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May 31 Oort's Constants, and the Rotation of the GalaxyWhen you look at the stars night after night, they seem to always be in the same position relative to each other. In fact, if you were to observe a constellation year after year for the rest of your life, the stars would always appear to be in the same orientation. However, they are not really fixed in space. Stars do move around. If you were to wait long enough, say thousands of years, then you’d begin to notice some small changes in some of the constellations. This motion of a star in the sky is called proper motion. Part of this is due to the fact that the stars are moving around the center of the galaxy in slightly differing orbits, and in some cases, such as Arcturus, very different orbits from that of the Sun. But, even if all the stars moved around the galaxy in perfectly circular orbits moving in the same direction, you would still observe proper motion. Why is this?
Out Milky Way Galaxy is a spiral galaxy. Spiral galaxies look like giant pinwheels. In a way, there are similarities in that the galaxies rotate. You can think of the disk of the galaxy as being like a giant Frisbee. You can draw spiral arms and dots on the Frisbee. The stars would be like little dots on the Frisbee. As you rotate the Frisbee, you simulate the rotation of the galaxy. This is a nice model, but it is wrong. You see, the Frisbee is a solid object. The galaxy is not. In fact, different parts of the galaxy take different times to go around. This is known as differential rotation. It is pretty typical of non-solid bodies: the Sun experiences differential rotation, the gas giant planets exhibit differential rotation, and galaxies have differential rotation. For our galaxy, the closer that an object is to the center of the galaxy, the less time that it takes to make a complete orbit. The Sun orbits the galaxy at about 220 km/s, taking nearly 220,000,000 years to go completely around (a period of time known as a galactic year or sometimes a cosmic year.) Stars somewhat closer to the center of the galaxy than the Sun move at close to the same speed, but they have a shorter distance to go around, so they take less time to make a complete orbit. Likewise, stars a bit farther out take somewhat longer to orbit. Naturally, this means that a star between us and the center of the galaxy will not always be between us and the center of the galaxy. This means that it is not always the same distance from us, too. If it started out between us and the center of the galaxy, it will be getting farther away from us. Depending upon the relative orientation of the star and the Sun around the galaxy, this star will exhibit proper motion as we see it from Earth, even if both it and the Sun were moving along in perfectly circular concentric coplanar orbits.
Interestingly enough, there are a couple of numbers that describe the relative orbital motions of the Sun and stars in our neighborhood of the galaxy. These we call Oort’s Constants, after the Swedish astronomer Jan Oort. Most people have heard of Oort’s name in conjunction with the hypothetical swarm of cometary bodies surrounding the Solar System that we call the Oort cloud. However, he never really thought of that as his biggest contributions to astronomy. He was more of a galaxy guy, and he did some very impressive work on studies of the Milky Way. This work, though, is almost entirely overlooked in introductory astronomy courses, with his (rather minor) contributions to comet studies overshadowing his other work.
There are two Oort constants. The first, called simply “A” is given by the equation: A = ½ (v_o / R_o – dv/dR) evaluated at R_o, where v_o is the orbital velocity of the Sun, R_o is Sun’s the distance from the center of the galaxy and dv/dR is the rate of change of orbital velocity with respect to orbital radius. This constant, A, is found to be about 14.5 km/s/kpc. It is sort of a measure of the shear of the galaxy, analogous to the tendency of a solid body to deform if part of it were to try to go more quickly around than another part.
The second Oort constant, “B”, is giving by: B = - ½ ( v_o / R_o + dv/dR) evaluated at R_o, where the terms have the same meaning as before. This constant is basically a measure of the vorticity of the stars in the disk of the galaxy, or rather their tendency to orbit about a particular point. B is found to be about -12 km/s/kpc.
Well, that might be more than you wanted to know about galactic dynamics, but I wanted to post a bit more technical thing for a change. I am sorry about the format of the equations, but I was having trouble figuring out how to input equations into my MSN blog.
-Astroprof
May 30 Cor CaroliAs summer is fast approaching in the Northern Hemisphere, the weather warms, and more people go out to public star parties. A very popular star to look at this time of year is Cor Caroli. This star, the brightest in the constellation Canes Venatici, holds the bayer designation of Alpha Canum Venaticorum. It is popular because it is a rather easy to find, and very pretty double star. It consists of an A0 star, which appears somewhat bluish in the telescope, and a dimmer F0 star, which appears yellowish. The color difference is easy to see, and this makes for a striking pair, somewhat reminiscent of the star Albireo, seen later in the summer (or later at night, now).
The two stars are separated in the telescope abou 20 arcseconds. At a distance of 110 lightyears for Cor Caroli, this means that the two stars are about 675 AU apart. An astronomical unit, or AU, is the distance between the Earth and the Sun. So, this means that these two stars are nearly 63 billion miles apart.
To find Cor Caroli, look first for the Ursa Major. Those of us in North America learn the Big Dipper asterism as part of Ursa Major. Follow the curve of the handle of the Big Dipper. Imagine that the curve of the handle is the arc of a circle. Near the center of curvature for that arc is a 3rd magnitude star standing mostly alone. That star is Cor Caroli. To the naked eye, and even in binoculars or most finder scopes, it appears as a single star. It is only with the telescope itself that you see it as a binary star, and a very pretty one at that.
The name Cor Caroli, itself, is somewhat interesting. Unlike most of the stars, whose names generally come to us from antiquity, and whose names are generally Arabic, this name is recent, and it is Latin. It means Charles' Heart, so named by Edmund Halley in honor of Charles II. A feminine form of the name Charles is Carol, and several women that I know named Carol have claimed the star as their own as Carol's Heart. I certainly won't argue! In French, the star is often known as Coeur de Charles and in German as Herz Karls.
The constellation itself, Canes Venatici, is the hunting dogs. It was created in the 17th Century by the astronomy Hevelius. Most of our constellations derive from Roman constellations. But, the Romans did not make every patch of the sky into a constellation, and this marks one of those areas without a clear constellation, so he created one. There are two stars of significance here in Canes Venatici, and these represent the two hunting dogs of legend, Chara and Asterion. Here, agreement breaks down. The northern dog is supposed to be Chara, with the southern one being Asterion. Of the two stars of any significance that make up Canes Venatici, the southern one is Alpha, what we call Cor Caroli. So, it is also Chara, and the next star, Beta Canum Venaticorum, is Asterion. However, many record the brighter star as Asterion and the dimmer star as Chara, making Beta Chara rather than Alpha. Ah, such confusion.
Of course, other people have seen this star, too. to the Chinese, it was Chang Chen, which is a seat or chair. It has also been named Al Kahb al Asad, the liver of the lion. I am not really sure what a lion is doing here, as this is far from Leo or even Leo Minor.
So, the next time you are out looking at the sky, look towards Cor Caroli and think about it.
-Astroprof May 28 Amateur Astronomer Observing ProgramsIn thinking about my next post, I thought that I'd do a follow-up to my
last post. So, this is also aimed at amateur astronomers. Often people will buy a telescope, or get one for Christmas, birthday, or whatever. Then, comes the task of learning how to use it. That is often a steep enough hurdle, even for some of the fancy goto telescopes that, once set up, will point themselves at whatever object the operator enters into a keypad. First, you need to know the sky. Second, you need to know what to look at. Knowing the sky means learning stars and constellations. I often suggest a simple bare-bones star chart, or a planesphere, or somesuch. A simple star monthly star chart can be found in many amateur astronomer magazines, or even online. Go outside, and learn which stars are which. You'll need this in order to find anything. Next, get practice using the telescope. Eventually, you get to where you can find lots of things. Now, as an amateur astronomer gets better and better at finding things, a problem eventually creeps up. First, many amateurs get tired of looking at the same things over and over again. After all, how many times can you look at the Orion Nebula? Saturn is cool, but unless you know what you are looking for, even it gets tiresome. You look at the Moon and marvel at how clearly you can see craters. Then what? At this point, many amateur astronomers get bored with their hobby, and they put their telescopes away. Is the problem that there aren't many things to look at? NO!!!!!! There are far more things that can be seen with amateur equipment than most people would ever have time to see all of. However, the problem is knowing what to look for. On any given night, there are hundreds of available interesting targets to point your telescope at. Of course, if all you know are a couple dozen things in the sky, you miss out. This is where an observing program comes in. If you plan ahead a little, you can enjoy a night out with the telescope. One of the first things that I suggest is to get an inexpensive star chart that shows lots of objects within reach of amateur telescopes. Find out what is up on the night that you are going out, and then look for these objects. This gets you started. But, it is only a start. Next, you will want to have a list of objects that you want to see. This is important, because the list then becomes a goal. You look at the first thing on the list, then the second, then the third, and so forth. OK, you might have to skip a couple, depending upon sky conditions, difficulty of seeing them, etc. Still, try to follow the list. Where do you get a list? There are several ways. First, you could make a list of your own. Pick out a constellation that is high in the sky when you want to observe. Look on a good star chart for objects in that constellation. Then, just go from object to object. I recall many nights when I got started in astronomy doing just that. It was lots of fun. Secondly, you could use a ready made list. Again, when a student, our astronomy laboratory manual had a list of various objects. There was a goal to see them. Also, several astronomy handbooks have lists of nice open clusters, interesting nebulae, etc. Follow those lists. Third, a ready made list is often available in amateur astronomy magazines. There is usually a monthly sky guide of some sort that gives a list of several interesting things to look that month. There you have a wonderful list! Even better, this list often has some explanation to go along with the list of objects. This will tell you what to look for, and what makes certain objects interesting. For example, it may tell you to look for the shadow of Saturn on its rings. Unless you were told that, you might miss it. The list may tell you to pay careful attention to the group of stars in the middle of some nebula, such as the Trapezium in the Orion Nebula. Again, this adds interest to the observation, even of an object that you've seen many times before. Or, the list may tell you that NGC 7006 is one of the most distant globular clusters of our galaxy. That makes seeing that tiny smudge very interesting. These get you going. But, still there is often a motivation issue. If you live where the sky is dark, and you have your own permanently mounted telescope easy to get to, then you can go observe with little problem. However, for most people, the sky at home is bright, the telescope has to be hauled out and set up --- sometimes quite a task itself. Often, you have to pack up the telescope and all your other equipment and drive for miles to get to a dark sky location. These all add obstacles to observing. So, you need something else to motivate you. Along come organized observing programs. The Astronomical League is a confederation of astronomy clubs here in the US. They have several wonderful observig programs for amateur astronomers. They call them "observing clubs." You select one that interests you, and on their web page they have a list of rules for the observing program and a list of targets. Once you see everything on the list, you send in your observations. Then, you get a little pin and a certificate, and your name is printed in their national newsletter. This really motivates a lot of people. Now you have a specific goal. You need to observe each object on the binary star list to get your certificate. This makes you want to observe those binaries. You need to observe each crater on the Moon list to get that certificate. That makes the Moon far more interesting to observe, since you are trying to match up a map with what you see in the eyepiece. Now, all those craters take on a special meaning for you. There is a list of objects that you are supposed to see with just binoculars. So, many amateurs head out with just binoculars to observe that list. Such a targeted program is a lot of fun, it really helps you get to know the sky, and it is a great motivator. For amateur astronomers who want to go on to even more serious work, they can monitor variable stars. There are far more variable stars than there are astronomers, so amateurs take up a lot of the slack in monitoring these stars. The American Association of Variable Star Observers collects their observations and makes them available to professional astronomers. There is even an organization called the Association of Lunar and Planetary Observers that collects amateur astronomers' data on planets, asteroids, and meteor showers. Many amateur astronomers move on to these serious observing programs where they are doing real science. Again, this is a good motivator to go out and make your observations. It doesn't matter what program you use. However, an organized observing program of some sort really does help get you out observing. -Astroprof May 26 Seeing RedI don't recall if I've talked about this or not, but here goes.
