How Did Eratosthenes Estimate The Size Of Earth In 240 B.c.?

Eratosthenes' Calculation of Globe's Circumference

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In 240 B.C., the Greek astronomer Eratosthenes made the first good measurement of the size of Earth. Past noting the angles of shadows in two cities on the Summer Solstice, and by performing the right calculations using his noesis of geometry and the distance betwixt the cities, Eratosthenes was able to make a remarkably authentic calculation of the circumference of World. Let's take a closer expect at how he did it!

Eratosthenes lived in the city of Alexandria, about the oral fissure of the Nile River by the Mediterranean declension, in northern Egypt. He knew that on a certain solar day each yr, the Summer Solstice, in the town of Syene in southern Egypt, there was no shadow at the bottom of a well. He realized that this meant the Sun was direct overhead in Syene at noon on that mean solar day each year.

Eratosthenes knew that the Sun was never direct overhead, even on the Summer Solstice, in his home city of Alexandria, which is farther north than Syene. He realized that he could determine how far away from straight overhead the Sun was in Alexandria by measuring the angle formed by a shadow from a vertical object. He measured the length of the shadow of a tall tower in Alexandria, and used simple geometry to calculate the angle between the shadow and the vertical tower. This angle turned out to exist near 7.2 degrees.

Side by side, Eratosthenes used a fleck more than geometry to reason that the shadow'due south bending would exist the same every bit the bending betwixt Alexandria and Syene as measured from the World's center. Conveniently, vii.2 degrees is 1/50th of a full circle ( l x seven.2� = 360� ). Eratosthenes understood that if he could determine the distance betwixt Alexandria and Syene, he would merely take to multiply that distance by 50 to find the circumference of Earth!

Here'southward where things become a bit tricky. Eratosthenes had the distance between the two cities measured. His records show that the distance was found to be v,000 stadia. The stadion (plural = stadia) was a common distance unit of the time. Unfortunately, there was non a universal, standard length for the stadion; then we don't know exactly which version of the stadion Eratosthenes used, and therefore are not exactly certain how accurate his solution was. He may have been right to inside less than 1%, a remarkable accomplishment! Or, if it was actually a different stadion that he used, he may have been off by about xvi%. That is still pretty expert! The actual polar circumference of Globe is just a bit over twoscore thou km (almost 24,860 miles).

Eratosthenes was a talented mathematician and geographer every bit well equally an astronomer. He made several other important contributions to scientific discipline. Eratosthenes devised a arrangement of breadth and longitude, and a calendar that included leap years. He invented the armillary sphere, a mechanical device used by early astronomers to demonstrate and predict the apparent motions of the stars in the sky. He also compiled a star itemize that included 675 stars. His measurement of the circumference of Earth was highly respected in his day, and fix the standard for many years thereafter. He may have also measured the distances from Earth to both the Moon and to the Sun, but the historical accounts of both deeds are, unfortunately, rather cryptic.

Eratosthenes' Adding of Earth's Circumference

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Eratosthenes was a Greek astronomer in ancient times. Around 240 B.C. he made the start good measurement of the size of the Earth. How did he do that?

Eratosthenes used the lengths of shadows to figure out how high in the sky the Sun was in a certain place on a sure twenty-four hours. He knew of another place where in that location was no shadow at all on the same solar day. That meant the Lord's day was straight overhead. He plant out the distance betwixt the two places, and so used some geometry to effigy out the rest. Let'southward take a closer expect!

Eratosthenes lived in the city of Alexandria. Alexandria is in northern Egypt. It is by the Nile River and the Mediterranean Body of water. There was a tall tower in Alexandria. Eratosthenes measured the length of the tower's shadow on the Summer Solstice. He used that information plus some geometry to figure out the angle between the Dominicus and direct up.

In that location was a boondocks in southern Egypt called Syene. There was a well in Syene. On the Summer Solstice, the Sun shone direct downwards the well to the very bottom. That meant the Lord's day must be direct overhead.

Eratosthenes had someone measure the altitude betwixt Alexandria and Syene. He used that distance, what he knew about the Sun'south angles, and a bit of geometry to figure out the size of the Earth.

We aren't quite certain what answer Eratosthenes came upward with, though. The distance between Alexandria and Syene was measured in stadia. The stadion was a distance unit that was oftentimes used in ancient times. However, not everybody used a stadion of the aforementioned length. If Eratosthenes used one length for the stadion, his reply was really, really good. The Earth is about twoscore thousand kilometers (about 24,860 miles) around. The measurement that Eratosthenes fabricated might have been within well-nigh 1% of this. That would exist amazing! Yet, he might accept used a different length stadion. If that is true, his answer was off by about 16%. That is all the same pretty skillful!

Eratosthenes may accept besides washed some measurements of the distance from Earth to the Moon and from Globe to the Sun. Unfortunately, the records of that are not very clear. Then we aren't quite sure whether he ever did brand those measurements, or what his answers really were if he did.

Eratosthenes' Calculation of Earth's Circumference

Click the green "forrard" button to step through the animation. (Note: If you cannot see the blitheness to a higher place, or it is non working properly, you may need to download the latest Flash player.)

Eratosthenes was a Greek astronomer in ancient times. Around 240 B.C. he made the start good measurement of the size of the Earth. How did he do that?

Eratosthenes used the lengths of shadows to figure out how high in the sky the Dominicus was in a certain place on a sure day. He knew of another identify where there was no shadow at all on the same mean solar day. That meant the Sun was directly overhead. He found out the distance between the ii places, then used some geometry to figure out the residual. Permit's take a closer look!

Eratosthenes lived in the urban center of Alexandria. Alexandria is in northern Egypt. It is by the Nile River and the Mediterranean Sea. There was a alpine belfry in Alexandria. Eratosthenes measured the length of the tower's shadow on the Summer Solstice. He used that data plus some geometry to figure out the angle betwixt the Sun and straight up.

There was a town in southern Egypt chosen Syene. In that location was a well in Syene. On the Summer Solstice, the Sun shone straight downward the well to the very bottom. That meant the Sun must exist straight overhead.

Eratosthenes had someone measure the distance between Alexandria and Syene. He used that distance, what he knew about the Sun'south angles, and a bit of geometry to figure out the size of the Globe.

So what respond did he get? We know now that Earth is almost 40 thousand kilometers (about 24,860 miles) around. We don't know for sure what reply Eratosthenes got. His measurement between Alexandria and Syene was in stadia. The stadion was used to measure distance in ancient times. It was used like a kilometer or a mile is used today. We don't know for sure how long the stadion that Eratosthenes used was. It might have been one length, or information technology might have been some other. Then possibly his answer was actually, actually good. It might have been within ane% of the right answer! Or information technology might not take been quite so practiced. Information technology may have been off by about 16%. Either way, his answer was at least pretty good.

Folio created July xx, 2007 by Randy Russell. Last modified July 31, 2007 by Randy Russell.
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