I’ve never paid much attention to the height of the Sun specifically, but I can say that even just when I was in college in Philadelphia, the constellations looked a bit off from what I was used to growing up in the Cleveland area. It doesn’t take much latitude difference to be noticeable.
The earth is 25,000 miles in diameter. 25,000 miles divided by 360 degrees is 69.4 miles. So if you travel south or north by that much, then the sun’s max angle above the horizon on that same day of the year would be different by one degree of arc.
So a little over 400 miles?
Thanks, so traveling 100-400 miles in any given day would be quite a chore for someone before automobiles or trains. I’m constantly amazed at the things they were able to work out back then. I know, in theory, measuring the earth’s circumference with sticks and shadows is pretty straightforward, but in practice, the margin of potential errors seems daunting. At least to layperson, me.
Didn’t he have a quadrant, astrolabe, and at least some astronomical tables? Though, even today, determining longitude without any kind of timepiece is definitely not for the inexperienced.
Sure, but you don’t have to perform two measurements hundreds of miles apart on the same day. You can do one measurement in one location on one day, and then you’ve got 364 days to get to the other location; on day 365, the sun and earth will be in the same relative positions as they were on the day of your first measurement, and then you can make your second measurement.
I’m not that familiar with astronomy, but the basic problem was that there are no easy observations that tell longitude. The heavens are a giant sphere (the Greeks said so) and so will look pretty much the same wherever you are. Things like the exact position of the moon at midnight might help, given a good set of tables. IIRC the original solution to the longitude problem was a reliable clock that was not affected by ship movements.
Well, sure, after you know the earth is round. Hari_Seldon’s response was to:
He seemed to be suggesting that you could get the idea that earth was round by easily traveling several hundred miles in a day and gazing up at the sun. His further response was the methodology of measuring the circumference after Erastosthenes already knew it was round. Maybe it’s true, it just doesn’t seem logical… again, to my layperson POV.
The lunar eclipse makes sense.
Accurately measuring longitude was such an important problem that over 300 years ago, Great Britain put up substantial substantial prize money to encourage the development of workable solutions.
A longer history of the problem:
Or you can have a colleague in the other city do the measurement for you. They had calendars, and scholars all over the world would have known and agreed when the northern solstice was.
Columbus surely had all of those things, but none of those helps you find longitude without a good timepiece (i.e., much better than anything Columbus had access to). In Columbus’s time, your options for finding longitude were very limited:
- Have a series of landmarks, each one visible from the previous one, and measure the bearing and distance from one to the next. Maybe doable on land, or with a lot of islands, but very difficult at sea.
- Measure your speed relative to the water, by throwing a buoy overboard, add it to an estimate of the speed of the water itself, and multiply that by your travel time (this time measurement doesn’t need to be nearly as precise as for a direct longitude measurement, but both speeds have significant error bars, especially the current speed).
- Set up a base somewhere, and wait for a lunar eclipse, and make careful records of the local time at which it happens, and compare that to to the time at some known reference location. This isn’t completely unrealistic: There’s at least one lunar eclipse per year, and each one is visible from over half the planet, but one measurement every year or two takes a long time to make a good map.
To see the effect of a change of latitude, you don’'t need to travel north/south in a single day, nor do you need to make an observation on the same day of the year in consecutive years. You just need to look up at the northern sky at night. The constellations around the celestial north pole will be higher in the sky the further north you are. To someone who is very familiar with the night sky, this will be obvious after a few hundred miles of travel, over any period of time, at any time of the year.
Yes, and the solution that won the prize was an accurate sea-going clock. (coupled with tables of astronomical measurements)
The other solution the article mentions is the position of the moon. The exact position of the moon at midnight local time (based on noon being “sun reaches top of its arc of travel”) could be used to tell you what longitude you were, but also required fancy tables and some figurin’. With fancier tables, any observation of the moon.
Specifically the position of the moon relative to different stars. Tables of such differences were amassed over decades - the various royal observatories were founded primarily to generate such tables as observed at the observatory, which became the longitude reference (most famously Greenwich, but there were competitors). Take distance measurements, correct for parallax of your approximate position relative to Greenwich, consult the tables to determine the current time in Greenwich. Use that number along with your local time (obtained by observing the sun to determine local noon) to calculate longitude.
Alternate means used observation of Jupiter’s moons (relative locations and occultations), but this observation was nearly impossible from the moving deck of a ship but was the preferred method for land-based measurements. An advantage of this method is no parallax error since Jupiter is so far away compared to the moon.
Occultation of various stars by the moon was also used, but was not frequent enough to be useful.
All of these methods required good weather and are more difficult from a rolling deck, requiring a lot of skill. The chronometer method, while it gives you Greenwich time without observations, still needs an accurate measure of local noon.
I can still find the North star etc on a clear nite.
It’s not the figurin’ that’s the hard part with that: It’s the precision needed, because you’re trying to determine a time to within minutes or less, based on something that completes a full cycle in a month.
The moons of Jupiter would be easier, since they only take a few hours to orbit, but then it turns out that there’s another wrinkle: They’re so far away that the speed of light is relevant, which makes it harder to predict where they’ll be at a given time. In fact, the first measurement of the speed of light was based on trying to explain this phenomenon.
You’re talking about a degree and a half. I really find it hard to believe that such a todifference is readily perceptible. For Eratosthenes, it was more like 7 degrees. And the fact that it was vertical in Aswan may also matter.
It’s perceptible when it means that \eta UMa, the tip of the handle of the Big Dipper, never sets in Cleveland, but does in Philadelphia.
Yes, presumably Eratosthenes could have skipped his well-based observations and simply measured the angle of the pole star in both locations. The key was knowing the north-south distance between the two observations. (and that the pole star was not exactly centered so time of night was relevant).
As mentioned, anyone travelling the earth could observe that the star background appeared to be a revolving sphere where as you travelled north-south, the arc of “directly overhead” moved and the pole star about which the sphere was rotating changed elevation. not a difficult leap to “Eureka! We’re on a giant sphere inside the heavenly sphere…”
Except that in that era, there was no pole star. The point that the Earth’s north pole points to moves around, a process called the precession of the equinoxes. Here’s a map of how it moves:
(Well, that image is not showing up in preview, probably because it’s a GIF, even though it doesn’t change. You’ll probably have to click on it to see it.)
Anyway, 2300 years ago when Eratosthenes was around, there was no star close to the north pole. Somewhere around the 14th century, a certain star started to get close and it got named Polaris. It was still about 4 degrees away from the pole at that time. Right now Polaris is about as close to the pole as it will ever get.
Just by happenstance I ran across a podcast that answers this question (pretty much). It’s Ask A Spaceman with Paul Sutter. “How do we know the earth is curved” episode. It’s a good listen.
Basically, all of the reasons posted here are so far.
It’s always dippy in Philadelphia.