Astronomy Down Under

This has been the talk of the Internet today, so I might well write about it as well... for the first time, scientists were able to capture images (in visible light, no less) of not one, but four extrasolar planets orbiting around two separate "normal" stars (we had already seen images of a planet orbiting a brown dwarf star).

First, we have star HR8799, a young star that is a bit larger than our Sun (1.5 times as massive and 5 times as bright) and that lies 130 light years away in the constellation Pegasus. Images taken with the Keck and Gemini North telescopes in Hawaii show three large planets orbiting this star; one is about seven times and other two are 10 times as massive as Jupiter. They orbit the start at distances ranging from 24 to 67 AU (the planetary limits of our own solar system are around 30 AU).

Apart from the historical value of directly imaging these planets, this event is significant for other reasons: this star is very similar to our own, and these large planets are orbiting it at a large distance, leaving space closer to the star for small rocky worlds; in other words, this might be a solar system similar to our own, which is something of a rarity among the hundreds of other solar systems we've already found.

Secondly, we have Fomalhaut, a larger star (2.3 times as massive and 16 times as bright as the Sun) 25 light years away in the constellation Pisces Austrinus, the southern fish. It's been known for a while that this star is surrounded by a large dust disk; in fact, the very sharp inner edge of this disk was a clue that there was a planet there, cleaning out debris just inside the disk. And, indeed, Hubble images do show a bright planet located there, in a very wide orbit around the star. The planet seems to be about twice as massive as Jupiter, and its brightness may indicate it is surrounded by a very large ring system.

The planet orbits the star once every 872 years at a distance that is almost four times the distance from Neptune to our Sun, but since Fomalhaut is brighter than our Sun its appearance would be similar to how the Sun appears when seen from Neptune. Just as is the case with HR 7899, Fomalhaut is a very young star and its solar system is still being formed, which helps in the detection of the planets: they're still hot enough that they radiate brightly in the infrared.

Both stars are visible with the naked eye from a dark sky site, and Fomalhaut should be easily visible even from a urban setting. If you are in Melbourne (or any place at the same latitude), Fomalhaut will be almost directly overhead today soon after sunset — it's bright enough that you can't really miss it. HR 7899 will be a bit harder to find; Pegasus will be visible on the northern sky in the middle of the night, and the Lowell Observatory press release has a diagram that will help you find the right star (it's likely you will need a binocular or small telescope, though).

For more details and images, in addition to the links in the text above, see the (very enthusiastic) Bad Astronomy blog and Centauri Dreams.

The Phoenix Mars Lander has stopped transmitting on 2 November, and NASA has declared the mission to be over. This was expected — Phoenix was never supposed to survive the Martian winter that is starting now, and will likely be fully encased in solid ice (probably CO₂ ice) during the long winter months. It failed due to the diminishing day light and the increasingly cold temperatures.

Dave Moshen Mosher, at the Discovery Channel's Space Disco blog, has a good post about the mission with links to many pictures and videos from the mission. It's a shame that the microphone installed on the probe ended up never working...

There's a slim chance that the probe might come back to life in the next summer, after the polar ice cap melts back and it gets enough sun light. It is very unlikely that this will happen, though — even though the probe is named "Phoenix"...

As I've already mentioned before, 2009 will be the International Year of Astronomy, and many activities are being scheduled for the whole year — both online and offline. One of this is the 365 Days of Astronomy podcast, a project that will publish one short podcast every day during the whole year.

A "test podcast" was already published, but the feed will actually go live on the 1st of January (for some time zone; it may be on the 31st of December or the 2nd of January depending on where you are...), and the project will depend heavily on contributions from interested listeners/readers — that means you. It doesn't matter that you don't have a podcast, or that you've never produced audio material: you can still participate. Go to the website, read the information that is there and volunteer to help in any way you can. Even if it is by just mentioning the project in your own blog.

2009 will be an interesting year!

If you like seeing close appearances of bright objects in the sky, this week is being very good for you (assuming the weather in your location is being better than here). Last Saturday, the (very thin crescent) Moon was very close to Venus soon after sunset; I went out to try to look at it, but the only clouded area on the sky was the western horizon up to some 45 degrees... so, no luck there.

