# A biography of eratosthenes the ancient scientist that measured the tilt of the earths axis

Cleomedes, On the Circular Motions of the Celestial Bodies de motu circulari corporum coelestium And it is necessary that the distance between Syene and Alexandria is one-fiftieth of the Earth's circumference. Since this distance is 5000 stades the circumference length is 250000 stades. Eratosthenes of Cyrene c. He was born in Cyrene, a place in Libya which is called today Shahhat. He worked on geometry and prime numbers. He was a director of the great Library of Alexandria. He is best remembered for his prime number sieve which, in modified form, is still an important tool in number theory research.

Eratosthenes measured the tilt of the Earth's axis with great accuracy and compiled a star catalogue containing 675 stars now lost ; he suggested that a leap day be added every fourth year and tried to construct an accurately-dated history.

## Eratosthenes of Cyrene

He became blind in his old age and is said to have committed suicide by starvation, like Democrit. Eratosthenes came to Alexandria from Athens to be the chief librarian of Ptolemy Euergetes.

He was not merely an astronomer and a geographer, but a poet and grammarian as well. His contemporaries jestingly called him Beta the Second, because he was said through the universality of his attainments to be "a second Plato" in philosophy, "a second Thales" in astronomy, and so on throughout the list. For the same reason he was called a Pentathlos which means and athlete in five disciplines. We know indirect what he did by Strabo and Cleomedes who wrote 150-200 years later about Eratosthenes.

Stories and Poems such as Hermes and Epigone. Thales made measurements with the aid of shadows using the gnomon, which is the most primitive, but which long remained the most important, of astronomical instruments.

## A biography of eratosthenes the ancient scientist that measured the tilt of the earths axis

It is believed that Eratosthenes invented an important modification of the gnomon which was elaborated afterwards by Hipparchus and called an armillary sphere. This consists essentially of a small gnomon, or perpendicular post, attached to a plane representing the Earth's equator and a hemisphere in imitation of the Earth's surface.

With the aid of this, the shadow cast by the sun could be very accurately measured. It involves no new principle.

### A biography of eratosthenes the ancient scientist that measured the tilt of the earths axis

Every perpendicular post or object of any kind placed in the sunlight casts a shadow from which the angles now in question could be roughly measured. The armillary sphere made angle measurements extremely accurate. In Syene there is a very deep well. Every year at noon on the day of the summer solstice 21 June the sunlight illuminates the water at the bottom of this well.

At that moment, the sun is directly overhead and there are no shadows in the city of Syene. Eratosthenes invented, probably around 205 BC, a very beautiful method to measure the circumference of the Earth.

Details of his method he published in a work On the measurement of the Earth which unfortunately was lost. We know indirect about his method from other authors, mainly Cleomedes and Theon of Smyrna. He reasoned that the change in angle of the shadow was caused by the spherical shape of the Earth Aristotle and others knew this earlier and that it would be possible from this angle to obtain the circumference of the Earth. If the sun light falls vertical in Syene then it will be also vertical in Alexandria and objects that are vertical in both cities, like an obelisk or a gnomon, will be parallel to the sun rays no shadow will be observed.

Eratosthenes knew that the sun is very far from the Earth so that the sun rays are almost perfectly parallel. Eratosthenes measured the distance to the sun as 804000000 stadia and the distance to the Moon as 780000 stadia from data obtained during lunar eclipses.

That is to say, out of the 360 degrees needed to travel all the way around the world, the two cities were 7. In other words he determined that the distance between Alexandria and Syene was one-fiftieth of the Earth's circumference. Some Remarks The distance between Alexandria and Syene is 729 km, not 800 km; The accuracy depends on the length of the stadium.

For a value of 157. Very interesting is that the measurement of the distance between Alexandria and Syene is based on the estimated average speed of a caravan of camels that traveled this distance! Camels traveled the distance many times to obtain an average estimate of the distance. Whether this is true is not clear. Therefore one can imagine that at that particular time one could not see at the reflected sunlight from the well was there any water in the well?

Strabo the known Geographer, another source of the experiment, says that Eratosthenes obtained 252000 and not 250000 stades Some even say that Eratosthenes used another methodthe so called dip-method: The scaphe dial, probably the oldest form of sundials.

Scaphe Greek boat a bowl-shaped cup within which the hour-lines are marked. At the time of summer solstice the shadow is shortest and falls exactly on the bottom line.

In the following time the shadow grows again until it reaches the top line at the time of winter solstice. The days are divided into temporal hours. Their length is not fixed but instead the time between sunrise and sunset is divided into 12 intervals of equal length. Klaus Kohl provides a possible method used by Eratosthenes with the scaphe to determine the circumference, avoiding the measurement of angles.

Their goal was to determine with precision and accuracy the distance a biography of eratosthenes the ancient scientist that measured the tilt of the earths axis the Earth's north pole and its equator. By dividing that great distance into ten million equal parts, the savants, in the name of the people of France and the good of all mankind, would create a new and natural standard of measure: The Earth's orbit around the Sun is very nearly circular, and it defines a plane in space called the ecliptic plane.

With respect to the perpendicular to the ecliptic plane which points to orbital norththe Earth's axis is tilted at an angle of 23.

When the Earth's north pole is tilted directly towards the Sun, the latter is highest in the sky in the northern hemispherewhich is what we called the summer solstice. When the north pole is tilted directly away from the Sun, the latter is lowest in the sky in the northern hemispherewhich is the winter solstice.

The intermediate positions are the vernal and autumnal equinoxes. How did Eratosthenes discover the method to determine the Earth diameter? Harness nominated for a Nebula award in 1985 Eratosthenes meets a shipwrecked alien, and if we ignore the many historical errors, learns from the alien how to do this! Today we do not know exactly which method he used, but he knew one or more methods to estimate the size of the Earth, all equal impressive.