed in the other direction just as hard.  This is an application of Newton’s Third Law of forces:  equal and opposite forces.  Thus there is a recoil when you emit light.  Now, don’t expect your flashlight to jump out of your hand when you turn it on.  The recoil is not very much.  However, there do exist such powerful lasers that the recoil is noticeable and measurable.  So, how does this apply in a discussion about asteroids?

 

This is where the Yarkovsky Effect comes in.  You see, any object whose temperature is higher than absolute zero (ie, everything), emits electromagnetic radiation.  The intensity of this radiation is given by the Stefan-Boltzmann Law.  This law says that the intensity of light goes as the fourth power of the temperature (measured in Kelvin).  Thus, a difference of 1% in temperature yields about a 2% difference in intensity.  A difference of 11% in temperature yields more than 50% difference in intensity.  Light pressure varies linearly with temperature.  So, an asteroid that has a temperature difference on one side as opposed to another would have about a slight force on it from the warmer side.   Asteroids rotate.  The side towards the sun heats up, and the side away from the Sun cools off.  Thus, as long as the asteroid does not rotate too quickly, an 11% temperature difference between different sides of the asteroid is not unreasonable.  As the asteroid rotates, that means that it is warmer on the sunset side than on the sunrise side.  Thus, there is a net force that has a component parallel to the orbital motion of the asteroid.  This is the Yarkovsky Effect, and it has the effect of speeding up, or slowing down the asteroid in its orbit.  This, then, would change the orbit of the asteroid.  It would tend to make the asteroid slowly drift either outwards from the Sun, or slowly inwards towards the Sun.  If the asteroids orbit is rather eccentric, as most are, then the effect would be more pronounced near perihelion (the point in the orbit at which it is closest to the Sun).  Then, the Yarkovsky Effect would not only shift the orbit in or out, but it could also change the eccentricity of the orbit.  All of this means that an asteroid safely away from a Kirkwood Gap could even drift into one.  Jupiter would then eventually kick it into a chaotic orbit. 

 

We can be pretty sure that one day, one of these things will be kicked into an orbit that intersects Earth.  Astronomers no longer wonder if another large impact will happen on Earth.  Rather, we now wonder when it will happen.

 

So, on that cheerful note, I’ll leave this.  I’ll pick up with more asteroid stuff soon.

 

-Astroprof