How is graticule made?
July 20, 2017 2:44 AM   Subscribe

I'd like to know why latitude and longitude are parallels and meridians and why they converge at the north pole. Maybe because degree grid cells break up into nice squares near the equator and mid-latitudes, but then fall apart at the poles (i.e., what time is it there? It seems totally arbitrary). Was this planned somehow? Did Eratosthenes or Hipparchus have a justification for the fact that meridians to go N-S and the parallels E-W, when it could just as easily have been the reverse?

And why is it a system of parallels and meridians (and not both parallels or both meridians?).

I would love to read a book on this if anyone has suggestions that aren't Dava Sobel's book on longitude because I read it already.
posted by stinker to Science & Nature (11 answers total) 7 users marked this as a favorite
Degree grid cells aren't squares anywhere. They're just close to squares at the equator & get closer to being square the smaller the area & the further from the poles you are.

Your question is closely tied up with the fact that it's impossible to create a mapping between the flat plane and the surface of a sphere that preserves both angles where lines meet and the straightness of straight lines. You can have one or the other, depending on which projection from the surface of the sphere to the plane you choose, but not both.

The parallels and meridians are arranged that way because they follow the rotation of the earth (ish - there's some fine detail that I'm handwaving away here). Parallels are called parallels because they're parallel lines on the surface of the sphere of constant latitude. Meridians are so-called because the Latin for noon is meridianum & each meridian is a half great circle from the north to south poles whose position is defined by the the sun being at it's maximum height - the sun crosses a given meridian exactly halfway between sunrise and sunset for that location.
posted by pharm at 3:46 AM on July 20 [6 favorites]

The system was designed to support navigation, not grid cells. You can determine your latitude by measuring the elevation of the North Star. You can move at constant longitude by following a compass.

If longitude used parallels, or latitude used meridians, you would have to define an arbitrary East Pole and West Pole. Those poles wouldn't correspond to anything you could easily measure using stars and compasses.

History of longitude.
posted by fuzz at 4:01 AM on July 20 [5 favorites]

So did Eratosthenes know about the revolution and rotation of the earth? Did that not require a heliocentric concept of astronomy? (I know Aristarchus first proposed the heliocentric model, but I didn't think it was generally known to/accepted by all.)
posted by stinker at 4:35 AM on July 20 [1 favorite]

I'm going to preface this with the fact that I'm winging my response and do not know any of the actual history, but that this is how I always understood it.

The earth is a sphere, but is special in that it is rotating around a single fixed axis, and that axis intersects the sphere at two antipodal points.

So given an arbitrary point on the sphere a good question to ask would be "what is the shortest path to the points where the axis intersects the surface of the sphere?" These resulting paths are the meridians. It doesn't make sense to have another set of meridians because there aren't another pair of naturally interesting points on the sphere.

The other interesting question you might ask of a given point on the sphere is "what is the path it take on the sphere as it rotates?" These are the parallels. Similarly to the meridians, another set of parallels wouldn't make sense because there is only one axis of rotation.
posted by noneuclidean at 4:41 AM on July 20 [4 favorites]

So did Eratosthenes know about the revolution and rotation of the earth? Did that not require a heliocentric concept of astronomy?

You don't need to know that the Sun is the center of the solar system in order to know that heavenly bodies rotate around the earth in a predictable way. (For these purposes it doesn't really matter whether the Earth rotates or the Earth sits still and the entire universe rotates around it). The poles are the fixed points in the sky, the point that the stars rotate around. That's really convenient for navigation, since you can always tell which direction the nearest pole is, just by looking at the stars.

And once you've defined a fixed point like a pole, it makes obvious sense to start drawing lines that define location in terms of how far you are from the pole (latitude) and what direction you are from the pole (longitude).
posted by firechicago at 4:54 AM on July 20 [5 favorites]

I don't see why you need a heliocentric model for latitude and longitude - the earth has to be a sphere for it to make sense, but it could just as easily be a sphere at the center of the universe. I don't think you need to know about the rotation of the earth for lat/long either - you just need a sphere with poles. It could be completely still.
posted by mskyle at 4:55 AM on July 20

Eratosthenes needed to know that the earth was a sphere (or close enough to one).

Heliocentrism is not necessary for this model - the earth rotating in place whilst the sun remains fixed and the earth being fixed whilst the sun orbits it on a 24 hour cycle are mathematically equivalent.
posted by pharm at 5:05 AM on July 20

Longitude & latitude allows you to define location fairly easily. Especially when looking at a flat map, navigation may be deceptive. On a globe, the shortest route is easily seen, but on a map, some areas are stretched.

Origin and Etymology of meridian
Middle English, from Anglo-French meridien, from meridien of noon, from Latin meridianus, from meridies noon, south, irregular from medius mid + dies day

Because the earth spins on a pole, the meridians go from pole to pole and define time as well as location. The parallels are actually parallel. If the earth tumbled randomly, there would surely be a different system, and also it would be quite odd. Spinning a globe may help clarify this.
posted by theora55 at 5:42 AM on July 20

You ask about the gird made up by the meridians and parallels as if the grid were the goal. They were not the goal.

The goal was describing a position on the earth, aka taking a fix. The simplest way to do this results in 'what angle you are from the poll' and 'how many degrees of rotation you are from some fixed meridian'. Longitude and latitude are direct consequence of the practical ways to achieve the goal of taking a fix. These techniques to take a fix are the significant ones because they can be measured with 'simple' instruments.

There are trade offs for this simplicity of taking a fix i.e. many calculations with latitude and longitude are complicated.

To summarize:
1) The Goal: How can I describe where I am?
2) Technique that could actually be used to achieve this goal: declination of sun, time past some meridian.
3) Unit system for that technique: latitude & longitude.
posted by bdc34 at 10:36 AM on July 20

I came in here to say what's already been said, and I love that one of the best answers about spherical geometry is from noneuclidean.
posted by RedOrGreen at 2:22 PM on July 20 [1 favorite]

This is one of those questions that's been sitting in the back of my mind since my initial post, so I have a couple clarifications and addenda that I need to write down so they stop bugging me.

First, I was mainly trying to answer your question as to why we don't use two sets of meridians or two sets of parallels, but that doesn't really answer how our current latitude and longitude system came about. bdc34 is spot on that the goal there should be to come up with a system to locate an arbitrary point on a sphere.

For that, my description of a parallel being the path traced around the sphere as it rotates is equivalent to the set of all points a fixed distance away from one of the poles. Even further, and to make some other things nicer, we define the equator to be the parallel that is equidistant from both poles and measure distance from that in degrees. All that pretty much comes naturally from our two interesting points and the rotation of the sphere.

However, and I think this is a little more important, to determine which meridian a point is on, there needs to be a fixed reference meridian, which we call the prime meridian. There is no natural meridian to use for this, so someone had to declare one. As you can imagine, there have been a lot of suggestions.

To go back to why don't we use two sets of parallels or two sets of meridians, if we wanted to ignore the naturally interesting points, I'm pretty sure (but not 100% positive) we could. There would just have to be two sets of antipodal points declared and then the parallels/meridians defined in reference to those points. I think would be easier to use with meridians that parallels, especially if the axes aren't orthogonal.
posted by noneuclidean at 5:21 AM on July 21

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