Tonight it is Jupiter's turn, with the Moon (now considerably less thin) very close to it and both setting around midnight. Jupiter is not as bright as Venus but it's no less spectacular (especially considering that the sky will be darker as it sets later). The sky is fully clouded here, I hope people have better luck in other locations...

(the times above are for Melbourne, and things will look different — that is, the Moon closer or farther away from Jupiter — depending on where you are)

Two weeks ago we described a set of coordinates we use to map the position of the objects we see on the sky; at the end of that article, I mentioned that the fact that the sky is not static (as seen from the Earth) affects the way we map positions in those coordinates to positions in the visible sky. In today's article we'll start to see exactly how the objects on the sky move and why they do so.

To a first approximation, most of the objects on the sky appear to move as if they were all fixed to the inside of a gigantic sphere with the Earth at its centre (the aptly named "celestial sphere"); the notable exceptions are the planets, the Sun, the Moon and a few other sporadic visitors such as comets and asteroids. For today we'll ignore those, though, and focus first on the simpler cases.

That (apparent) movement is the result of the (very real) movement of the Earth in relation to the rest of the universe; one can, of course, take the " geocentric" view and talk about celestial objects moving, if that makes things easier to understand — as long as it remains clear that the movement we see directly is apparent, not real.

First, some introduction. From any given point on the surface of the Earth, it's possible to see the "projection" of the Earth's pole onto the celestial sphere (as described in the last article); the point where that projection falls is the celestial pole (north or south, depending on which hemisphere you happen to be on). If you measure the angle between the celestial pole and the horizon, you'll find out that it's identical to your latitude. In other words: if you're in Melbourne, at a latitude of approximately 37 degrees south, the south celestial pole will be approximately 37 degrees above the southern horizon.

Similarly, from any given point on Earth you can see the projection of the equator onto the celestial sphere: that's, obviously, the celestial equator. It will describe a great circle across your local sky, tilted with relation to your horizon by an angle that equals 90° minus your latitude (because the equator is perpendicular to the poles); from Melbourne, the celestial equator is tilted by 53° with relation to the horizon, and the highest point in the line of the equator is 53° above the northern horizon.

As we all know, the Earth rotates around its axis, towards the east, once every approximately 24 hours. The result of this movement is that the objects we see on the sky will seem to rise from the eastern horizon, move across the sky and set on the western horizon some time later. This apparent movement is actually an "orbit" around the celestial poles, parallel to the celestial equator, and this has some interesting effects.

The first is that the actual path of an object across the sky will depend on your local latitude. If you're standing exactly on the equator, objects will rise straight up from the eastern horizon and set straight down on the west. If you happen to be on one of the poles, on the other hand, objects will not rise or set: whatever objects are visible will remain visible, circling the horizon always at the same distance from it. At any other latitude, objects will describe a path that is tilted with relation to the horizon by 90° minus your latitude — that is, tilted in the same way as the equator (and this is useful in navigation: measuring the angle of the path of stars equates to measuring your latitude). The picture above shows this movement from a mid-latitude, with the celestial equator running very visibly through the middle of the image (I'll leave as an exercise to the reader to determine where the picture was taken from the angle between the equator and the horizon).

The second effect is that, if the declination of a star is larger than 90° minus your local latitude, that star will never set. Why is that? Well, if the declination of the star is larger than 90° minus your local latitude, the distance in degrees between that star and the nearest pole is less than your local latitude, and thus less than the distance between the pole and the horizon, and that means that the whole path of the star across the sky is visible. The star is then said to be a circumpolar star from your location (being on the pole, at latitude 90°, is a special case of this — every star visible from the pole is circumpolar). The picture on the left, a long exposure image showing the movement of the stars over several hours, shows this and the location of the southern celestial pole very clearly (photo taken in Brunswick by Michael Efford - click for larger version and more info).

There is, of course, the opposite case: from any location but the equator, some stars will be permanently below the horizon. They are, say, anti-circumpolar: they circle the opposite pole to the one that is visible. Going again to our observer in Melbourne, the constellation Crux, at a declination around 60° south, will be always visible on the sky, at every hour of every day, while Ursa Major, at around 55° north, will never be visible.

And that's it for today. Next week, we'll start looking into the slightly more complex movements that result from the Earth orbiting the Sun.