With summer coming on, the weather is nice, and sometimes people have
more free time. Often stargazing picks up a bit in the
summer. There are often more public star parties through the
summer, too. So, a lot of people new to astronomy and stargazing
decide to do some of their first observing. Now, they know that
it is dark out at night (that's the whole point!), so they bring a
flashlight with them. Here is where the problem comes in.
You see, the way that your eye works, in bright light two things
happen. One, your eyes adjust the size of the pupil to admit more
or less light depending upon the ambient light conditions. When
it is bright, your pupils contract to admit less light, and when it is
dark, your pupils widen to admit more light. This allows the eye
to work in much the same way over wider ranges of light. Second,
your eyes use a chemical called rhodopsin, or sometimes visual purple,
to see. Rhodopsin is hightly photosensitive (duh!). But,
this means that it is quickly bleached and becomes ineffective when
exposed to high light intensities. So, bright light uses up the
rhodopsin in the eye. But, you need the rhodopsin to see.
In dim light, you need all the rhodopsin that you can get. So, if
you expose your eyes to bright light, then you are in the dark, you
can't see for a while. It takes about 30 minutes for the
rhodopsin to regenerate, and they you can see in the dark well.
Interestingly, this is why really bright security lights are exactly
the wrong thing to use at night. If you are under the light, then
they night blind you to everything once you step out of the light, or
try to look into a shadow. So, when you use your flashlight to see, the extra light uses up more rhodopsin, and they you can't see in the dark. Often at star parties, people will come up with flashlights on, and we ask them to turn them off. Then, they can't see. They are apt to bump into things. Now, we can see them perfectly fine, because we've not been in the bright light. Of course, most things in the sky are dim, so when you are night blind, then you can't see them. It takes time to get dark adapted again (as I said, about 30 minutes). But sometimes, you just need some light. Starlight often isn't enough to read charts by. Sometimes, you need to look for something that you dropped in the grass, or perhaps you are looking for something in the bottom of a telescope case, or something. Perhaps you want to walk down a tree lined path, and even starlight doesn't penetrate. Then, what? Well, you have to resort of a flashlight. But, if you are careful, you can do so without losing dark adaption. It turns out that your eye has two receptors: rods and cones. The cones are used for color perception. The rods are used for black and white. The rods also are more sensitive in low light conditions. When it is actully dark out, you see in black and white. Try it sometime! You are unable to perceive color in very low light conditions! That is also why many things in the telescope look black and white, even though they have pretty colors when viewed through much larger telescopes or when you take a photo of them. Now, interestingly, the rods use a little different type of rhodopsin that absorbs more green and blue light. That means that red light doesn't bother it as much. So, if you use a red flashlight, then you can see without losing your dark adaption. Now, I should point out that you are still better off using as dim of a red light as possible. How do you get a red filtered flashlight? Well, many sporting goods places sell flashlights like I used in the Boy Scouts that have red filters that you can insert. Outdoorsmen use these to avoid damaging their dark adaption. You can also find them in military surplus stores. Or, you can make your own by taking an ordinary flashlight and putting a red film over the front. I have even seen flashlights with red fingernail polish on the front of them. All of that works. Red socks often don't, though, because the white light shines between the red fibers. Many astronomy suppliers now sell special astronomy flashlights that use red LED lights. These are even better than the other forms of red lights, because the light really is red. The other forms often leak some of the other colors, but normally not enough to notice unless you are really serious. Anyway, if you are seeing red, then you will likely see better when you turn off the light. Enjoy your nightime viewing! -Astroprof May 25 Some Solar StatsThe Sun is big. It’s bright, too. But, how big and bright is it? Very! Well, the astrophysicist in me wants numbers! I know that at least a few of my readers also like to put numbers to things. So here are some solar statistics for you.
The Sun has a mass of 1.99x1030kg and a radius of 6.96x105km. OK, so what? Let’s put this into perspective. This means that the Sun has a mass of 330,000 Earths. You could line up 109 Earths across the Sun, from one side to the other. Well, volume goes as the cube of the radius, so that means that you could fit 1,300,000 Earths inside of the Sun. Well, more or less, that is. The Sun is really just a giant ball of hot gas, so it doesn’t really have a surface (see my post about the Earth’s atmosphere from yesterday). So the numbers for physical size of the Sun are sort of an estimate. This “edge” of the Sun is defined by where the Sun gets thin enough and cool enough for light to begin to shine through its gasses.
Speaking of light, the Sun is pretty bright. The Sun shines with a light output of 3.85x1026 Watts. That means that each square meter of the Sun’s surface shines as brightly as just over one million 60 Watt light bulbs! Wow. Now, aren’t you glad that you don’t have to foot the bill for that! Here in Texas, where the electric rates are among the highest in the nation, that means that you’d have to pay $213,000 per day just to light that one meter of the Sun’s surface!!!! (That is computed using the electric rates on my electric bill that I just got last week.) And, of course, the Sun has a LOT of square meters of surface area!
Well, that other numbers can we get from this data? Well, we know that the Sun is composed of 91.2% hydrogen and 8.7% helium (by number of atoms). You will normally see in textbooks that the Sun is 71% hydrogen and 27% helium, but that is by mass. Remember that helium has about four times the mass of hydrogen. Well, this means that if you do a little mathematics, the Sun has roughly 9.3x1056 atoms in it!
You’ll notice that I am using scientific notation a lot here. That is because these numbers are just too ridiculously huge to write out otherwise. People often toss around the term “astronomically big number” without having a clue what an astronomically big number really is. The students in my introductory astronomy course for non-majors are simply shocked when they see these huge numbers all over the place. Even the majors’ students are a bit overwhelmed when it sinks in how big these numbers are that we are working with.
Let’s see. What else can we figure? Well, if you know the mass and radius of an object, you can compute the acceleration of gravity at its surface. Using the appropriate formula on the Sun, we find that at the Sun’s “surface” the gravity is roughly 28 times that of Earth. In other words, you’d feel like you weighed 28 times more on the surface of the Sun than you do on Earth. Well, you wouldn’t feel it for long. First, that level of g-force would make you black out instantly, and would kill you soon after. That would be merciful, though, since if you were on the surface of the Sun, you’d burn up in just about no time, flat. Oh, well.
Overall, the Sun has a density of about 1.4 grams per cubic centimeter. This is roughly ¼ of the density of Earth, though it is in the ballpark of the density of planets like Jupiter or Saturn. Now, this is the overall density. As you get closer to the center of the Sun, it gets denser. At the center of the Sun, the density of the Sun is roughly 160 metric tons per cubic meter. This works out to be about 0.16 kilograms per cubic centimeter. Let’s put this in perspective. Lead is famous for being heavy. This is about 14.2 times the density of lead. People don’t think about it, but gold is actually more dense than lead (and prettier). The center of the Sun is 8.3 times denser than pure gold.
The Sun’s a long way from Earth, too. The Sun is about 1.5x108 km from Earth. That means that you could put about 108 Suns side by side between the Sun and the Earth, or just under 11,800 Earths side by side. We call the average distance between the Earth and the Sun an astronomical unit.
So, there you have a few solar statistics. I could go on, but this gets the idea of how big the Sun is compared with Earth.
-Astroprof
May 24 Outer SpaceSo, how high is outer space? How high do you have to be until you are in space? Like a lot of the questions that I've tackled, this one seems simple at first, but more complicated when you look at it closely.
The dictionary definition of outer space is that space that is beyond the atmosphere. Well, that seems simple enough. However, when you look at it, it is a bit more complicated. The atmosphere is a system of gasses. Gasses don’t have a sharp or defined edge as do liquids or solids. An atmosphere, thus, just fades away into space. The air is held to the surface of a world by the world’s gravity. It is thicker and under higher pressure the closer you are to the surface of the world. As you get higher, the atmosphere gets thinner and thinner, until you are in space. But there is no sharp edge.
Let’s take Earth’s atmosphere, for example. Most of the atmosphere is confined to the lowest 10 miles. Once you get above this altitude, the air is very thin indeed. In fact, if you are more than a four or five miles up, say where many commercial airliners fly, then the air is so thin that you can’t even breathe. You’d pass out and eventually die of lack of oxygen. Higher than about 20 miles or so, then the air is so thin that air passing over aerodynamic surfaces on an aircraft is unable to provide enough lift to fly and air passing over an aircraft’s control surfaces does not provide enough force to properly maneuver the aircraft. At least this is more or less true for conventional aircraft. You might argue that the Space Shuttle can maneuver at these altitudes. Yes, but while the Space Shuttle might look like an airplane, and my behave sort of like one at low speeds and altitudes, it most definitely does not use the same sort of forces when it is at those altitudes. But, I digress.
The Earth’s atmosphere is composed of several parts. The lowest part is the Troposphere. It extends up to about 7 miles (12km) or so, give or take a mile. The troposphere is marked by a decrease in pressure and temperature with altitude. However, when the air is thin enough, ultraviolet light can break apart oxygen molecules, which then can recombine into ozone. This ozone then absorbs UV light, warming it. So, in such thin air, the temperature will actually increase with altitude. The part of the atmosphere where this happens in the Stratosphere. The stratosphere extends up until about 50km (31 miles). The next layer of the atmosphere is very thin and tenuous. Here, aircraft can not fly as aircraft because the air is so thin. It is called the Mesosphere. In the Mesosphere the temperature again drops with altitude. The Mesosphere extends up to about 80km (about 50 miles). Above the mesosphere, the air is so thin that individual atoms and molecules pick up energy and seldom run into one another to share that energy. The more energetic atoms and molecules move farther against gravity, and so higher. This means that the temperature increases with altitude. We call this the Thermosphere, and it extends to about 300 – 400 km (185 – 250 miles). Above this is a tenuous region of individual atoms and particles just flying around Earth. This is the Exosphere, and it goes out for thousands, or even tens of thousands of kilometers. That means the Space Shuttle, Hubble Space Telescope, and International Space Station are actually flying through the top of the thermosphere! This means that they will bump against atoms and molecules from time to time, slowing them down. Granted it is a tiny effect, but it adds up over time. Slowing down causes them to fall to a slightly lower orbit, there they run into more things, slowing them more. Unless the space station or space telescope are boosted to a higher orbit now and then, they will fall back to Earth. All low Earth orbits have this problem. We call it orbital decay, and it results from the fact that, though in space, these bodies are technically still in Earth’s atmosphere!
