I’m reading about an early method of estimating the circumference of the earth. The idea was to walk at night due south or north and measure how far one degree of the earth’s curve was from the starting position. Then multiply that times 360 and voila. But how did they know they had walked “one degree of the earth’s curve” if they didn’t know how far around the earth was? Would using a protractor allow them to do that by tracking the north star for one degree?
The story is that Eratosthenes measured the altitude of the sun (not the north star, whichever it was back then), by measuring the length of the shadow of a vertical rod at noon on the summer solstice. Do this at two different places on the same meridian, between which you know the distance…
Yes, I’m familiar with that story (in a slightly different form), but I’m talking about a different event. The question remains: can you determine one degree of distance of the earth’s circumference by using a protractor in earth (or astrolabe, I guess) and see when the north star is one degree away from where it was when you started?
Sort of, but strictly speaking we have to say no, it’s not quite that simple. There is no star exactly over the North Pole, so even a star pretty close will constantly circle around the pole (even sitting still you will observe it moving over a degree), and you have to take that into account. Here is one method used in practice. Another reference, also describing the solar method.
Being a Southern Hemispherean I have no innate sense of the North Star (or even ‘North’) as a thing, I’m probably getting this well wrong. However …
Picturing a triangle in my mind with apex at the North Star, and travelling North, the angle will not reduce in a uniform way because you are travelling on a curved surface. Walking, say 1 million steps north from the Equator will reduce the angle to the N star differently than if you took those steps N from Paris or Moscow.
The relevant reference point would not be the North Star, but the Centre of the Earth, which you don’t have sight of to measure against. Using a sextant to measure against the N Star would require tables or an adapter to give you correct latitude.
The star in question does’t need to be over the north pole. It doesn’t even need to be a star.
Stand whereever you are. Measure the elevation of e.g. Jupiter above your local horizontal using a sextant-like device with a bubble level. Ride your horse due poleward until Jupiter measures 1 degree closer to the horizon (or one degree farther from zenith, whichever is easier to measure with your tools. However far you rode, that’s 1/360th of the way around the Earth. The real answer is on the order of 60-65 miles, so a few hours on horseback. All of this needs only Ancient Greek level of tech.
For sure a better calc would correct for the inclination of Jupiter’s orbit & the effect of the few hours of Earth rotation projected into the plane of your ride. But you’d get a decent number even ignoring all that.
Jupiter won’t sit still for you. Go stand in eg Chicago and don’t ride anywhere. You will observe it setting and rising, with its elevation changing on the order of 10 degrees per hour at times. Start watching it at twilight, and a few hours later it will be below the horizon.
You can measure its peak elevation though, then move to another location and measure its peak elevation on the following night. Of course measuring on consecutive nights will introduce errors of its own, but they should be pretty small
So it seems, so far, at least, that the story I read about is doubtful because it doesn’t seem as if one can walk “one degree of the earth’s circumference.” Not, at least, without knowing how far that would be to begin with. I thought you might be able to do this by taking a reading of the altitude of the north star (even though it’s not exactly stationary) and then walking until it’s one degree off from where it was when you started. The story as I read it seemed unlikely for other reasons, but I wonder about the possibility of its being true at least in theory. So far, it doesn’t seem so.
If there were a star exactly at the North Celestial Pole, then it really would be as simple as taking its altitude measurement with an astrolabe of some sort, and walking until that altitude increased by one degree. This works precisely because the surface of the Earth is curved, so the fact that the Earth is curved is not a problem.
As it happens, alpha Ursa Minoris is not exactly at the North Celestial Pole, but this presents only minor difficulties. One can still use its average position as one’s reference point, or its position at a particular time of night, for the same effect.
Stephen Callahan’s sail boat was sunk in the Atlantic by a whale. He says in his book Adrift that he did a fair job of estimating his latitude as he drifted in a raft using the horizon and the north star. He used a pencil and created a crude protractor if I recall.
I have to say, I don’t know how well this would work on a day to day basis. You would need perfectly calm seas for one thing, and he was in a small inflatable raft. But I’m neither a sailor, or have been adrift in the ocean. I suppose in such a circumstance you could try to average it out.
It sounds like you think it’s not possible to do this. It definitely is - it’s just not likely that someone would do it in one shot without a bit of a workup;
You can walk a distance, then take measurements of some reference object and from this measurement (which will be less than one degree, or more than one degree), calculate how far off your walk was from actually walking one degree of the Earth’s surface, then subsequently walk this distance and repeat/refine your measurements until you get it right.
Get a piece of string approximately 25,000 miles long…
Well, one way would be by time. We’ve known for centuries the time period from noon to noon, and that 1/360th of that would be one degree of rotation (or of solar orbit if you assume this is before heliocentricity was recognized).
Even if you have a reasonable accurate timepiece, it brings us back to a question of determining the place where the sun is directly overhead. For simplicity, let’s assume you have a portable stovepipe or hollow log with a plumb bob on it, and you mark where the sun shines straight down onto the equator at noon on June 20. On June 21, based on experiments you’ve been conducting for a couple of weeks that give you a good idea where to be, you mark where it’s shining straight down 4 minutes after noon. Rough—and obviously owing a debt to Eratosthenes for experimental design—but it would yield a reliable number.
Since a degree of latitude is going to be about sixty nautical miles (was exactly that historically), you’re certainly not going to cover it on foot in a single night. But it would be something you could do from night to night if you spent those nights not walking, but instead following the movement of stars and recording your observations, then comparing to what is observed at other locations. Although even Polaris is going to trace a small circle about the pole each day, it will be the same path from night to night (just like all the other stars in the “firmament”) over the course of a human lifetime and thus fixed enough for comparison.
Currently, Polaris is about half a degree from the actual pole. It hasn’t always been that close. Because of precession, the pole moves over time, making a big circle on the night sky over a period of 26,000 years. About 5 or 6 hundred years ago, Polaris got close enough (a few degrees) to the pole that it got its name; it wasn’t called Polaris before then. In classical times, there was no one star that close to the pole. You have to go back 5000 years to find a naked-eye star that was actually on the pole. See here for more details:
This is one of the reasons that I questioned the story as it was written. Supposedly, in order to estimate the circumference, someone walked one night one degree of the curve, then walked back, and calculations of that distance resulted in an estimate of about 60 miles. No one is able to walk that far in a night, let alone make the return trip. Aside from that impossibility, I wondered about the theory - walking one degree, and how it could be done. This allegedly occurred in about 150 A.D. by Ptolemy. I think it may have been a theoretical plan but there are too many problems with it to be pulled off.
It seems entirely plausible to me (apart from the whole “one night” thing) if one considers that the observer didn’t necessarily have to measure the distance himself, but could have relied upon known/well-established distances between cities that frequently interacted with one another, perhaps along the coast with shared visual reference points between them (like a mountain peak). I wouldn’t expect it to be a single night of observation, but multiple nights to reduce error.
The ‘one night’ bit is the impossible part. You cannot walk that distance in a night; it’s the best part of three contiguous marathons - you’d have trouble running it in one night, even with unlimited stamina.
But the rest of the thing is possible. Here’s a guy that did it on a bike: How I Proved the Earth is Round (with my Bike and Two Sticks) - YouTube
60 miles is roughly 100 km, the record for racewalking is 9.5 hours
The record for running appears to be ~6 hours:
Certainly nights last longer than 6 hours (or even 12)
Brian