I'm a bit late in writing about this, but... the 68^th edition of the Carnival of Space is now up at Crowlspace. The general theme this week is interstellar travel and the difficulties associated with it — but you can find much more. Enjoy!

Last week we saw how it makes sense to use angles and arcs to identify the position of places on the spherical surface of the Earth. We arrived at a grid of great circles, and the intersections between north-south and east-west circles define two coordinates for each point: a longitude (east or west) and a latitude (north or south). We also saw that two special circles mark the origin of each of the coordinates: the equator marks the 0° line for latitudes, and the prime meridian marks the 0° line for longitudes. The equator is physically defined as being equidistant from both poles, while the prime meridian is arbitrarily selected.

Well, as seen from Earth, the sky looks like a very big sphere with the Earth at its centre. Because of this, it makes sense to use a similar system of coordinates to identify the positions of celestial objects. Note that I'm talking strictly about the apparent position of the objects on the 2D "internal surface" of the sky as seen from Earth — the universe is a three-dimensional place, and you won't be able to use positions represented in this way to, say, chart a navigation course between any of these objects. Of course, if you are in a position in which you may be asked to chart such a course, I expect you'd already know this.

We start by extending some of the terrestrial features onto the sky. For example, the celestial poles are simply "above" the Earth poles: you extend the rotational axis of the Earth upwards until it "touches" the celestial sphere, and that's the celestial pole. And it turns out that these are important points in the sky as well as on the Earth: if you stay out one night and look at the movement of the stars as the night progresses, they all seem to rotate around the celestial poles.

Similarly, the celestial equator is simply a projection of our own familiar line of latitude zero onto the sky; it is a great circle on the sky that is equidistant from both poles. And, having poles and an equator, we can easily get the an equivalent to latitudes; celestial latitudes are called "declinations" and are represented in the same way as latitudes on Earth (as degrees north or south of the equator, from 0° at the equator to 90° at the poles).

Now, the celestial equivalent to longitudes is a bit more complicated. You see, the sky "moves"; that is, as seen from the ground, the sky seems to rotate around the Earth, from the east to the west, at approximately one revolution per day. This means that we can't simply project the terrestrial prime meridian onto the sky to get the celestial prime meridian: the portion of the sky onto which the projection would happen would change by the minute and the coordinates would be useless. We need to do something different.

Let's start talking about the idea of "local sky". From any given point on Earth, at any given moment an observer can see half of the sky (assuming a clear night and an open horizon); which half is something that will change as the Earth rotates. On this view of the sky, we need to define two important imaginary points. One is "straight up", or the point directly overhead (from the point of view of the observer); this we call "zenith". The other is in the opposite direction, "straight down", or the point directly below the observer's feet; this we call "nadir" (if you're standing at the South Pole, the zenith is the south celestial pole and the nadir is the north celestial pole).

Now, the portion of the sky you can see (that is, your local sky) will change continuously, and so will the celestial positions of your zenith and nadir (unless you happen to be at the poles). More exactly, the declination (celestial latitude) of your zenith and nadir will remain static (and will be identical to your latitude on Earth), while the "celestial longitude" will change. But, importantly, this means that what is in your local sky will depend not only on where you are, but also on when you are there - and not just on the time of day, but also on the time of year.

How do we define the celestial longitudes, then? They are, indeed, similar to the terrestrial ones, but we need to define an origin based on celestial features. The origin that was chosen for this coordinate is the line where the sun is at the time of the vernal equinox (spring equinox in the north hemisphere, autumn in the south); this is a fixed location on the sky.

There is one more difference, though: we don't use degrees for this coordinate, we use time. The sky was divided into 24 north-south bands, each one of which takes approximately one hour to move a distance equal to its width across the sky; these bands are then the second basis for the grid system defining celestial coordinates, and the coordinate they define is called "right ascension". Each band is numbered as 1 hour and, predictably, divided into 60 minutes of 60 seconds each; it is similar to degrees, but the notation uses "h", "m" and "s" rather than the symbols for degrees, arcminutes and arcseconds. Also, the hours were numbered from the origin increasing continuously towards the east. There is no east or west right ascension, but a single coordinate that ranges from 0h0m0s to 23h59m59s.

