Monthly Archives: April 2020

Longitude doesn’t represent distance—there, I said it

In the last post I said I’d tell you how Eratosthanes knew how many degrees of longitude Benghazi is from Alexandria.

We know that lines or parallels of latitude are about 69 miles apart. Latitude measures degrees of two 90° quarter-circles, each starting at the Equator and ending at the poles. The Equator is 0° and the North & South poles are 90°.

Longitude measures time. Or to be more precise, longitude converts time into degrees of a 360° circle. “WHAT?” I hear you holler as you spring from your comfy chair. “Have you finally lost your marbles, Manders?”

Al-Biruni (973–1048), another one of those amazingly-accomplished scholars

Ptolemy’s geocentric vision of the universe reckoned that Earth doesn’t move—she is stationary while the heavens whirl around her. But a Persian scholar, Al-Biruni, thought that the Earth spins on her axis—just like the globe in your classroom. If that were true (and of course it is), you’ll realize that the Earth spins all the way around every day, every 24 hours.

I drew 24 sections on this sphere—for the 24 hours it takes for Earth to spin around on her axis. Each line is a meridian, a longitude line.

THAT CHANGES EVERYTHING! Mapmakers could divide the Earth’s surface into 24 units. Each unit would represent one hour. Each unit would also represent 15 degrees. Why? Because there are 360 degrees in a circle. 360 divided by 24 equals 15. Now I ask you, who was it who divided the day into two 12-hour halves? Who was it who came up with Base Sixty counting, which makes it so easy to divide 360 by 24? Who? WHO?

Thanks, Sumerians!

The Sumerians, that’s who! I love those guys!

Getting back to Eratosthanes’ experiment: if that lunar eclipse began at 12:36 am Alexandria time and midnight Benghazi time, Eratosthanes knew that Benghazi is 36 minutes west of Alexandria. The Earth rotates on her axis 360° every day, 15° every hour, and 1° every 4 minutes. So, 36 minutes difference in time from Alexandria to Benghazi ÷ 4 = 9 degrees of longitude. Thinking of a chunk of time as a chunk of a circle, Eratosthanes could confidently mark Benghazi’s longitude on a map.

Back to the beginning of The Western Civ User’s Guide to Time & Space

Eratosthanes and longitude

Old-time tv newsrooms had clocks on the wall set to local times of the big cities.

How did Eratosthanes or Ptolemy determine where the longitude lines should go? I got this from the History Stack Exchange site:

Longitude is calculated by comparing the elevation of an astronomical object to the pre-calculated (or observed) elevation of the same object at a reference location at the precisely simultaneous moment in time. Everything in the sky rotates once around that vast celestial sphere every 24 hours, so the more precisely one can establish simultaneity the more precise one’s measurement of longitude will be.

Whew! In other words: 2 people standing in 2 different places can measure the height in the sky of the moon, or the Sun, or the North Star to figure out how far east or west they are from each other. BUT—the measurement must be taken at exactly the same moment. Eratosthanes figured a way to find longitude without the measuring. Eratosthanes (in Alexandria) and an assistant (in someplace to the west—maybe Benghazi?) watched a lunar eclipse. They agreed to mark the exact local time the eclipse began. The local times won’t be the same, right? When it’s midnight in Benghazi, it will be 12:36 am in Alexandria. The difference in their times told Eratosthanes how many degrees apart from each other they were.

I’ll tell you how in the next post.

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We don’t have Ptolemy’s original map. It’s one of those documents lost to history. Lucky for us there’s a copy made by monks centuries after Ptolemy shuffled off the ol’ mortal coil. I drew this version of Ptolemy’s map showing only the longitude lines. He drew them curved to give you the idea that the world is round.

So Eratosthanes and Ptolemy knew that the Earth was round. And it was relatively easy to locate the big latitudes like the Equator and Tropics. To find each degree of latitude was a little more difficult—you need to accurately sight the Sun or moon or a star. Eratosthanes located his latitude in Alexandria by measuring the angle of a shadow at noon of the solstice. After the astrolabe was invented mapmakers used that device to find their latitude.

