Historic Mystery

[quddusaliquddus]

Hi all :D,
I was wondering if someone could help me. My physics teacher once told me about this unsolved mystery - and I have a vague memory of it. I was hoping someone could help me find out what it is.

Basically it was something to do with astronomy and about a Greek astronomer. I think he made simultaneous astronomical observations at great distances apart maybe in Egypt. The mystery is how he did it simultaneusly

Who was this person and what did he do?

I know its vague - googling hasnt helped - maybe someone with more general knowledge thna me could help me out. If not - then oh well.

Thanks

Q

[turbo]

Eratosthenes did not make simultaneous measurements. He knew that a particularly deep well in Syene was fully illuminated by sunlight one day a year and he knew that on that same day, a vertical stick in Alexandria would cast a shadow. By measuring this shadow, and using geometry to calculate the arc created by the curvature of the Earth between Syene and Alaxexandria, he came up with a surprisingly good estimate of the circumference of the Earth. Google Eratosthenes for the whole story and the calculations.

[quddusaliquddus]

Thanks for the info. Im not sure if its him but you might be right.

[quddusaliquddus]

Hi. Just read up on it. It is him. The mystery is how he measure the distance between the cities. Am i right?

[turbo]

Hi. Just read up on it. It is him. The mystery is how he measure the distance between the cities. Am i right?Distances were measured by very accurate pacing. Such distances were of military importance if you had to consider the logistics of moving troops from one city to to another.

[russ_watters]

AFAIK, the only mystery is the conversion between the units he used and what we use today.

[turbo]

AFAIK, the only mystery is the conversion between the units he used and what we use today.IIR, that's the big one, Russ. What is a stadia in modern units?

It's for sure that the Greeks knew what they were measuring, though. The calculations involved in getting mounted scouts from one place to another and deciding what kind of troop-staffing they could get with chariot-based teams, supply-wagons, infantry, etc in what times.... stuff like that could make or break a dynasty.

[quddusaliquddus]

Im not too good with physics even less with history - but how could he have timed it right?

[turbo]

Im not too good with physics even less with history - but how could he have timed it right?The Egyptians and the Greeks were very precise about their calendars. No mystery.

[quddusaliquddus]

Dont wanna sound arrogant or anything - but I still dont get it. :confused:

How could he know the its midday in one city while being in another city. Were their clocks that sophisticated?

[Vanadium 50]

How could he know the its midday in one city while being in another city. Were their clocks that sophisticated?

He picked two cities that were (almost) on a north-south line: Alexandria and Syrene.

[mgb_phys]

It didn't have to be synchronised.
You can visit Alexandria on midsummers day (which the Egyptians and Greeks knew) and measure the angle, then you either visit Syrene any another year on midsummers and measure the angle - or you know from reading the guidebooks about the well in Syrene and just pick Alexandria to do the other test.

[quddusaliquddus]

But how would he know precisely at what moment the well is directly under the sun when he is in another city? If he goes to both cities in misummer then both places would not produce any shadows. I dont quiet understand.

[mgb_phys]

Syrene is almost on the tropic of cancer and so the sun is perfectly overhead on midsummer's day. Alexandria is about 31deg north and so on midsummers day the minimum angle would be around 7.5 deg (31-23.5deg)

All you have to be able to do is find midsummers day - which is easy with just a stick in the sand.

[quddusaliquddus]

Just say he knew the day the well wouldnt have a shadow in one city. Then he would be at the other city on that day. Now - how would he know at what point in time the well is shadowless?

[turbo]

Just say he knew the day the well wouldnt have a shadow in one city. Then he would be at the other city on that day. Now - how would he know at what point in time the well is shadowless?He didn't have to know the time of day via a clock or some other machine. The Sun is a pretty good indicator of mid-day. When it is as overhead as it can get at your latitude, it is noon-time at your location. This is NOT a mystery, though we should be impressed by his rigorous and inventive techniques that he used to obtain his estimate.

[quddusaliquddus]

Im sorry. Im probably not getting it or something. There are two cities. We need to measure the shadow in one when its noon in the other. Now - how do you know at what point it is noon in the other city while you are in the second city (where theres a stick in the ground)? Maybe im confusing myself or something.

Edit
Ofcourse its easy to know when its noon where you are. But how would he know its noon somewhere else?

[turbo]

If you are at the same longitude, it's noon at the same time every day, regardless of your latitude. Maybe it's a mystery how some Greek scientist figured out how to make use of this information 2000 years ago, but I'd rather lay this to human ingenuity and perception. This is not an especially tough problem. Kids replicate this measurement every year as an academic exercise, as you will discover if you dig a bit.

[quddusaliquddus]

Thanks. I get it now.

[russ_watters]

It's noon when the sun is at it's highest, so it is easy to find local noon.

[Chronos]

Eras must have spent many months getting the stake just right to take his measurement - which as Turbo noted - was very good. The trick was in the calibration, not the result.

[HallsofIvy]

Just say he knew the day the well wouldnt have a shadow in one city. Then he would be at the other city on that day. Now - how would he know at what point in time the well is shadowless?

It isn't necessary that the measurements be made at the same time of day- and if the two cities are not directly north and south of each other, you would not want to. The crucial thing is that the measurements be made at a time when the two shadows are shortest. Of course, in Syrene, which is on the tropic of cancer, that would mean when there was no shadow at all- the sun shining directly down the well.

[turbo]

The critical point is that the cities should be at about the same longitude. If not, the paced-off distance between the cities would be too long, and would throw off the calculation. Maps may have been good enough back then to allow for some correction for this error, but pacing off a N-S line would produce the most accurate estimate.

[Vanadium 50]

Actually, although it's simplest to do when the two cities are at the same longitude, it's not strictly necessary. What you need to know is the north-south separation of the two cities. That's simplest if the two cities are at the same longitude, but it can be finessed otherwise.

Of course, the more complications you include, the more inaccuracies can creep into your final number.

[turbo]

Actually, although it's simplest to do when the two cities are at the same longitude, it's not strictly necessary. What you need to know is the north-south separation of the two cities. That's simplest if the two cities are at the same longitude, but it can be finessed otherwise.

Of course, the more complications you include, the more inaccuracies can creep into your final number.Until the circumference of the Earth is known (or estimated) it would be very difficult to factor out the E-W component of the paced off distance between cities at different longitudes. With today's maps, etc, the problem seems trivial, but back then, it was not.