Together, declination and right ascension uniquely define a position in the sky, and can be used to locate any object visible from Earth. They don't tell you directly where to look at, though: they need to be translated according to your local position and to the time of day and year into an actual direction towards which you can look at to find the object being pointed to. But this is something that we'll look into a bit later, as we need more background to work that out.

Next week, we'll start looking into the way the Earth moves and what they mean for our view of the sky.

In the last two weeks we saw the process that led us to know that we live in a spherical planet, and also how we managed to discover how large this planet is. Of course, I could have simply told you that in one sentence - "the Earth is a sphere with a circumference of approximately 40,000km" - but actually seeing the methods people used to discover this is as important as knowing this, if not more: it tells us about the process of learning and of dealing with errors that all science needs to go through.

This week, let's take a look at how we can use what we know to help us locate places in the surface of the Earth, and later we'll see how whatever system we use for this can also be used on the sky.

In the ancient world, maps were intrinsically local items: they were centred on an important location -- usually the location where they were made, or alternatively the capital of the empire -- and would tell people the distances and directions to faraway places. This is, of course, only partially useful, since people rarely go from place to place in a straight line. And it grows less useful for larger distances, not only because there's less of a chance of going in a straight line, but also because, for sufficiently large distances, the curvature of the Earth starts to have a noticeable effect.

The need for better maps grew as empires grew larger and as it became harder to approximate the Earth to a flat plane where paths are straight lines. Our planet is, to a first approximation, a sphere, and this gives us a clue that circles, angles and arcs may be more important than planes and lines.

The standard way to measure arcs on a circle, inherited from the ancient Babylon, starts by dividing the circle into 360 equal parts called degrees (or degrees of arc, to avoid confusion with temperatures), denoted by °. One degree is a very small part of a circle: if you extend your arm and hold your thumb up, it will cover approximately one degree of your visual field. However, when you're dealing with a circle the size of the Earth one degree is not small enough; therefore, we need to subdivide it further. One degree is divided into 60 minutes of arc (denoted by '), and each minute of arc is further divided into 60 seconds of arc (denoted by "). An arc of 7 degrees, 25 minutes and 10 seconds is written as 7°25'10".

If these names and numbers (60 minutes, 60 seconds) sound familiar, you're right: that's the same way we divide time. The division of arcs came first, though, and the names of the units of time are derived from the names from the divisions of arcs, not the other way around. You may also ask what is the thing with multiples of 60. This is another thing we inherited from Babylon: 60 is a number that is exactly divisible by a whole lot of other numbers (2, 3, 4, 5, 6, 10, 12, 15, 20, 30) and this reduces the need to use complicated fractions.

Back to minutes and seconds. One second of arc is very, very small. In fact, one minute of arc is approximately the resolution of the human eye: you can tell objects apart if they are at least one minute of arc apart; it's likely that one pixel in the screen of your computer is larger than one minute or arc. One second of arc, or one arcsecond, is the limit of the resolution of optical telescopes, and it's also a unit we'll see much more of later on.

With this in mind, we can start using angles to locate position on the surface of the planet. The way to do this is to establish a series of arcs defining a grid on this surface. We start by doing two primary divisions:

• first, the equator, which is a great circle dividing north from south located perpendicular to the line connecting the two poles; the position of the two poles is determined by the movement of the planet, as we'll see next week
• second, a meridian, going through the poles and perpendicular to the Equator, dividing east from west

These divisions define a simple set of two coordinates, one north-south and the other east-west. Now, the equator has a well-defined location due to the fact that the poles are in fixed positions (as we'll see next week), but the meridian we choose as the basis of our coordinate system -- or the prime meridian -- can be basically anywhere. Since the 1880s, by international convention, it is defined as the meridian that goes through the Naval Observatory in Greenwich, just outside London, in England. This position was, not surprisingly, chosen by the English, and adopted internationally simply because the English made very good maps -- it was a de facto standard long before it was set by convention.

Using these two great circles, we can now define a grid that will allow us to define the position of anything on the surface of the Earth with ease: the position of a point is defined by two angles, or arcs:

• one, known as longitude, is the distance from the prime meridian, to the east or west
• the other, known as latitude, is the distance from the equator, north or south

This same set of coordinates can be extended to the sky, which also looks to an observer on Earth as a sphere seen from the inside. But we'll look into that next week.