Latitude lines are parallel, so each degree of latitude is about 69 miles from the next one. On the other hand, longitude lines travel from north to south poles. They join at the poles and are farthest apart from each other at the Equator. There are 360 degrees in a circle; the Earth is round; so there are 360 lines of longitude. If you’ve been following this history from a year ago, you remember that our pals the Sumerians came up with Base 60 method of counting—that’s why there are 360 degrees in a circle.

One of those longitude lines needs to be zero degrees. Which one? There’s no natural starting point for longitude (like the Equator is Point Zero for latitude). Eratosthanes started his system of longitude in Alexandria, where he lived. Alexandria—and every place due north or south of it—was zero degrees: the Alexandrian Prime Meridian. It was also 360 degrees, because it represented the beginning and end of a full circle.

So far, so good. Here’s the kicker, though: how do you measure longitude? How do you know where, say, 87° is on Earth in real life so you can put it on a map?

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The Tropics

Here’s something interesting: the Tropic of Cancer and the Tropic of Capricorn don’t stay put. They move around a little bit. The Tropic of Cancer marks where the Sun will shine the longest in the northern hemisphere for this year—that is, the summer solstice. It’s at around 23-24 degrees north. On the summer solstice, June 21st-ish, the Sun will shine directly over the Tropic of Cancer.

The Tropic of Capricorn marks where the Sun will shine the longest in the southern hemisphere—that is, the winter solstice. It’s at around 23-24 degrees south. On the winter solstice, December 21st-ish, the Sun will shine directly over the Tropic of Capricorn.


Here’s kind of what they look like on a flat map.

The reason the Sun shines directly on the Tropic of Cancer in summer and the Tropic of Capricorn in winter is that our Earth is tilted as she revolves around the Sun. We learned that way back when we read about Eratosthanes.

It takes one year for Earth to orbit the Sun. When the Northern Hemisphere is tilted toward the Sun it’s Summer there. When the Southern Hemisphere is tilted toward the Sun it’s Summer there.

Latitude and Longitude

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The Equator

Human brains are marvelous. Something we humans are able to do is look at a round object, like the Earth, and draw it flattened out as a map. Then, get this: other humans are able to look at the flat map and comprehend a round Earth. Yay, us!

Ptolemy was the first to think of drawing lines of longitude and latitude on a map. Longitude lines travel from north to south poles. Latitude lines travel east to west and are parallel to the Equator. Together they make a grid on a flat map. Longitude and latitude lines are man-made; they don’t exist except on maps. Longitude and latitude lines are the way we organize the Earth’s surface so we can navigate on it. You assign the lines names or numbers.

Latitude lines (also called parallels) are circles that run around the circumference of the Earth and are measured in degrees. The Equator divides the Earth into northern and southern hemispheres (hemi = half, sphere = globe). It’s at 0 degrees. The North & South poles are at 90 degrees.

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Let’s talk about maps. For most of history, maps weren’t particularly accurate for navigation. They were bird’s-eye views of cities or else fanciful drawings that included pictures of weird sea-serpents and bizarre inhabitants of unexplored lands. Maps were expensive because they were hand-drawn works of art.

Old Maps With Sea Monsters

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It’s been a long trip so far

I want to take a moment to thank everyone who’s been hanging with me throughout this little history. I feel like I’ve been telling a year-and-a-half-long joke and I’m just about to get to the punchline.

Since January last year, we discovered how people in the past measured space and measured time. We followed along as travelers ventured further and further from home—traders and explorers became bold enough to make long voyages across the oceans without knowing exactly where they were. To navigate, you need to measure both time and space. Most of the inventions that measure time and space didn’t appear until around the 1500s.

Here’s what you need if you plan to cross an ocean and would like to know where you are going:
1. an accurate map, to know what you’re looking for
2. a compass, to orient the map
3. an astrolabe, to find latitude (how far north or south you are)
4. universal time, to find longitude (how far east or west you are)—Galileo proposed that if you can see the positions of Jupiter’s moons, and you know what time it is locally, you can figure out your longitude. Jupiter’s moons would be a universal clock.
5. an accurate clock, to know local time

The Exploration Age sailors set sail without an accurate map or clock, because those things didn’t exist yet (a pendulum clock doesn’t work on a rocking ship).
Astrolabes or Jupiter’s moons are only useful when the sky is clear. So, even in the 1500s sailors didn’t have all the tools they needed for navigating.

