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.
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