So, how do we define being in space? As you see, the atmosphere has no sharp edge. Rather, it just fades away. So, we arbitrarily make up some altitude and say that is the top of the atmosphere. Beyond that is “outer space.”
So, what is this magic altitude? In the United States, NASA has traditionally declared an altitude of 50 miles to be the beginning of space. Astronauts are really just members of the astronaut core until they first fly past 50 miles. Then, they get their official astronaut wings. 50 miles works as well as any other defining number in the US, since we still use imperial units. However, for the rest of the world, using metric units, 50 miles is 80km, and that is not such a nice round number. So, the FAI (Fédération Aéronautique Internationale), which is an international sanctioning body for keeping track of aeronautical records, defines outer space as being above 100km (62 miles). To win the Ansari prize, SpaceShip One had to carry a pilot above 100km twice within a specified time frame. For those of us stuck on the ground or in commercial airliners, the distinction hardly matters!
However, this does raise an interesting point. We think of spacecraft as launching into space on a rocket lifting off from a launch pad. However, what about flying into space? NASA, for a long time, had a dream of a Spaceplane that would fly into space and then land again as an aircraft. Could this really be done? Well, the X-15 experimental rocket planes did very much this sort of thing. In fact, these planes flew so high that they could no longer be controlled by their aerodynamic surfaces. At those altitudes, they were controlled with thrusters, just like on a spacecraft. Furthermore, 13 of the X-15 flights, ranging from July, 1962, to August, 1968, actually flew higher than the 50 mile altitude used in the United States to designate spaceflight! Two flights, both by Joe Walker, on July 19, 1963, and August 22, 1963, were even higher than 100km, the FAI mark for spaceflight! So, one would be justified to think of the X-15 as a spacecraft, and as a spaceplane.
-Astroprof
May 22 The Malmquist BiasWhat is the Malmquist Bias? It sounds like the title of some sort of action novel, or a spy thriller, or some such. Well, no, it is simply a term from astronomy. It is a special case of what in science we call a selection effect in data. The Malmquist bias is named for the Swedish astronomer Gunner Malmquist (February 21, 1893, to June 27, 1982) who first described this effect in data.
Let me first explain a selection effect for the non-scientists reading this. Science is supposed to be objective, and experiments are supposed to control for as many variables as possible. However, sometimes the way that you make measurements can affect the data. Lets give some examples of this effect outside of the natural sciences. For example, if you do a written survey to assess literacy, you find that just about everyone can read. Well, duh. Only the people who can read actually could fill out the survey! If you want to determine how Americans feel about gun control, you'd likely find a very different result if you surveyed attendees of a national Republican convention than you would if you surveyed attendees of a national Democratic convention. If you wanted to find whether or not college graduates believe that they got a good value for their education, you would want to survey people who graduated from college. How would you go about finding a list of such people? You could find a list of people who defaulted on student loans and survey them. You could also find a list of contributers to an alumni association and survey them. Both sets of people would be list of college graduates. But, you would likely get different results from your surveys. These are examples of where the experimental sample was in some way flawed. All three cases involved samples selected for ease of getting the sample. However, some self selection has already occurred prior to the experimental sampling. The results, therefore, did not answer the original question, but rather answered the question as applied to the subset studied.
The Malmquist bias is a sort of selection effect based upon observations. In astronomy, we generally just have to look at the data that we can collect. We are not able to actively experiment and influence or interact with our system. We just look. This has its own limitations and imposes a particular type of selection effects. We see things best that are more easily seen. For example, it we were biolgists studying a forest and wanted to know what was the most abundant organism in the forest. Well, the first response is TREES! Well, the trees are obvious, of course. The trees sort of define the forest. They are the first thing that you see. You can see the trees from far away. An aerial survey shows the trees. But when you get closer, you see that there are more birds than trees. So, would birds be the dominant lifeform? No, because if you get even closer, you see that insects vastly outnumber the birds. Then, insects are the most abundant thing in the forest, right? No, again. Bacteria outnumber the insects even more than the insects outnumber the birds. However, the bacteria are so much smaller than anything else that it is very difficult to observe them. You certainly can't see them from satellite or aerial photos!
As with the forest example, the Malmquist bias is a selection effect that comes from how easy or how hard it is to see different things. In particular, the Malmquist bias says that low luminosity objects are under-represented in data from more distant samples. That means that if you are a professional astronomer, you need to address this effect before your conclusions can be believable. I usually see the Malmquist bias discussed in papers about galaxies, but Malmquist himself proposed the effect for stars. Let me explain.
Suppose that you want to know what is the most common type of star. That is simple, you might say. Just look at all the stars that you see in the sky, find out what type of star they are, plot the data in a histogram of some sort, and see what category comes up with the biggest number. Simple! Also, wrong. For you see, the more distant an object is, the dimmer that it appears. Distant stars look much dimmer than nearby ones of the same type. So stars that are so dim as to be hard to see even if they are nearby, you won't be able to see at all if they are far away. Stars that are very bright nearby will still be bright enough to be seen so far away that you'll be able to see them at distances so great that all other stars are too dim to see. What this means is that you undercount the dim objects. We know that red dwarf stars are the most abundant type of star, but if you are walking outdoors at night with a friend who is an astronomer, don't ask him/her to show you one! Even the nearby ones are too dim to see with the naked eye. And most are even too dim to see through the eyepiece with telescopes that most amateur astronomers use. Yet, we can study the nearest stars and see that they are the most common type. Though we don't see them at great distances, we believe that they are there in the same numbers as they are in our part of the galaxy. If that is the case, then red dwarf stars are by far the most numerous star in the galaxy, even if they are not the most common type of star observed.
Likewise, the Malmquist bias works with galaxies. When we look at distant galaxy clusters, we tend to see only the large bright members of the galaxy cluster. The smaller ones are too dim to easily detect. We find lots of the smaller galaxies in our Local Group of galaxies. However, we don't see them in very distant galaxy clusters because they are small and dim, and just to hard to spot at those great distances. They should still be there, though. We might assume that they are there in the same numbers as in our Local Group. Hmm. Well, this might be a problem. For you see, the farther away that you look, the farther back in time that you look. Are the numbers of dwarf galaxies constant, or does the number get smaller over time as they are consumed through collisions with the larger galaxies? Perhaps small clouds of gas collapse to form new dwarf galaxies at some point. There are some proponents of both ideas. The problem is that we have a tough time finding the dwarf galaxies at great distances. So here, the Malmquist bias rears its head, and it is harder to put to rest when you are talking about cosmological distances, and the corresponding differences in the age of the samples studied. The more distant galaxy samples exist at a younger time in the life of the universe than do the nearby samples. So, does the lack of observation mean that there were fewer dwarf galaxies, or is this a Malmquist bias effect? If it is a Malmquist bias, what does that mean, if anything? You see the problem. It sure makes things complicated.
So, to refresh your memory. The Malquist Bias is an observational selection effect in which the dimmer objects are under-represented in samples of data from great distances. This is because the farther away, the dimmer that something appears. If it is dim to start with, then it just too dim to see at great distances. You have to then infer the presence of the dim objects at great distances. If you don't feel comfortable doing that, then you can only compare data samples made as similar distances. For example, if you are studying galaxy groups, you can only compare galaxy groups at distances of 1500 Mpc (Mpc, or megaparsec, is 3,260,000 lightyears) with other galaxy groups located at about 1500 Mpc. A comparison of a 1500 Mpc galaxy group with one located at only 10 Mpc is not really valid unless you address the Malmquist bias and whether or not undercounting the dwarf galaxies will affect your conclusions.
-Astroprof
May 20 Apollo to the Moon!So, how many men have been to the Moon? I get asked this question
now and then. Hmm. You'd think that it'd be a simple
answer. Like so many things, though, it depends upon how you
define your terms. What do you mean "to the Moon"? Well, you might say that "to the Moon" means landing on the Moon. In that case, the answer is simple. 12 men have been to the Moon. Neil Armstrong and Buzz Aldrin landed in the Sea of Tranquility July 20, 1969, with the Apollo 11 mission. In Apollo 12, Pete Conrad and Alan Bean landed near the unmanned Surveyor 3 craft in the Ocean of Storms on November 19, 1969. Alan Shepard and Edgar Mitchell of Apollo 14 landed in the Fra Mauro region on February 5, 1971. On July 26, 1971, David Scott and James Irwin of Apollo 15 landed near Hadley Rille in the Sea of Rain. Apollo 16 saw John Yound and Charles Duke land in the lunar highlands near the Descartes Crater on April 21, 1972. And, the last two men to land on the Moon, Eugene Cernan and Harrison Schmitt, landed at the Taurus-Littrow valley on December 11, 1972. Oh, but you might define "going to the Moon" a bit differently. For example, Apollo 8 was the first manned mission to the Moon, with Frank Borman, Bill Anders, and Jim Lovell, arriving December 24, 1968. However, Apollo 8 did not carry a Lunar Module, so no landing was possible. Instead, the Command Module just circled the Moon, and came back to Earth. However, doesn't that count as going to the Moon? Apollo 10 also flew to the Moon without landing. Apollo 13 was supposed to land near Fra Mauro, but an exploding oxygen tank aborted the landing portion of the mission, and the spacecraft simply looped around the Moon and came back to Earth. Each of the missions that landing on the Moon had a third astronaut who remained onboard the Command Module orbiting the Moon while the other two astronauts landed. Hmm. That makes for nine missions to the Moon. Each carried three astronauts, so there were 27 men sent to the Moon, right? Well, sort of. You see, some of those astronauts went more than once. So, if you are asking how many individuals went to the Moon, then 27 is double counting, so we need to go back and not count those that went more than once. Eugene Cernan flew on Apollo 10 around the Moon, and landed with Apollo 17. Likewise, John Young also flew around the Moon with Apollo 10, and he landed on the Moon with Apollo 16. Lovell, flew around the Moon on both Apollo 8 and Apollo 13. These three men flew twice, so that means that only 24 different individuals flew to the Moon. So, that's your little bit of Apollo trivia for the day. -Astroprof May 19 Star SizesHow big are stars? Well, they come in all sizes. Compared with Earth, they are all very big. But, the size of a star does not depend only on the mass of a star. For example, a star with half the mass of the Sun won’t be half the size of the Sun. In fact, depending upon what stage the star is in its life, it can be hundreds of times the size of our Sun. When a star begins to die, the core compresses and becomes hotter, and this makes the outer portions of the star expand and cool. The result is what we call a red giant star. The biggest stars are truly huge. Some red supergiants can be so big that many millions of stars the size of the Sun would fit inside them, and yet only dozens of times the mass of the Sun. That makes them mostly a very thin gas! The smallest stars are on the order of the size of Jupiter, the largest planet in our solar system. They may be the size of Jupiter, but they would have a hundred times the mass of Jupiter.
