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Astronomy 101 - Lesson 9 - The Sky In Motion (2)

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In the last instalment, I described the effects of the rotation of the Earth on how we see the stars above us (and on which stars we see and which ones we don't). That's all very well, but there's one other major type of movement of our planet that affects, and much, the way the sky looks like: we also orbit our Sun, and complete one orbit in one year.

The orbit of the Earth around the Sun has one major, immediate effect: the position of the Sun on the sky (against the background of stars) changes as the year goes by; the Sun will complete a full circle of the sky in a year, which means that its position changes by about one degree a day (360 degrees in a circle, 365 days in a year) — one degree is about twice the apparent diameter of a full moon. Of course, this is not directly visible: we can't see the stars around the Sun during the day. What we will notice is that the field of stars that is visible at night will subtly change from day to day — the whole field will seem to move westwards by about one degree a day.

One important thing to notice is that this apparent movement of the Sun relative to the stars (or of the stars relative to the Sun) is not parallel to the Equator: it is, in fact, tilted by approximately 23.5° (the exact angle changes over time; nowadays it's more like 23.44°, or 23°26'). This tilt has one very significant effect on Earth, but that's the subject of our next article: the four seasons.

Ecliptic, by Tauʻolunga; click to enlargeThe apparent path of the Sun on the sky has a special name: it's called the ecliptic. This is also the path followed (with varying degrees of precision) by the other planets in their path on the sky, as we'll see in the future. The ecliptic goes through several constellations — to be more precise, twelve. These are called the zodiacal constellations, or the constellations of the zodiac (from the Greek meaning "circle of animals" — most zodiacal constellations are represented by animals). One can see how twelve constellations resulted not only in the twelve astrological signs, but also in the twelve months of the year.

There are four special points on the ecliptic that are worth mentioning:

  • the solstices: these are the points of maximum north or south drift (or declination) of the Sun; the northern solstice happens in June, while the southern solstice happens in December
  • the equinoxes: these are the points of minimum declination, that is, where the Sun crosses the celestial Equator; they are called the autumnal equinox (which happens in September), when the Sun crosses the Equator moving northward, and the vernal equinox (in March), moving southward.

And that's it for today. As I mentioned, in the next article we'll explore in more details the effects of the tilt in our orbit and the significance of the solstices and equinoxes.

Astronomy 101 - Lesson 8 - The Sky In Motion (1)

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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.

Astronomy 101 - Lesson 7 - Mapping the Sky

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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.

Astronomy 101 - Lesson 6 - Mapping Our World

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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 1st 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 3rd 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.

Astronomy 101 - Lesson 4 - Spherical Earth

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Nowadays, everyone knows that the planet we live in is, to a first approximation, shaped like a sphere. However, from the earliest known writings, we see that most cultures saw Earth as being a flat and finite area. That is relatively easy to understand: in ancient times, very few people ever travelled more than a few kilometres from their place of birth; the distance any given person might travel was limited by how much he or she could walk, and that is not very much — especially when you don't really have a reason to move that much. And, from the point of view of a person moving very little, the world is indeed flat; the curvature of the Earth has no visible effect in a small scale.

Therefore, we have the representations of the world made by the early Mediterranean peoples showing that sea at the centre, the known European, African and Asian lands around it, and a very large ocean all around that. The South American Incas had a similar view, with themselves at the centre and land extending a certain distance in all directions, with a more or less rectangular shape and four corners. Egyptians also saw Earth as flat and surrounded by mountains on which the large tent that is the sky is grounded, and even the Bible offers a similar view. Other cultures had more metaphorical views, such as that of the disc of the Earth lying on the back of four elephants, who are on top of a giant turtle swimming on an infinite sea; it's unlikely that these representation were ever intended to be taken as literally true, however (unless you happen to live in Discworld).