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Heliocentric blasphemy!

“We can’t torquemada heliocentrism; we can’t torquemada Copernicism; we can’t torquemada anything!”

We learned about how Aristotle and Ptolemy promoted the idea that the Earth is the center of the universe; she doesn’t move; all the planets and stars revolve around her. This is called geocentrism.

Copernicus had questions: if the planets and stars revolve around the Earth, howcome their orbits aren’t all perfect circles? He proposed that the Sun is the center of the universe and the planets and stars revolve around him. This is called heliocentrism.

When Galileo, with his newly-built telescope, observed moons revolving around Jupiter he could plainly see that not every heavenly body revolved around the Earth. Copernicus was right—at least Jupiter’s moons revolve around Jupiter. If Jupiter’s moons weren’t geocentric, how much else of the universe wasn’t geocentric?

This is the scientific method that is Galileo’s gift to us. He observed and asked questions and looked for proof.

Galileo was a brilliant self-promoter and made friends in high places. Nevertheless, his assertion that Aristotle was wrong got him in trouble with the Catholic Church. It’s not really clear to me what it was exactly that got him in hot water. Yes, there’s a passage in the Bible about the moon and Sun standing still (Joshua 10:13), but so what? The moon and Sun could still appear to stand still in a heliocentric universe.

It may be as simple as: Protestantism was still fresh; Christians were reading and interpreting the Bible for themselves (before moveable type only the priests had copies of the Bible); the Catholic Church’s establishment saw its power being challenged. Then Galileo came along and said everything you believe about God’s creation isn’t so. That may have been enough to cheese off the Church and put Galileo in front of the Inquisition.

Galileo did himself no favors when he published a fictional argument between 3 guys—to explain and prove his thesis—and made the guy with the pope’s point of view the moron. The upshot was heliocentrism was found to be heretical (against biblical belief) and Galileo was told never again to publish his heliocentric blasphemy. He was put under house arrest for the rest of his life.

It’s easy nowadays to paint the Church as the anti-science bad guy. This was indeed an embarrassing day for Christianity. If you look at the entire history of the Church, though, she’s done way more to encourage science and learning than to suppress it. Going back to Charlemagne, monasteries were the place you went to find books by classical thinkers, painstakingly translated into Latin by the monks. Most universities were originally Christian institutions. Anyhoo, a more recent pope finally admitted—after all these centuries—Galileo was right (thanks for linking this, Chuck Dillon!).

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Who needs a GPS?

Here’s something fun: a chart of Jupiter’s moons, showing where they will be on today’s date according to your location. Of course, Galileo proposed finding your location by observing Jupiter’s moons: you find their positions and note your local time. Those 2 bits of information are enough to tell where you are on Earth.

Here’s where you can get an app for observing Jupiter’s moons.

Here’s an animated chart you can download:

Let me see what moons are like on Jupiter

The moons of Jupiter travel around her at a regular rate, like the hands of a clock. Galileo thought that you could use the moons as a universal clock. With that clock as a reference point, you could use local time to figure out where you are on Earth.

This sounds like a great idea, but how does it work? I’m guessing that you look at Jupiter, see where her moons are, and calculate where you are on Earth based on which moons you can see. For instance, on Wednesday, May 25, if you’re in North America and you have a telescope you can watch Io and Europa pass in front of Jupiter. If you live on the east coast you’ll see them only starting out; on the west coast you’ll see them only at the end. If you live in the middle of North America you’ll see most of the passage.

Since they know exactly when those moons will be zipping across the face of Jupiter and how long it will take, astronomers are able to make charts of the moons’ progress showing local times everywhere on Earth.

This strikes me as a huge amount of work to figure out where you are on Earth. Then again, I’m holding a cell phone with a GPS (Global Positioning System) so it’s pretty easy for me to know exactly where I am. If I were floating around in the ocean in the 1600s, with no GPS, I imagine I’d be pretty desperate to know exactly where I were and would consider breaking out the old telescope to have a squint at Jupiter and her moons.

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