So, how do we measure the size of a star? That is tough. It is tough enough to measure the size of a planet, and you can see them as disks in a telescope! To measure the size of a planet, you first need to know how far the planet is from Earth. Then, you look through a telescope at the planet. The size of the planet can then be determined by how big the planet appears in the telescope. You measure the angular size of the planet, as it appears in the telescope. The actual diameter of the planet will be given multiplying the distance of the planet times the tangent of its angular size. In principle, this would work with stars, too. However, stars are much farther away than planets. The problem is that at the great distances of stars, they appear very tiny in the sky. In fact, the diffraction of light passing through a telescope blurs the image of the star so much that the blur is larger than the image of the star! This makes it impossible to determine the actual size of the star. Only a couple of stars are so large that they can be imaged as anything but a dot. The size of those stars can thus be directly measured. The sizes of the rest of the stars can only be determined with quite a bit more work.
The first thing in determining the sizes of stars is to realize that they shine because they are hot. There is a relationship in thermodynamics, called the Stefan-Boltzmann Law, that relates how bright an object shines to its surface area and to its temperature. If we assume that stars are spherical, then this works out very easily. As it turns out, stars are not perfect spheres, but the approximation is good for most stars. A few, though, such as Regulus, are decidedly NOT spheres (they are oblate spheroids), and so a different approach is needed. But, let’s keep it simple. For spherical stars, you can do a bit of algebra on the Stefan-Boltzmann law to find that the radius of the star (measured in solar radii) is approximately equal to square root of the luminosity of the star (measured in solar luminosities) divided by the temperature squared (measured in solar temperatures). Huh? What does this mean? Well, it turns out that the equations get simplest if you do comparisons rather than outright computations. So, we often compare values to those of the Sun, since the Sun is the nearest star to us and the easiest to measure. So luminosity measured in solar luminosities means how many times brighter than the Sun. A star of 12.3 solar luminosities is 12.3 times brighter than the Sun, and a star of 0.25 solar luminosities is ¼ as bright as the Sun. Likewise, solar temperatures are relative to the Sun’s temperature. A temperature of 1.5 solar temperatures means 50% hotter than the Sun (measured in Kelvin). A temperature of 0.82 solar temperatures means that the Kelvin temperature of the star is 82% that of the Sun. And, of course, solar radii are size measurements relative to the radius of the Sun.
OK, so we have a neat little formula that tells us how big the star is, compared to the Sun, as long as we know how bright it is and how hot it is. But, how do we find these measurements?
To find the temperature, you look at the light from the star. The hotter the star, the more blue it appears. The cooler the star, the more red it appears. In particular, you can determine the temperature of the star by measuring what color of light the star gives off most intensely and then using something called Wien’s Law. Wien’s law tells us that the temperature of a star, measured in Kelvin, is equal to 0.0029 divided by the wavelength of the most intense color of light radiated (measured in meters). Then, to find the temperature in solar temperatures, divide this value by 5800K (the temperature of the Sun).
Finding the brightness of the star is a bit trickier. First, you have to find the absolute magnitude of the star. To do that, you need to know the distance of the star. Finding the distance of a star can be tricky. For fairly nearby stars, it isn’t too bad. We use parallax. First you determine very accurately the position of the star. Then, six months later, Earth has moved to the other side of the Sun. If the star is near enough, then it appears to shift slightly in the sky due to the motion of the Earth. You measure the position very carefully again. You then compute the angular shift of the star in arcseconds. An arcsecond is 1/3600 of a degree. Half of this angular shift is the parallax angle. The distance of the star in units of parsecs is equal to the reciprocal of the parallax angle measured in arcseconds. Great! Now we have the distance. Next, to determine the absolute magnitude, you measure the apparent magnitude (how bright the star appears in the sky). The absolute magnitude is equal to the apparent magnitude plus 5 minus 5 times the logarithm of the distance in parsecs. That is: M = m + 5 – 5log(d).
OK, we have the absolute magnitude. Now what? Next, you compare the absolute magnitude of the star to the absolute magnitude of the Sun: 4.85. The brightness of the star in terms of solar luminosities is equal to 2.512 raised to the power (4.85 minus the absolute magnitude of the star). Now, you are ready to go back the first equation that I gave, since you now have the brightness of the star in solar luminosities and the temperature in solar temperatures.
So, that’s a bit of work to find the size of a star! Still, that is basically what you need to do. Astronomy is, in some ways, a very difficult science. We don’t always get to directly measure what we want to measure. We sometimes have to make all sorts of other measurements and then piece them together like a jigsaw puzzle to get what we want. Of course, I think that is fun!
-Astroprof May 18 Huygens and Saturn's RingsSeventeenth Century Dutch scientist Christiaan Huygens holds a special role in astronomy. He is the first astronomer to realize that Saturn was surrounded by a ring system. Huygens was not really the first to see Saturn's rings. That honor probably should go to Galileo. However, Galileo's telescope was nowhere near as good as Huygens' telescope. As a consequence, Galileo didn't recognize the rings for what they were. He reported that it looked as if Saturn sometimes had "ears." Working with a telescope better than Galileo's, Huygens was able to get somewhat better views of the strange features on Saturn. To him, it appeared that Saturn had "handles." Huygens, together with his brother, constructed a much better telescope. This telescope allowed him to see the rings much better than Galileo. Carefully studying Saturn for many months, he came to the conclusion that Saturn's strange appearance was due to a ring encircling the planet. Huygens didn't want to publish his finding without substantially greater study and some sort of explanation for the rings. However, he also didn't want to lose credit for his discovery. So, this presented a problem: how to claim a discovery but keep it secret until he had a better grip on it.
Huygens' caution was understandable. Only a half century earlier, Giordano Bruno was burned at the stake for his declaration that Copernicus was right about the Earth and the planets going around the Sun, and that such motion meant that Earth was a planet and that the planets were potentially Earth's, complete with inhabitants. It was only a quarter Century after Galileo's trial. Though the Seventeenth Century was a time when science was beginning to make huge strides forward, there was great resistance to these strides when they seemed to run counter to how most people thought. But, as I said, great strides were being made. Though Galileo's findings got him into hot water (Actually, the way that he presented the findings got him into FAR more hot water than the findings themselves!), within a quarter century most people had accepted his work. By the middle of the Seventeenth Century, when Huygens was doing his work, pretty much everyone had accepted the Kepler's variation of the Copernican system, with planets moving around the Sun in elliptical orbits. People were even ready to accept Bruno's contention that this made Earth a planet, and the planets worlds like Earth. Inhabitants on those worlds was still a far fetched idea, but it no longer got you burned at the stake. Even Kepler had written a fictional account of beings living on the Moon (sort of the first science fiction novel!). Galileo's findings that Jupiter had moons was taken as confirmed fact. All this in just a few decades! But, still, ...
In studying Saturn and Saturn's "handles" or, as he now knew them to be, rings, Huygens also discovered a Moon orbiting Saturn. We now call this moon Titan. Huygens correctly reasoned that since Galileo's findings of four moons orbiting Jupiter was now accepted as true, then the discovery of a moon, or moons, orbiting Saturn would be accepted quite readily. So, in 1656, Huygens publishes De Saturni luna observatio nova, a paper describing his discovery of a hitherto unseen moon of Saturn. In this paper, he constructs an anagram that spelled out "Annulo cingitur, tenui, plano, nusquam cohaerente, ad eclipticam inclinato." This is Latin for "There's a ring surrounding the planet, nowhere touching it." So, if anyone else publishes a paper claiming discovery of the ring, and such discovery is aclaimed, then he could point at the anagram and show that he had found the ring first. On the other hand, if it turned out not to be a ring, then he would not lose face. Also, if someone else announced the discovery of a ring and got into trouble, then Huygens could remain silent about his discovery. Incidentally, the Polish astronomer Johannes Hevelius published a treatise the same year on Saturn. In his work, Hevelius suggested that the strange appearance of Saturn's handles were due to protrusions from the planet itself.
Finally, in 1659, Huygens publishes Systema Saturnium, in which work he explains that handles, ears, and other contrived explanations don't really account for Saturn's shape. He then publically proposed that a solid ring circled the planet, maintaining an orientation above the planet's equator, and maintaining a fixed orientation with respect to the ecliptic (the plane of Earth's orbit around the Sun). This made for varying views of the ring during Saturn's 29 year orbit around the Sun. Though not immediately accepted, Huygens' treatise at least did not result in his persecution. Within a decade, though, most astronomers had finally accepted that Saturn did, in fact, have a ring. Giovanni Cassini's discovery of a gap in the ring, though, gave the first clue that the rings were not solid. In fact, Cassini showed that the rings were unlikely to be solid due to tidal stresses in the ring material. He proposed that the rings were actually a swarm of tiny satellites that simply looked like a solid ring from Earth due to the huge number of objects orbiting Saturn so close to one another. This idea eventually turned out to be correct.
As was typical in Huygens' day, few scientists restricted themselves to only one aspect of science. So, Huygens did far more than just astronomy. He developed the wavefront model of optics, and he invented a pendulum clock. Huygens' weight driven pendulum clock turned out to be the most accurate style of timepiece developed to that date, and continued to be for many years thereafter. He also published a paper on probability theory, and he studied elastic collisions (collisions that conserve both momentum and kinetic energy). Huygens did continue work in astronomy, though. He observed markings on the surface of Mars. By timing how long it took for these markings to return to the same point on the disk of the planet, he was able to measure the rotational rate of Mars, showing it to be nearly the same as that of Earth.
It was in honor of Christiaan Huygens that the probe that detached from the Cassini Spacecraft to study the surface of Titan was named the Huygens Probe.
-Astroprof
May 16 Coal Powered AircraftNow for an aviation related entry! I was reading in the local paper recently about coal powered aircraft. Naturally, one things of steam engines, with a boilerman stoking a fire with a shovel. Yeah, right. Like that sort of thing would fly. Granted, I recall some fanciful stories about similar coal/steam driven flying machines written in the early 20th Century. I guess, you'd call them early science fiction. Needless to say, it was more fiction than science.
However, this is not the intent of the research. Rather, the researchers, including leaders in the field working at Penn State, are looking at an alternative to jet fuel that is derived from coal. So, they are looking at some liquid or gas fuel that is derived from coal. This, in fact, is not unreasonable. In fact, there already exist methods to gasify or liquify coal to produce fluids similar to natural gas or to diesel or fuel oil. None of these products are useful as aviation fuel, but the researchers are developing something that might do the trick.