The path that leads to our current understanding of the Earth starts, as so much else, with the ancient Greeks. Having pioneered the study of geometry, the Greeks had a love for symmetry and perfection and tended to try to impose this love on the natural world. Pythagoras, in the 6th century BC, was one of the earliest proponents of the idea that the Earth must be a sphere, as that is the most perfect shape for an object, and the Earth, being the place where man and the gods live, must adhere to this ideal of perfection. Of course, he had no evidence for that; this is purely an aesthetic argument. Plato, a century later, defended the same ideas for the same reason, but he was taken much more seriously than Pythagoras, and his ideas had a large influence on people of the time.

A few decades later, Aristotle defended once more the idea of an spherical Earth, but differently from his predecessors he had evidences supporting his idea. In his book "On the Heavens", he came up with three basic arguments:

  • one has a different view of the stars from places at the south than from places further north; some stars appear higher in the sky the further south you go, as if from places in the north your view of the sky is obscured by the curvature of the Earth

  • the shadow of the Earth projected on the Moon during a lunar eclipse is always round; if the Earth were anything but a sphere, you'd see different shapes for the shadow depending on the angle of the Sun at the time of the eclipse

  • and, since objects tend to fall towards the centre of the Earth, the force of attraction towards the centre would tend to cause the Earth to assume a spherical shape; this argument is incredibly advanced for its time, as it basically stands on the idea of gravity overcoming the tensile strength of the material forming the Earth to shape it like a sphere

By the 3rd century BC, then, everyone in the western world knew that the Earth was an sphere, fixed in the centre of the Universe, with several other spheres (planets, Moon, stars) rotating around it. This allowed people to ask the next question: how big is this sphere? Aristotle guessed that it was very large (because the effects of travel on the position of stars are very small), and this reinforced the idea the Earth was fixed; but how large, exactly, is it? We'll see about that next week.

Astronomy 101 - Lesson 3 - The Night Sky

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The sky at nightAfter the basic introductory material of the first two weeks, it's time to start looking at the main subject of astronomy: the sky. If you go outside at night in a location with reasonably dark skies and you stay up all night, you will be able to see about 6,000 stars. That may look like a lot, but it's not: our constellation, the Milky Way, contains approximately 200 billion stars, and it is only one of billions and billions of galaxies in the visible universe. 6,000 is really not that much.

What we do see are only the nearest stars to our own, plus a few very bright distant ones. We also see other types of objects: for example, planets, easily recognised because they will change locations from day to day against the background of stars. In dark skies you can also see other galaxies: Andromeda, our nearest large neighbour, can be seen easily with the naked eye as a fuzzy blob, and the Large and Small Magellanic Clouds, two dwarf galaxies which were once thought to be orbiting the Milky Way, can be seen very clearly from southern hemisphere locations. And, if you look to the skies for a while, you will almost certainly see artificial satellites moving very quickly as they circle the Earth, and very likely the odd meteor will show up from time to time.

[caption id="attachment_140" align="aligncenter" width="418" caption="Tridimensional visualisation of the stars in the constellation Orion"]Tridimensional visualisation of the stars in the constellation Orion[/caption]

One interesting aspect of the human brain is its ability — or need — to identify patterns in the world around it. That is the reason why we aggregate the stars into constellations: they are nothing more than patterns formed by connecting the "dots" in the sky. It is very important to know that the stars in any given constellation are not physically together; the pattern they form is an artefact of "projecting" a 3D universe into an apparent 2D sky. If you were to move a large distance from the Earth, the patterns in the sky would be significantly different from the ones we know.

In general, the constellations are figures formed by the brightest stars we can see; some do look like what they're supposed to represent (for example, Scorpius (pictured, right) or Orion), but some require a significant degree of imagination (such as Pisces or Lynx). Every culture on Earth invented its own set of constellations; and, as the sky we see today is not significantly different from that of hundreds or thousands of years ago, many of those are similar, but many more are entirely different. Some cultures (notably the Incas and the Australian aborigines) even recognised "constellations" that were in fact dark areas of the sky.

Our current set of 88 official constellations owes much to Ptolemy, who defined an original set of 48 constellations covering the North sky (which was all he could see), many of which survived to this day. When European explorers started moving south of the Equator, they started inventing new constellations with the new stars they saw. This brought a new set of themes to the sky; mythical themes still abounded, but some biblical terms also made their way onto the sky during these period, as did some pieces of modern scientific equipment (Horologium, the clock, is one example). At some point, over 150 constellations were known and widely used, with some overlap happening between them.