As we saw last week, once it became clear to everyone that we live on a spherical Earth, the next question was "how big is it?". Since one can't well go out and measure it directly, indirect methods have to be used -- which brings us back to geometry. And the first person known to have used geometry to estimate the size of our planet was Erathostenes, who at the time was the librarian at the Library of Alexandria.

Erathostenes knew, thanks to travellers, that in the Egyptian city of Syene (currently Aswan) the Sun would be directly overhead at noon on the day of the summer solstice (which means to us that the city sits at the Tropic of Cancer). He also knew that this was not the case for Alexandria, where he lived, and this meant that he could use this difference to calculate the size of the globe.

What he did was to measure the angle of the rays of the Sun in Alexandria at noon on the summer solstice, and using his knowledge of geometry he knew that this was the same angle formed at the centre of the Earth by lines going from there to each of the two cities (Syene and Alexandria). This is a lot of words to explain what can be seen in the (greatly exagerated) figure; the red lines represent the rays of the Sun, each bold dark line represents one of the two cities, and both angles labelled as α are the same. He measured this angle to be 1/50 of a full circle (or 7°12'), and he knew the distance between the two cities to be 5,000 stadia. This, of course, gives us a size of 250,000 stadia for the circumference of the Earth.

And now we have a problem: how much is that, exactly? The answer is, we're not sure; no one knows how much was a stadion for Erathostenes. Archaeological evidence points to a length of 185m to a stadion in Athens, which would result in a circumference of 46,250km, or about 15% larger than reality -- 40,075.16 km. He might have been much closer, though: different places had different stadia, and some evidence points to smaller ones being used in Alexandria. Also, the numbers in his calculations (1/50 and 5,000) are suspiciously round; since we only know of Erathostenes' work through third-party accounts, it is likely that the numbers were rounded at some point and that his calculations were much more precise.

This calculation reinforced the idea that the Earth was fixed, as it was definitely too big to be moved; and, being fixed while everything else moved, it was also clear that it was the centre of the universe.

A few centuries later, in the 1^st century AD, another eminent figure tried his hand at calculating the size of the Earth: Ptolemy. He worked using the positions of the stars and their apparent change in position as a person travels, and he reached a circumference of 33,300km. That is very wrong, but since his methods make sense and the results were reproducible, this value was accepted for a long time and was used by everyone until the Middle Ages.

Around the 3^rd century AD, the idea of a flat Earth was revived, mostly by Christians who were intent on throwing away all of the "pagan" knowledge of the time. Among the general population, the idea of flat vs. spherical Earth had its ebbs and flows from them on, but among educated people there was never any doubt about the shape of the planet. In the 1300s, with the Renaissance, the spherical Earth stages a come back and this becomes common knowledge once more.

It is at this time that Ptolemy's underestimated numbers had an important effect in history: if we assume that the Earth is only as large as he thought it was, then the western tip of Europe is not that far away from the eastern tip of Asia, and this is one of the factors that inspired the westward navigation of the Portuguese and Spanish in the late 1400s, which resulted in the colonisation of the Americas. As you see, astronomy can indeed change the course of history, and we'll see more examples of this in the future.

That's it for this week. For more detail on this subject, I suggest reading the Wikipedia article on the History of Geodesy. Next week, we'll start to add detail to our map of the Earth and of the sky.

A partial lunar eclipse will grace our skies during this weekend and, while timing (and temperature) will certainly be less than ideal for Australian observers, it should provide a good spectacle for those brave ones who choose to go out.

In Melbourne, the eclipse will be cut short by the Moon setting (and the Sun rising) before it ends, but (weather permitting) one should be able to see it almost at its maximum. The umbral eclipse will start at 5:35am on Sunday (19:35 UTC on Saturday) and the maximum eclipse happens at 7:10am; infuriatingly, the Sun will rise at 7:02am and the Moon will set at 7:04am... but, if you live further west, you get to see more of it, and observers in Perth get to see the full umbral eclipse.

Still, if the weather is good and you can get a good, unobstructed view of the western horizon and you can get yourself out of bed at 5:30am on a Sunday, it will be a good show. If the weather is not that good, you can check a live webcast of the eclipse (as seen from Birmingham, UK) at the Lunar Observers website — assuming the weather there is good, of course.