So, how does this work? I have not read much on the specifics of the procedure, but there are several things that we can guess from the properties that aviation fuel needs. Basically, there are two types of aviation fuel: Avgas (basically a high octane gasoline) and various grades of jet fuel (basically high grade kerosine). The liquification process will produce a thicker, less explosive fuel, more like kerosine than like gasoline. So, the new fuel will be a jet fuel. Jet fuel has some specific needs that keep gasoline from being used as a suitable fuel. For one, gasoline is too volatile and explosive. It would tend to ignite prematurely at the injector rather than dispersing in the combustion chamber of the engine. Also, gasoline breaks down much too easily in high temperatures typical of jet engines. High performance jet engines also tend to have even more specific needs. The compression of air during intake into the engine makes the engine itself very hot, not to mention heat from combustion. Getting rid of the excess heat is an issue. This is where the high grade jet fuel comes in. Kerosine can tolerate quite high temperatures without breaking down or spontaneously igniting --- much higher temperatures than gasoline. Kerosine also has a much higher boiling point, also a plus in high temperature environments. And, kerosine has a fairly high specific heat, so a given volume of kerosine can absorb more heat to raise it to a high temperature than an equal amount of gasoline. These properties mean that the jet fuel itself can be used to cool the engine. The fuel circulates and picks up heat before being injected into the engine to burn. This has an added advantage of putting the surplus heat back into the engine's exhaust. The way that a jet engine works is that air enters the engine at a much lower speed than it exits the engine. Momentum is the product of mass times velocity. So, a higher exhaust velocity has higher momentum. The difference in momentum between the air into the engine and the exhaust gasses is called impulse. Newton's third law says that for every force, there is an equal and opposite force. Accelerating the gasses to exit faster than they come into the engine requires a force. So, there is an equal and opposite force on the engine, driving the aircraft forward. (Note that this description is strictly for a ramjet, a turbojet, or a scramjet. Turbofans, increasingly popular with commercial airlines, use the jet engine to drive a large fan that provides as much or more thrust than the jet exhaust. Turboprops are similar, in that a jet drives the propeller.) The force on the gasses comes from an increase in pressure of the gas in the combustion chamber. This increase in pressure results from heating the gas through burning the fuel. In addition to the heat, burning fuel converts liquid fuel into gas. Converting a liquid to a gas typically results in an increase of volume of nearly 100,000% (assuming constant pressure), so this is the major source of pressure in the engine. Additional heat can't hurt, though it would represent such a tiny percent increase in thrust that I'd imagine it to be virtually undetectable. Thust, jet fuel must be stable under very high temperatures. By the way, the same rationale is why one of the most commonly used rocket fuels is RP-1, basically very highly refined high grade kerosine. Rocket engines work the same way as jet engines, only they don't take in air.
So, how does all this lead to coal power? Well, the Air Force has been working on alternative jet fuels for many years. One problem with very high performance engines is that they typically heat their kerosine fuel about as high as can be safely done, meaning that extra cooling is needed besides just the fuel. Naturally greater efficiency and performance would result from a fuel that could do the job by itself. Also, the United States imports most of its oil. This imported oil, of course, is the source of the kerosine jet fuel. From simple national defense arguments, it is clear that it would be a very good idea for the military to depend upon some fuel source that does not come from other countries. OK, this is why the government stockpiles oil, but still ... . The United States, however, has vast supplies of coal. The problem with coal is that it is harder to transport than the liquids derived from petroleum. Coal is also much heavier than kerosine and burns slower, so it is not useful in aircraft engines. Hmm.
But, wait. I said that you can liquify or gasify coal. This produces a fluid more useful for our purposes. The Germans did something like this during World War II. However, the process for converting coal to a liquid or gas is expensive. It is cheaper to buy and refine crude oil. Well, it was cheaper, I should say. With oil becoming more expensive, coal is looking better. The newer forms of the procedure produce a liquid with properties not too dissimilar to kerosine. In fact, one advantage is that the new fluid is stable to even higher temperature than most kerosine products. This makes it an ideal fuel for high performance jet engines. The Penn State group has produced what seems to be a perfect ballance, called JP900. The name means that it is stable to 900 degrees Fahrenheit (over 480C). Even better, it seems to burn cleaner, and with the same energy content. The only catch is that it costs a lot to make. However, if oil prices remain high, the cost factor is not such a problem. Furthermore, those jet fighters drink jet fuel at an amazing rate. The Air Force alone accounts for over half of the entire government's fuel bill! Well, I suppose that if the Navy didn't use so many nuclear reactors, they' be up there, too. Still, a fuel source that doesn't depend upon foreign oil would be a significant advantage. Now, if it works for military jets, perhaps it can be adapted for civilian jets, too. This too, could become important if the cost of fuel stays so high. After all, airlines can't keep spending more than they make forever, can they? And if it works in airplanes, could truck engines eventually be adapted? The more of this fuel that is produced, the cheaper it will be to make it.
What also interests me, given my interest in space, is that JP900 will have properties very similar to RP-1, only a bit cheaper. Hmm. Also, it burns cleaner, meaning that as a rocket fuel it would cause less damage to the stratosphere as it shoots through. Again, hmm. I hope that the fuel gets perfected soon. It would be interesting to see if RP-1 gets a run for its money as a dominent rocket fuel.
-Astroprof
May 15 Sputnik 3It was May 15, 1958. At the Baikonur launch facility deep in the
heart of the Soviet Union, a massive R-7 rocket roared to life at 07:12
UT. The R-7, basically a slightly modified SS-6 ICBM, and its
derivatives have been the main launch vehicle for the Soviet Union and
for Russia --- a tribute to Sergei Korolev, its designer. On this
date, the R-7 carried the third Soviet satellite into orbit, dubbed
Sputnik 3. This third Soviet launch was seen as just another step forward for the Soviet Union by most of the public. However, it shook the US space experts. At a mass of over 1.3 metric tons, Sputnik 3 was bigger than all US spacecraft currently under construction put together. Sputnik 3 was, in fact, bigger than all spacecraft launched from both the United States and the Soviet Union put together (with one exception being a failed launch of a similar Soviet craft a month earlier). Sputnik 3 was also heavily instrumented. It became apparent to US space experts that the Soviet Union had a booster capable of launching a manned spacecraft. The United States had nothing of the sort operational at the time. Also, the heavy instrumentation of Sputnik 3, though mostly geophysical in nature, could have included surveilance equipment. In fact, Korolov was looking to launching later Sputniks as the first spy satellites. Fortunately for the US, a tape recorder aboard Sputnik 3 malfunctioned, giving US scientists a chance to complete analysis of data from the two working Explorer spacecraft (Explorers 1 and 3, since Explorer 2 failed to reach orbit). This allowed James van Allen to announce the discovery of belts of radiation surrounding Earth. Explorer 1 had been launched January 31, 1958, and Explorer 3 launched March 26, 1958, and both spacecraft carried geiger counters onboard, which made the discovery. The Soviets almost beat us to the discovery, though. Korolev had really wanted to launch the heavy and highly instrumented Sputnik first. However, he was convinced to start cautiously with smaller satellites. So, Sputnik 1, launched October 4, 1957, was a small craft carrying only a radio transmitter. Even small as it was, it was roughly about the mass of the first three Explorer spacecraft combined. Sputnik 2, several times more massive, but still just a bit over 1/3 the mass of Sputnik 3, carried the dog Laika into orbit. Sputnik 1 was a major public relations coop for the Soviet Union, as the first satellite put into orbit. Sputnik 2, the second manmade satellite, was also a major news story, as it carried the first living being into orbit: a dog. Eventually, the United States put animals into space, but we waited until we could bring them back again. Laika was on a one way trip. She was supposed to live for about a week, but actually baked to death within a couple hours due to loss of insulation from her capsule during launch. There was no provision to bring her back to Earth. I am not sure why there wasn't a bigger outcry against the Soviets for sending the dog to certain death rather than holding off until a reentry module could be constructed. At any rate, Sputnik 3 provided useful data on the environment of near Earth space during its year or so of operation. Eventually, Sputnik 3's orbit decayed and it reentered Earth's atmosphere April 6, 1960. In typical Soviet fashion, data collected by Sputnik 3 was pretty much kept quiet. Also, in typical Soviet fashion, Sputnik 3 was actually the fourth Sputnik launched. The one a month earlier failed to reach orbit when it booster failed prematurely. The Soviets kept that quiet, and it was many years until the truth was finally known. So, that is the story of the third Sputnik placed into orbit. -Astroprof May 13 Full Moon NamesHappy Flower Moon! Well grades are done. I got them all turned in to the registrar. The semester is over!!!!! I think that I look forward to that more than most of my students. This has always been a stressful time of the year for me. I sort of envy my friends who are not in academia. They get to take vacations and do all sorts of things while I am in this final stressful push. Pretty much my whole life takes a back seat to finishing the semester. Adding to that is the fact that our administrators pile on end of year paperwork. Well, it isn't really end of year paper work, since the academic year goes through the end of the summer. However, many of our faculty don't teach in the summer, so they figure that none of us are around, and thus they hit us with end of year paper work. Heck, if they made the deadline the middle of summer, then the faculty not teaching in the summer would either come in to do it, or else they'd do it before they leave. But, administrators don't always think that way. Anyway, it is now time for another astronomical posting. Hmm. Looking back on my few astronomical postings, I seem to be fixated on the Moon. Yeah, the last posting was for new amateur astronomers, but most have been about the Moon. Oh, well. If I'm going to fixate on something, the Moon is at least astronomical! So, early this morning (Central time zone here where I live in the United States) the Moon was full. Yeah, it looked full the night before, and it will look full tonight. In fact, it looked full to the casual observer for a couple of nights. However, the full moon occurs when the moon is as close to being opposite the Sun in the sky as it is going to get. It normally doesn't get exactly opposite. When it does, then of course the Earth is exactly between the Moon and the Sun, so the Earth's shadow falls on the Moon and we get a lunar eclipse. But it always gets pretty close to opposite about every 29.5 days. That is the full moon. With a telescope, you can see that there is virtually nowhere that you can see shadows at that time, since you are looking from the same direction as the Sun. A night before or after, the Moon will show a thin bank around one edge or the other (technically, we call the edge of the Moon the limb of the Moon) where you see shadow. Being opposite the Sun, the full moon rises as sunset and sets at sunrise. Any other phase of the Moon rises before or after sunset and sets either before or after sunrise. The farther the Moon is from full, the bigger this effect, which is why you see the Moon in the daylight sometimes. The farthest the Moon can be from full is new moon, when it is as close to aligned with the Sun as possible on the sunward side of the Earth. On that day, the Moon rises at sunrise and sets at sunset. Well, as I said, the full moon was early this morning. To be exact, the full moon was at 06:51 UT. The UT means "Universal Time," which is the local mean time at the prime meridian. For those of you not in astronomy, read that as Greenwich Mean Time. 06:51 UT corresponds to 1:51am CDT here in Texas. Normally, there is supposed to be a six hour time difference here, but since we are on daylight saving time, we add an hour to hour clock, making this five hour difference, instead. The full moon, being exactly opposite the Sun in the sky, is interesting because, as I said, it rises at sunset, sets at sunrise, and thus is up all night. In