In the late 1800s, the organisation that was to become the International Astronomical Union defined the current set of 88 constellations, including their well-defined boundaries. This allows us to refer to objects that are not part of the figure of a constellation as still belonging to it if they fall within its boundary. Also, the whole sky is covered by these 88 constellations.

As a result of this, many constellations were abandoned and forgotten; my personal favorite is Felis, the cat. Others, such as Argo Navis, the ship of the Argonauts, were split into several (in this case, Carina, the keel, Puppis, the poop, and Vela, the sails).

It's worth noting that most cultures also had individual names for the brightest stars in the sky, and that most of those stars are still referred to by name. Most of the surviving names are Arabic (Rigel, Aldebaran, Deneb...), but Greek (Sirius, Arcturus...) and Latin (Polaris, Spica...) are also common.

For unnamed stars, the most commonly used designation is the Bayer designation, which uses a letter of the Greek alphabet followed by the Latin name of the constellation to which the star belongs, in the genitive form; letters are assigned in order of brightness, alpha (α) being the brightest. Most people have heard of the star "Alpha Centauri", and now you know that this refers to the brightest star in the constellation Centaurus, the centaur.

However, the strict order of brightness is not always followed for historical reasons; when the letters were originally assigned (by the German astronomer Johann Bayer, in the early 1600s) there was no way of accurately measuring the brightness, so constellations with similarly bright stars may have them in the wrong order. Orion is a particularly good example of this, with its beta (β) star (Rigel) being the brightest and its delta (δ), Mintaka, being the sixth, rather than fourth, brightest.

This concludes our first look at the universe outside our planet. Starting from the next week, we will spend quite some time closer to home, looking at the Earth, the Moon and the rest of the solar system before venturing out towards the stars.

Astronomy 101 - Lesson 2 - Units

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After speaking for a while about numbers, it's time to see what we can do with them; for this, let's take a look at the units of measurement commonly used in astronomy (which are not that different from the ones used in day-to-day life in most of the world, in fact). Basically, most of the time we will speak of measuring length in metres - which expands to square metres for area and cubic metres for volume -, mass in grams and time in seconds (or multiples thereof); these are the basic units of the International System of Units, or SI.

Before we go into any detail about them, let's take some time to look at the multiples that are commonly used. In general, these multiples follow, once again, powers of ten, and some specific powers of ten can be "abbreviated" by prefixes added to the name of the unit being used. The prefixes you are more likely to see are:

  • large: kilo (103), mega (106), giga (109), tera (1012), peta (1015)

  • small: centi (10-2), mili (10-3), micro (10-6), nano (10-9), femto (10-12), pico (10-15)

Do not confuse these with the prefixes commonly used in the computer world, where they have a different meaning associated to powers of 2 rather than 10; a kilobyte is 210 (or 1024) bytes, not 103 (or 1000) bytes, no matter what the manufacturer of your hard-drive tries to tell you.

Time The original definition of a second made it to be 1/86,400 of a mean solar day (which is the period of time between local noon in two consecutive days). This suffers from the problem that the mean solar day increases by about 1.4 milliseconds a century; the current definition, therefore, is based on properties of the radioactive decay of atoms of a Cesium isotope, which is, once again, thought to be the same anywhere in the universe.

Note that time units don't always follow powers of ten: one rarely refers to kiloseconds or megaseconds (other than in some sci-fi novels), but rather one talks of hours, minutes, days etc. We do use milliseconds, microseconds and other smaller units, though, and it's not uncommon to hear of kilo-, mega- or gigayears.

Length As mentioned above, the basic unit of length is the metre. This unit was originally defined by the French, soon after their revolution, to be 1/10,000,000 of the distance from the North Pole to the equator. This is clearly a less than useful definition (and they were slightly off in their measurement, anyway), so the current definition is actually based on the speed of light; specifically, it is the length travelled by light in a vacuum in a period of 1/299,792,458 of a second. The speed of light in the vacuum is believed to be a global invariant in the universe so, should we ever move out of this planet, our units will still make some sense.