an earlier post, I mentioned that the light of the Moon is enough to read by. In fact, you can do all sorts of things by the light of the full moon. If you are dark adapted, you can fish by the light of the Moon, drive by the light of the Moon, and even see someone sneaking up on you. That is why during World War II, almost all American amphibious landings were at full moon. That way, when night came, the defenders could not easily sneak up on our soldiers in the dark, since there wasn't much dark! Now, with night vision goggles, we turn things around and do all our invasions at new moon, when it is as dark as possible. But, another thing that you can do by the light of the full moon is farming. When you are harvesting crops, you might want to keep going after sunset. The Moon gives plenty of light to keep working after dark. Often harvesting occurs in September or October, so the full moon that occurs nearest the Autumnal Equinox (normally about September 22 or 23) is called the Harvest Moon here in the Northern Hemisphere. The full moon the following month is often called the Hunter's Moon. People have often heard these terms. However, there are names associated with the rest of the full moons, too. While pretty much everyone agrees on the name of the full moon closest to the Autumnal Equinox and the full moon following that one, there isn't nearly as much agreement on the names for the rest of the full moons. So, what I am about to tell you is just one interpretation. The full moon closest to the Winter Solstice, about December 21 or 22, is called the Cold Moon, or the Frost Moon, or the Christmas Moon (particularly if it occurs in the week after the solstice). The first full moon of the year is generally the Wolf Moon. The second full moon of the year is often the Ice Moon or the Snow Moon. Interesting enough, the full moon in November is also sometimes called the Snow Moon, particularly farther to the North, say in Canada, or the Frost Moon if the December full moon is not called that. Sometimes, the November Moon is called the Beaver Moon, at least it was in places where beaver hunting was a big deal. The March full moon is sometimes the Storm Moon, the Worm Moon, or the Sap Moon, depending where you are from. In southern Canada, it was often the Crow Moon. If it occurs in the first three weeks of March, it is sometimes called the Lenten Moon in regions where there is a strong Catholic influence. The full moon in April is often the Growing Moon, the Planting Moon, or the Egg Moon. Once in a while, the April full moon is called the Rainy Moon, since in most of the country it rains a lot in April. (This has always confused me as to why they put National Astronomy Day in April! You seldom get to see anything.) In the Northwest, the April moon was the Fish Moon, as fish were swimming upstream to spawn. Overriding each of these is the term Easter Moon for the first full moon following March 21. The rule for computing Easter is that Easter is the Sunday following the first full moon after March 21. Finally, we get to this month's full moon: the May full moon. This is often called the Flower Moon. After all the rain in April, flowers grow in May. Well, that is what is supposed to happen. Actually, what normally happens around here is that weeds grow. I guess that they often have flowers, too, but they are icky flowers that produce pollin that upsets everyone's allergies. Up north, say in Canada, the May full moon was mostly the Hare Moon. I guess that they have more rabbits than flowers in May. Often their June moon was the Flower Moon. I have also heard Corn Planting Moon and Milk Moon for the May full moon. Now we talk about the summer moons. The June full moon is sometimes called the Strawberry Moon. In Europe, it is often the Rose Moon. Here in Texas, though, the roses have all pretty much dried up for the summer by June. The July full moon is sometimes the Buck Moon or the Hay Moon, depending upon whether you live in a forested area or a prairie. Often it is the Thunder Moon, because thunderstorms often occur in July due to the high levels of surface heating that occur then. Around here a full moon beteen mid July and mid August is often the Hot Moon. The August full moon is sometimes the Grain Moon or the Dog Moon (particularly if early in the month). Near the Great Lakes, it is the Sturgeon Moon. You might wonder, if there is a Dog Moon, then is there a Cat Moon? Well, not officially, but I think that cats claim pretty much all of them --- at least mine does! If the first full moon of October occurs closest to the Autumnal Equinox, then it is the Harvest Moon, not the September full moon. In that case, the September full moon is the Wine Moon, the Singing Moon, or the Elk Moon. Of course, if you put all three together, then you get a drunk elk singing. Hmm. Anyway, as you see, the names there isn't really any great agreement here as to the names of the full moons. Most of these names are local in origin, so applying them across the board doesn't really make sense. Still, it is sort of fun to call the full moon something. And, of course, it is interesting that the Flower Moon is occuring the day before Mother's Day here in the USA this year. So, enjoy the Flower Moon! -Astroprof May 12 Setting Up and Using Your First TelescopeA while back, while at a public star party, someone came up and asked me a question. Well, OK, so that happens at every star party. Well, this question was from someone who had recently purchases a small telescope. I get these all the time. Many people go to the store, buy a telescope, get it out of the box, and then realize that they don't know how to use it. I am not sure why this is a surprise. After all, if they bought a piano, do they think that it would come with a ten page instruction booklet explaining how to be a concert pianist? Buying a set of high end pots and pans does not make someone an expert chef. For some reason, though, they think that buying a telescope is different, and that they should be able to set it up, look through it, and see HST quality pictures. Well, folks, it doesn't work that way! In fact, setting up the telescope often involves adjustments that are not obvious. Very few telescopes can be used effectivly right out of the box. To make matters worse, over and over I see the same thing: the less that someone knows about using a telescope, the more difficult to use telescope that they buy.
So, what makes the telescope easy or difficult to use? Well, the mount is one thing. Telescope mounts come in a couple of different varieties: altitude-azimuth mounts and equatorial mounts. The equatorial mounts are useful because they have one axis parallel to the rotation of the Earth. That means that they only need to turn in one direction, and at a constant rate, to track an object in the sky. Altitude-azimuth mounts need to move on both axies of rotation to track something. Most inexpensive mounts are altitude-azimuth in nature. That means more complicated motion. That is OK, but it means more work for you. Often I tell people that if they want to buy a telescope for astronomical work, an equatorial mount is a worthy investment, even if they are buying a purely manually operated mount. A tracking motor is a very nice accessory. Generally, I tell people that they should never purchase a refractor on anything but an equatorial mount. OK, I have seen some decent refractors on altitude-azimuth mounts, but they are rare. As for reflectors, small ones should also always be on an equatorial mount. The large ones, though, as long as they are used at fairly low power, work well on a Dobsonian mount ( a type of altitude-azimuth mount). Personally, I think that the Dobsonian variant is about the only type of manual altitude-azimuth mount useful for astronomy. There is a caveat here, though. Computer controlled and guided telescopes can operate with pretty much any type of mount. You set them up and then tell them what you want to point at. If you set them up right, then they will automatically point themselves at (or near, more likely) the thing that you wanted to look at. They will then keep the telescope pointed at the object, no matter how complicate the motion needed to do so. Of course, you pay more for that capability, but the prices are dropping very quickly. I imagine that in the not too distant future, the majority of all amateur astronomer telescopes will have this goto capability.
For equatorial mounts, you need to align one axis with the rotational axis of Earth. This is called polar alignment. There are several ways of doing this. I won't go into them here. If all that you want to do is look at something for a while, then even a rough alignment will do the trick. Altitude-azimuth mounts don't need polar alignment, so they are easier to set up.
The other important thing is to have a STABLE mount. You also want some way to make fine adjustments. At the last star party, a kid brought a telescope that his parents had bought him for me to show him how to use. Well, it was a cheap refractor, was on an altitude-azimuth mount, and the mount wobbled every time that you touched it. There were no fine adjust controls. So, even if you got the object that you wanted in the field of view, then it would move out of view, and you had no easy way to get it back into the field of view. That meant loosening the screws holding the telescope in position. However, the mount was so loose that any touch to those screws sent the image several fields of view from the eyepiece. There was also a massive amount of backlash in the mount, so you could get it set on something, but tightening the set screws moved the telescope off of the target. Even if you managed to tighten the screws, then when you removed your hand, the weight of the telescope moved it off target ... even with the mount locked in place! The kid was really disappointed that I couldn't show him an easy way to use his telescope. Well, the sad truth is that there WAS no easy way to use that telescope! So, you want a STABLE mount, fine adjust controls, and no slop in the controls. I have seen some where there was so much packing grease in the mount that when you moved the controls, the telescope would keep moving for 5 to 7 seconds after you quit turnig the adjustment knobs! If you have such a problem, then clean the packing grease out of the gears. WD-40 seems to do a good job of washing most of the grease out.
OK, so now you are set, right? Nope. You need to make sure that the finder scope is pointing at the same place as the telescope. Look back at my earlier blog entry on finder scopes to read more about them. This is your sighting aid. You will need it, since the telescope itself sees such a small portion of the sky that you must have it set pretty much on target to start with. That is what the finder is for, but it only works if it is pointed where the telescope is pointed.
Now, you are set to use the telescope, right? Well, sort of. Next you want to select the right eyepiece. The magnification of the telescope is the ratio of the telescope's focal lenght to that of the eyepiece. The longer focal length eyepiece, the lower the magnification. Normally, that is what you are after: low magnification to start with. It is tough enough finding something, so low power lets you see the biggest portion of the sky, and that makes it easiest to find something. Then, you can go to higher power if you want. Often, you find the clearest views at low power, however. That is the other problem that most beginners make. They try to use the highest power available. How do you know what the focal length of the eyepiece is? It should be written on it somewhere. You can't go by the physical size of the eyepiece. That is often related to the focal length, but it is not always true that the largest eyepiece has the longest focal length. It depends somewhat on the composition of the eyepiece. There are different types, most using varying number of lenses in them. This can make for all the eyepieces being the same length, the longest focal length being the longest eyepiece, or even the shortest focal length being the longest eyepiece. So, you need to read the focal length from the eyepiece itself. Also, the higher the magnification, the dimmer an object normally will look. So keep that in mind, too.
OK, you've got low power, a stable mount, aligned finder, ..., you're ready to go, right? Yep. Not the fun starts. It takes practice and skill to find something. It is MUCH tougher than it looks. I'd recommend something easy for a first attempt --- like the Moon. It is amazing how long it takes someone first using a telescope to find the Moon. Then, you can go for something bright, like Jupiter. Take your time. Get used to finding bright things first, then dim things. Eventually, you can go for things too dim to see. Huh. How can you find something too dim to see? Simple. You can look on a star chart. You might find that the object of interest M-X for example, is located just north of a little triangle of stars that is east of a fairly bright star that you can see with the naked eye. So, you point the telescope towards the bright star. Get it centered in both the telescope and the finder scope. Then, looking through the finder, you slide over to the little triangle of stars. Then, you move to where the cross hairs of the finder point right where the star chart says that the object is located. Now, if everything worked right, when you look in the telescope, you can see the object. Normally, you just missed it, but by using the fine adjust knobs to move the telescope a couple of fields of view in every direction, you'll find it. This procedure is called "star hopping."
Now, if you have one of those cool computer controlled telescopes, you just input M-X and it will point towards it all by itself. Well, that is in theory. There are a few telescopes that have GPS systems so that you turn them on, and they know how they are oriented and can align themselves. Most, however, you have to do the work. This means pointing the telescope at two or three known stars. The telescope then knows how it is oriented and can then point to something else. But to point at those stars, you need to know which stars are which and how to find them. That means doing all of the steps in the paragraph above. So, you still need to learn to star hop.
Finally, an new amateur astronomer came to me at a recent star party and asked about the little number scales along the axies of the telescope. This person had already learned to align the finder and to star hop. But, she wanted to know about what we call "setting circles." For a polar aligned equatorial mount, the axies of rotation of the telescope also correspond to the motion east and west in the sky, and north and south in the sky. These are along the grid lines of the celestial coordinate system. So, you can use this alignment to more easily find something. The celestial equivalent of latitude is called declination. The celestial equivalent of longitude is called right ascension. So, you would just have to point the telescope at a known star. You then can adjust the movable circles on the telescope to read the correct right ascension and declination for the star. Then, you just adjust the telescope until the right ascension and declination are reading the same as object M-X that you wanted to look at. If everything went well, then when you look in the telescope, you will see M-X. Again, how well this works depends on how well polar aligned the telescope is in the first place and how well you set the circles. Any errors in either will make for errors in the result. Often it is good to set circles from a star fairly close to the object of interest. Also, the longer the time since when you set the circles to the corret right ascension and declination of the reference star, then the more time that error can creap into the system. Also, on many older systems, the setting circles don't track, so they need to be set immediately before you use them. So, do this procedure quickly. The longer the time delay, the less likely that you'll point the telescope at the right spot in the sky. Really, setting circles is what the computers are doing in the computer controlled telescopes.
So, that is how you set up and use a telescope.
-Astroprof May 11 A very poor investment.Well, I've given my last finals. Grades are due tomorrow. I
told my students that all their work is due last week. I don't
have time to grade anything but finals before grades are due.
Well, these two show up to the final and plead with me to take their
term papers (due almost a month ago). I tell them that it is way
too late. Anyway, they plead. So, I tell them to leave the
papers, and if and only if I have time, that I will look
at them, but I won't promise anything. Well, I looked.
Neither paper seemed quite right. Hey, what do you expect?
The students don't have time to write a good paper during final exams
week! Well, these were not badly
written. That was a first clue. Second, they were not the
right format, and they weren't quite the narrow topic that I
wanted. So, I decided to look them up. Sure enough.
Both were plagiarized. One was cut and past from a couple of
wikipedia articles. The other, though, was different. Normally, my students just cut and past from web pages, or else they just use an entire web site. Heck, one student turned in a paper that said "Click Here" to access more information. Yeah, right. Another one used equation numbers that started at 24. Yeah, like that wasn't lifted from somewhere. Another semester, two students both plagiarized from the SAME web site. They copied different sections, but the end of one paper overlapped several paragraphs with the beginning of the other one. What was even more stupid was that they were lab partners!!! One student clearly didn't understand the concept and photocopied an encyclopedia article and turned it it. Yeah, like I wasn't going to catch that one. OK, so what was special about this semester's plagiarism? Well, I did a search on a key phrase of the paper, and lo and behold there was his paper! OK, it wasn't the whole paper. It was only the first page. You see, the first page of the paper was shown as an example of what the rest was like on a term paper site where you can buy a term paper. This particular one was rather expensive at $75. So, this student pays big bucks for a paper that winds up hurting their grade. He'd have been better taking a zero. That makes this a very poor investment choice. Do they really get away with turning these things in with their other classes? I find that every semester I find plagiarized papers. It has been several years now that I have not found one. Another physics faculty member at my college also assigns papers, and has had the same result. We both every semester find at least one, and usually more than one plagiarized paper. Do we just look harder than the other faculty, or does everyone catch students? Or perhaps, the students just think that they can pull off something like this with a science professor that might be caught by someone in the humanities? I don't know. Oh, and my colleague also found an intact term paper online from a student this semester. I have noticed that just about every term paper turned in very late, as in finals week, is plagiarized. The students are not slow in writing the paper, nor are they waiting for a book to come in from another campus or something. One student once had ordered a book and it was late arriving, but he came and asked me about turning in the paper late after the book arrived. He actually did a very good paper. But the rest are just about always a case of the student blowing off the paper, and suddenly realizing that they want a grade for it, but only have 30 minutes to an hour to write it. So, they cut and past off of the internet. I haven't caught one who purchased a paper before. That is a new one. Perhaps a few have slipped past me. That's a sad thought, since I already find between 5 and 10% of my students' term papers are plagiarized. I know that I am missing some. This semester I made an extra point of warning them about not plagiarizing. I still got three. Well, that isn't surprising, since the students who plagiarize don't listen to me anyway. That is obvious from their exam and laboratory scores. Anyway, it is really frustrating. -Astroprof Cough, cough, can I borrow your calculator?So, I am giving my last final today. This student comes in looking like death warmed over. He coughs, gurgles, drips, drools, etc. Get gets up several times during the final to blow his nose. Well, I am finishing up grading a final from last night. So, he comes up and wants to borrow my calculator. I am thinking, "Yuck! Germs!!!". Anyway, I am using my calculator grading the other papers! Come on now. This is a FINAL EXAM. Shouldn't they think to bring a calculator by now? OK, it is an astronomy class, not the hardcore physics class. Still, they knew that they'd need to compute some things. Good grief.
So, he finally finishes. He is next to last to finish, of course, coughing the whole time. Then he turns in his scantron, ..., damp. OK. Is this sweat, humidity, mucus, ..., what? Ich. Germs!!!!! Hey, if I wanted to do germs, I'd be a biologist, or an MD like my brother. I went into astrophysics. How many germs do we deal with in astrophysics? None, I tell you. None. Now, I have this infected scantron to handle. Yuck. Grades are due tomorrow, so, I guess that I have no choice. I just have to wash my hands very well afterwards.
Oh, well. These are the hazards that come with being a college professor. I am off to grade, grade, grade.
-Astroprof May 10 The Origin of the MoonWhere did the Moon come from? Once astronomers came to realize that it wasn’t always there, then the natural question was to ask how it got there. However, the Moon is far enough away that getting good data that can be used to answer the question proved difficult until the space age. True, telescopes helped, and the larger telescopes available by the middle of the Twentieth Century helped even more. Unmanned probes flying past the Moon in the early 1960’s helped as well, and unmanned missions landing on the Moon by the mid 1960’s helped even more. However, even better data came from the observations made during the Apollo missions. And the best data was from data collected on the ground during the Apollo landings of 1969 through 1972 and from analysis of the rocks brought back to Earth from the Moon. In fact, these data changed our views of the origin of the Moon.
Prior to Apollo, three theories competed for an explanation for the origin of the Moon. One was the coformation, or coaccretion model. Planets are believed to form from the material swirling around a star as it forms. Instabilities in this disk of material might collapse to form a planet. In fact, we think that this is exactly how Jupiter and Saturn may have formed. However, we now believe that the other planets formed from an accumulation of smaller bodies. Such an accumulation makes formation of a double system, such as Earth and Moon difficult to explain. In the manner that Jupiter and Saturn formed, the material collapsing to form the planets might also collapse to form moons. This may be how the larger moons of Jupiter and Saturn formed. But, these are modern ideas. In the 1960’s, it was thought that perhaps all planets collapsed directly out of the proplyd (the disk of material surrounding the newly formed Sun). So, the idea that the Moon may have simply formed at the same time as the Earth, out of the same material, seemed reasonable. One of the biggest problems for this model to explain is why the Moon orbits in a plane well off of the plane of Earth’s equator. The larger moons of Jupiter and Saturn orbit near those planets’ equatorial planes. In fact, that is exactly where a moon should orbit if it formed in this manner. Our Moon, though, orbits closer to the ecliptic than to the celestial equator.
A second idea for the origin of the Moon was the capture model. According to this model, the Moon formed elsewhere and passed too close to Earth, where the Earth’s gravity captured the Moon into orbit. Again, in the 1960’s astronomers were beginning to suspect that planets may have formed as smaller bodies, planetessimals, that then accreted to form the larger planets. Perhaps, they reasoned, the Moon was such a planetessimal. However, this model has a very difficult time explaining how the Moon’s orbit became so nearly circular.
The third model for the formation of the Moon is the fission model. According to this model, Earth once spun much faster than it currently rotates. A large chunk of the Earth split off and flew into space to make the Moon. This model can be traced to a suggestion made by George Darwin (Charles Darwin’s son). George Darwin knew computed that tidal forces between Earth and the Moon should be making the Moon move farther from Earth. In fact, this was confirmed by the Apollo missions. The Moon moves, on average, just under 4cm farther from Earth each year. These tidal forces also slow the rotational rate of the Earth. Darwin overestimated the recessional rate, though, and believed that the Moon split from Earth rather recently compared with the age of the Earth. Of course, explaining how a chunk of Earth could just fly into space is difficult. Also, such a fission would certainly produce a moon with an equatorial orbit, which our Moon does not have.
At any rate, each of these models can make specific predictions of what we expect to find when we look at the rocks from the Moon. With actual moonrocks returned by the Apollo astronauts, we could test these models. For example, if the Moon formed some place else in the Solar System, it would have different isotope ratios from Earth rocks. These isotope ratios are almost like fingerprints as to how far from the Sun something forms. The isotope ratios of the moonrocks are identical to those of Earth, saying that the Moon formed at Earth’s distance from the Sun. This suggests some sort of relation between the Earth and the Moon’s formation. Secondly, if the Earth formed from the same material that was collapsing to form Earth, or if the Moon formed from a part of Earth that was flung into space, then the moonrocks would be the same as Earth rocks. However, we find the Moon has no minerals that we do not know on Earth, but it does not have all minerals that we do find on Earth. The Moon appears to be poor in volatile minerals and rich in refractory minerals. Volatile minerals are those that will vaporize at low temperatures, and refractory minerals are those that will survive high temperatures. These findings show that the Moon has gone through a different formation process than Earth. The moonrocks brought back by the astronauts are ancient, too. They seem to be nearly as old as the Solar System itself. This seems to argue against the Moon splitting from Earth recently. Also, the Moon has different proportions of materials than Earth has. For example, the Moon has a tiny core and a crust much thicker than Earth’s. The Moon, in fact, is mostly crust and mantle material. This argues against the Earth and Moon forming from the same collection of material.