As a side note, there are a few other units of length that are very common, and very useful, in astronomy, and you should get yourself acquainted with them:

  • Astronomical Unit, or AU: this is the average distance between the Earth and the Sun, and equals approximately 1.496 x 108 km (or, more commonly, 150 million km); this is normally used to refer to distances in planetary systems

  • light year: the distance travelled by light in a vacuum in the period of one year, it equals just under 10 trillion km, or 9.46 x 1012 km (and one year, in this context, is exactly 365.25 days of 86,400 seconds each, and yes, this is an important data point; there are several ways of measuring a year and even a day, and we'll come back to this at a later date), or about 63,240 AUs

  • parsec: this unit is a bit more complicated, and we'll discuss it later; for now, just remember that it's equal to about 3.26 light years, and that despite the fact that this seems like an arbitrary number there is a good reason for it

Mass Once again, we have an original definition that is different to the modern one. Originally, one kilogram was defined as the mass of 1 litre of pure water (and 1 litre is 1 cubic decimetre), while the current definition says that 1kg is the mass of the standard kilogram prototype, a block of a platinum-iridium alloy stored in France (and one gram is, of course, 1/1,000 of that). This is still not a very satisfying definition (especially considering new reports that claim this block may be slowly losing mass; this definition is therefore likely to change in the coming decades.

Very important: mass is not weight. Mass measures the amount of material in an object, while weight measures the effects of gravity on that object (and, being a measure of force, its SI unit is the newton). In other words, mass is an intrinsic and (mostly) unchanging property of an object, while weight is a local property dependent on the local gravitational field. To make this a bit more clear, objects aboard the International Space Station may well have no weight, but their mass remains the same as on the ground.

That said, the way mass is usually measured is by measuring weight and assuming a constant gravitational field, which works very well in the surface of the Earth (this is not true if a balance-beam scale is used, as it actually compares the mass of the object being measured with a known mass in the scale; this type of scale can be used wherever there is some gravity and will give the same reading anywhere).

And this is it for today. Next week, we finally start looking upward and talk about what we can see on the night sky.

Much of astronomy has to deal with large numbers; astronomical numbers, in more senses than one. For example, the average distance from the Earth to the Sun is 149,597,870.691 kilometres — or, more commonly, 150 million kilometres. The mass of the Sun is approximately 1,989,100,000,000,000,000,000,000,000,000 kg, and I'm not even going to try to write that in words. The approximate age of the Earth is 4.6 billion years, while the age of the universe is closer to 15 billion years.

It is probably very clear from the paragraph above that these large numbers are very hard to work with — or even to write. It's even hard to get an instinctive grasp of how large they really are; at some point, really, all you have are way too many zeroes. That's the reason why scientists use a more compact notation for very large — or very small — numbers. This notation (not surprisingly known as "scientific notation") divides the number in two parts and uses the magic of the powers of ten to get rid of all those zeros. Those two parts are the mantissa and the exponent.

In short, the mantissa is the part of the number that we are reasonably sure of. Look again at that number describing the mass of the Sun; it should be pretty obvious that those zeroes are just "filler"; we don't know what all those digits are supposed to be, but we are fairly confident about the first five non-zero digits. Those five digits will form the mantissa.

The exponent indicates how large the number is. It tells us how many zeroes go after the mantissa or, more generally, how much we need to move the decimal point of the mantissa to get to the real number. In other words, it tells us which power of ten must be multiplied by the mantissa to get the number we're trying to express.

Let's get back to the examples above. As a general rule, the mantissa will always be kept between 1 and 10; so, the average distance from the Earth to the Sun would be written as 1.49597870691 x 108 km — or, if want to be a bit more compact, 1.5 x 108 km — meaning that, starting from 1.5, we move the decimal point 8 positions to the right to arrive at the intended number. The mass of the Sun, in the same notation, is merely 1.9891 x 1030 kg, which is certainly much more readable than the other version.