So, all of the pre-Apollo Moon formation models seem to not hold up under the evidence gained by the Apollo astronauts. Thus, we need a new model for the formation of the Moon. However, by the mid 1970’s a new model was proposed independently of one another by astronomers Alastair Cameron and William Hartmann. This model can be called the collisional ejection theory. According to this model, the newly formed Earth was struck obliquely be a very large planetessimal, perhaps something nearly the size of Mars. This collision blasts a large amount of material from Earth and the colliding body. Most of the material comes from the mantles and crust of these bodies, just like the composition of the Moon. Computer simulations of this collision show a large amount of this material coalescing into a body in Earth orbit. Tidal interactions with the Sun cause this material to coalesce into an orbit not too far from the ecliptic, just like the Moon. The material would coalesce closer to the Earth than the Moon’s distance, but as we know, the Moon is moving away from us, and would have moved to its current distance had it formed closer as proposed. The collision would be very violent and it would have experienced the material to very high heat loads, explaining why the Moon is poor in volatile minerals. As a bonus, the collision ejection model also would explain why Earth’s crust is the thinnest of all the terrestrial planets’ crusts.
For these, and other reasons, most astronomers now seem to go along with the collision ejection theory as the way that the Moon formed. If you want to read more about this model, then you can read Dana Mackenzie’s excellent book on the subject entitled The Big Splat. As you might guess from the name, the book is aimed at lay readers, without all of the mathematics that you get from texts aimed at astronomers. The book is a very good and very interesting read, and I highly recommend it.
-Astroprof May 09 The best Moon observingWhen is the best time to observe the Moon? People often ask me this. They assume that the best time will be full moon. Well, full moon is coming in a few days. So, that's the best time to set up your telescope and look, right? Well, probably not. Really, it depends upon what you want to observe. The Moon is pretty complex, so the best time to observe features might not all come at the same time. In fact, what I like to see are the craters and mountain ranges. Actually, the two are related. The Moon does not have plate tectonics like Earth, and no tall volcanic mountains. The mountain ranges on the Moon are really the walls of giant impact basins. The mountain ranges and the crater walls are similar in color to their surroundings, so there isn't much contrast. That means that they are tough to make out, sometimes. However, when the Sun is hitting them at a low angle, then they cast long shadows on one side. The contrast between the black shadow and the brighter material makes the craters and mountains stand out. You can often see features that you could not otherwise see very easily. At full moon, the sun appears to be shining straight down on the Moon, as seen from Earth, so there are no shadows. However, at the quarter moon phases, then the Sun shines from the left or right, and so sunrise or sunset on the Moon runs right down the middle of it, as seen from Earth. That makes features near the middle of the Moon stand out. A crescent moon makes features to the left or right of the mid line stand out better (depending upon whether it is a waning crescent or a waxing crescent). Theoretically, a similar effect should happen at gibbous phases, but personally I think the crescent moons show better relief. What is particularly cool is when the terminator (the sunrise/sunset line) runs right through a mountain range. Then, you can see occasional peaks of mountains on the dark side of the line sticking up into the light. They look like little white dots just to the dark side of the Moon. Really cool.
So, does that mean that the full moon is worthless for observing? No! As it turns out, if you are looking to observe the seas, then the full moon is excellent. The Moon doesn't have any water, of course. The things that we call seas are really flood basalts that filled some of the largest impact basins and sometimes (as inthe case of the Ocean of Storms) some of the surrounding land. These flood basalts are darker in color than the surrounding highlands, so they do stand out even during full moon. The basalts are also ever so slightly bluer than the highland rocks. So, I often use a red filter to observe the full moon. This has a double benefit of both improving contrast between the seas and the highlands, but also it dims the Moon. The full moon is annoyingly bright when viewed through an unfiltered telescope. The red filter is easy on the eyes. Interestingly, I also find that a yellow filter tends to show off some of the rays of the craters better.
Speaking of bright moons, the full moon is so bright that you can read by the light of it outdoors at night. City people don't always believe me when I say that, but it is true! Let yourself get slightly dark adapted, and you can read by the light of the Moon! It is amazingly bright out at night during full moon. Go out this weekend and see for yourself. Even in the city, with all the light pollution, it is bright.
-Astroprof May 08 But, I just HAVE to pass this class!OK. It is final exams week. Every year, every semester ends the same way. Students who have put absolutely NO work into the class all semester suddenly want to know what they have to do to pass the class. Well, that is pretty straight forward. I lay it out the first day of the semester. All that is needed is written down and passed out to them the first day. It is called the course syllabus. Read it.
Then, there are the rest of the standard students that I get every semester coming to see me at the end of the semester.
Students A and B:
They don't understand the last third of the class. Can I explain it to them? Yes. That is what I have been doing for the last month. If you had come to lecture then you might have gotten it.
Student C:
I just have to pass this class. I am graduating Friday. My grandparents are flying in from out of state. What can I do to pass the class? At this point, ..., nothing. You missed one exam. You didn't turn in any homework. You have an average of about 50 in the lab. And of the exams that you did take, you barely got a D on them. "Can I write a paper?" the student asks. Well, given that grades are due in just a few days, no. Besides my not having time to grade a paper, any paper that you whip up at the last minute here can't have very extensive research done on it. Besides, don't you have any other finals that you need to work on? Where would you find the time to write a paper? Any paper that you can write in just few hours available at this time will be either total crap, or else it will be plagiarized to the max. Either way, you fail. Sorry. You should have put effort into the class BEFORE the last few days.
Student D:
I need to get an A in the class to get into the XYZ program in the fall. What can I do? Retake it this summer. Otherwise, if you get a 175 out of a possible 100 on the final, then you could get an A.
Student E:
When is the final going to be? Well, what does the syllabus say? I lost the syllabus. OK, then what does the college's final exam schedule say? Where do I find that? Well, how about in the campus newspaper, on the college web page, or on the bulletin board outside the classroom.
Student F:
How many points do I have? Add up the grades on the papers I turned back. I threw them away. Then, why do you think that I care more about how many points you have than you do?
Student G:
Can you write me a letter of recommendation by tomorrow? Sure. I have nothing better to do with my time this week. Just one question: Who the hell are you???????? It is always amazing that students who have only occasionally come to class on days other than lab or test days, and who have never spoken to you all semester, and who are making a solid C, suddenly want a glowing letter of recommendation. And, of course, it is always something that has to be done right away, and always at the end of the semester.
Student H:
I haven't been to class all semester. Can I have an incomplete? No.
Student I:
I am having my wisdom teath out on the day of the final. Can I take later in the week? Huh???? Is this an emergency? Are your teath impacting on your brain or something? OK, well maybe they are. This is an elective procedure. Please elect to do it some other time!!!!
AAAAAAAARRRRRRRRRRRRGGGGGGGGGGGGG!!!!!!!!!!!!!!!!!
And of course, it isn't just me. All of us get these same sort of things, in one form or another. It makes you wonder how these people got into college in the first place.
Oh, I will work with students, and I bend over backwards to help them in any way that I can. However, NOW is too late to start working on trying to pass the class.
-Astroprof May 07 The biggest moonsSo, just what is the largest moon in the Solar System? Well, that sort of depends upon how you define “largest.” Most any textbook will tell you that Ganymede is the largest moon. This was not always the case. That is, I mean that the books used to say differently, not that the moons were different sizes! When I was first learning about the Solar System, most books claimed that Titan was largest. So, what changed?
Well, let’s give a bit of background. Ganymede is one of the four largest moons of Jupiter. In fact, it is the largest of Jupiter’s moons. Ganymede is, in fact, quite large. At 5262km diameter, Ganymede is even larger than the planet Mercury, which is only 4879km in diameter. Made of a mixture of rock and ice, Ganymede would be considered a planet were it not in orbit around Jupiter.
Titan is Saturn’s largest moon. Most textbooks list Titan as having a diameter of 5150km. Incidentally, that is still larger than the planet Mercury. But, why would the older textbooks say that Titan is larger than Ganymede? Well, this is because Titan has an atmosphere with a cloud layer. Titan’s even has a pretty decent nitrogen rich atmosphere, with slightly higher density than Earth’s atmosphere. Titan’s clouds are quite thick, forming a cloud back 200km above Titan’s surface. So, measuring from cloud top to cloud top, you get a diameter of 5550km. Even before 1980, when Voyager I gave the first close-up data, we knew that Titan had an appreciable atmosphere. However, no one really thought that the clouds would be so high. After all, just about all of Earth’s clouds lie below 10km altitude. Even if Titan’s clouds were two or three times higher, that would still make the diameter of the moon somewhat larger than Ganymede. So, why are Titan’s clouds so high? Well, the answer comes from the fact that Titan has a lower gravity than Earth. So, the atmosphere balloons out much higher. A similar sort of effect is at work with Saturn and Jupiter. Saturn has nearly 1/3 the mass of Jupiter, but it is only somewhat smaller in physical size (about 84% the diameter).
So, this makes which one bigger? As I said, most books simply list Ganymede as largest. But Titan has an atmosphere and clouds. Where a moon or planet end? When we talk about Earth or Mars, we usually give the size of the solid body as the size of the planet. However, when we talk bout Jupiter or Saturn, we give the size as the diameter of the planet from cloud top to cloud top. Of course, Saturn and Jupiter have fairly small solid cores, and it would seem silly to give a diameter that is only 15% of what you see, wouldn’t it? So, which method do we use to give the sizes of the moons? Hmm. That is why you sometimes, even today, see some lists that have Titan on top, and Ganymede as second largest. For sure, if you are trying to land a spacecraft on one or the other, you’d worry more about the edge of Titan’s atmosphere, which is even farther out than the cloud tops.
However, just to complicate the matter, there is another way to measure moon size, and that is relative to the size of the planet. By this measure, neither Ganymede nor Titan rate at the top. The winner is Charon, one of Pluto’s moons. At 1190km, it isn’t very big, but compared to Pluto’s 2390km it is positively huge: nearly 50% the planet’s size. This makes Pluto and Charon nearly a double planet.
For that matter, the Earth’s moon ranks very high on this way of looking at things. Our Moon, at 3475km, the Moon is 27% of Earth’s diameter. Ganymede is only a bit under 4% of Jupiter’s diameter, and Titan is less than 5% of Saturn’s diameter, even using the cloud top to cloud top diameter. Why such a discrepancy between Titan and Ganymede to their planets compared with the Moon and Charon to their planets? Well, we think that this is because of how they formed. Ganymede, Titan, and many other of the moons likely formed as a consequence of their parent planets’ forming, likely from material coming together to form those planets. However, our Moon and Charon likely formed from giant impacts on their parent bodies. These impacts carved out large amounts of material that coalesced to form Charon and our Moon.
Anyway, as long time readers of this blog will see, we have once again come to a point where a simple question doesn’t really have a simple answer that everyone agrees upon. Back long ago, we started these labels of things, and we started our lists long before we knew about what we were talking about. Unfortunately, this means that we didn’t always categorize things best, or list them right. Oh, well. At least, it gives me a chance to have something to blog about.
-Astroprof
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