What the scientific notation does is to allow us to write and, more importantly, read numbers much more efficiently. It keeps all those zeroes out of the way and allows us to concentrate on what we actually know about the quantity we're talking about. It also makes it much easier to compare large numbers; the exponent will tell you at a glance the magnitude of the numbers in question.

And, as I mentioned, it also works the other way: a negative exponent will tell you how many positions to the left you need to move the decimal point, allowing you to easily represent very small numbers. The diameter of a hydrogen atom, for example, is 0.0000000000106 metres — or 1.06 x 10-11 metres.

The next lesson will be about units, and it will focus on what we can measure with these numbers, with special attention to the astronomically relevant units of measurement.

Astronomy 101

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I was listening to the latest episode of The Skeptics Guide to the Universe podcast last night, and there was a discussion that was basically about whether it's worth trying to educate the public about science and trying to fight the seemingly endless influx of pseudo-science all around us. The discussion (started by this post) was mostly centred on "alternative medicine" claims (not surprising, since Steven Novella is a doctor); one of the pieces of information mentioned was that negative studies - that is, studies proving that a particular therapy does not work - have never convinced any "true believer" to abandon anything. But this applies to other areas as well; I mean, the fact that astrology has been repeatedly proven to be bunk has not caused it to be abandoned. This has many people in "our" camp feeling somewhat depressed at the apparent futility of trying to educate people who don't want to be educated.

This is an interesting problem. After all, why is it that we have so much trouble getting the general population to accept and believe in scientific information (properly researched and reviewed), while the purveyors of "alternative" information find such a receptive public? I don't have an answer to that; I wish I did. Part of it is probably the tendency of people not to trust information coming from those perceived to be in a position of authority; the "alternative" guys usually try to align themselves with "normal" people, which is why, for example, saying that a particular therapy was "invented by a school teacher" is seen as a good thing. This comes from a lack of understanding about how science operates and where scientific information comes from: ideas survive not based on the authority of their proponents, but on their merits - at least in the long term.

On a vaguely related note: not too long ago, I also read (or heard) a criticism by someone - sorry, I honestly can't remember who, when and where this was - saying that, despite the incredible number of scientific blogs available nowadays, there aren't many that act as "gentle introductions" to scientific subjects. To be fair, that's not entirely true - at least if you extend the word "blog" to also include podcasts. The Evolution 101 series was a great introduction to basic and advanced concepts about evolution and natural selection; Astronomy Cast is a great resource for astronomy-related concepts, as is Phil Plait's blog (especially the videos he publishes occasionally). And I'm sure there are others out there.

Still, this combination of factors is why I've decided to start writing regularly about the "basics of astronomy"; this will be my "astronomy 101" series. I realise that there may be a few of those around, on- and offline; still, I think I can add something to the "astrosphere", and this will have the added benefit of helping me focus on, and review, things I should - and probably do - already know; making me "structure" my knowledge better, in a way. Also, I have a feeling that scientific-literate people have some responsibility for putting information out there and for trying to get more people to our side.

The structure I'll follow will be loosely based on university-level introductory astronomy courses and on a few books (most prominently the famous Universe, by Freedman and Kaufmann); when relevant, I will mention bibliography or add links to more detailed material.

My intention is to post new material once a week; I originally planned on writing longer articles once a fortnight, but I guess shorter, more frequent ones will work out better. If not, I can always change the style; it's not like I on a contract, or anything...

I hope everything works out well and that someone out finds my texts interesting. The series starts later this week.

Articles already published:

  1. Astronomical Numbers (18/07/2008)
  2. Units of Measurement (25/07/2008)
  3. The Night Sky (02/08/2008)
  4. Spherical Earth (09/08/2008)
  5. The Size of the Earth (16/08/2008)
  6. Mapping Our World (23/08/2008)
  7. Mapping the Sky (30/08/2008)
  8. The Sky In Motion (1) (13/09/2008)
  9. The Sky In Motion (2) (25/11/2008)

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