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Eratosthenes was told that on the first day of summer at Syene, Egypt (near modern Aswan), sunlight struck the bottom of a vertical well at noon. This indicated that the Sun was directly over the well—meaning that Syene was on a direct line from the center of Earth to the Sun. At the corresponding time and date in Alexandria, Eratosthenes observed the shadow a column made and saw that the Sun was not directly overhead, but was slightly south of the zenith, so that its rays made an angle with the vertical equal to about 1/50 of a circle (7°). Because the Sun’s rays striking the two cities are parallel to one another, why would the two rays not make the same angle with Earth’s surface? Eratosthenes reasoned that the curvature of the round Earth meant that “straight up” was not the same in the two cities. And the measurement of the angle in Alexandria, he realized, allowed him to figure out the size of Earth. Alexandria, he saw, must be 1/50 of Earth’s circumference north of Syene ( [link] ). Alexandria had been measured to be 5000 stadia north of Syene. (The stadium was a Greek unit of length, derived from the length of the racetrack in a stadium.) Eratosthenes thus found that Earth’s circumference must be 50 × 5000, or 250,000 stadia.

How eratosthenes measured the size of earth.

How Eratosthenes Measured the Size of Earth. This diagram shows about 1/4 of the Earth’s circumference, with the center of the Earth at lower left. The surface of the Earth is depicted with a blue line. On the surface a column is drawn near the center of the illustration and is labeled “Column at Alexandria”. In the upper right-hand portion of the diagram the Sun is depicted as a yellow disk with parallel rays of light striking the Earth near the column. The column is shown casting a small shadow to its left. A line is drawn from the tip of the shadow to the top of the column. This line coincides with one of the parallel light rays coming from the Sun. The angle between the vertical side of the column and the ray of light casting the shadow is labeled with the Greek letter “theta”. To the right of the column a well is depicted penetrating into the Earth from the surface and is labeled “Well at Syene”. The rays of light do not cast a shadow at the well. The distance between the column and the well is indicated with “4400 stadia”. A red line is drawn downward through the center of the well down to the center of the Earth. Another red line is drawn downward along the side of the column to the center of the Earth, converging with the line from the well. The angle between these lines is labeled with the Greek letter “theta”. Inset is a figure of the whole Earth with parallel rays of light striking the surface perpendicular to the equator. The “Tropic of Cancer”, “Equator”, “Prime Meridian”, and “Tropic of Capricorn” are all labeled
Eratosthenes measured the size of Earth by observing the angle at which the Sun’s rays hit our planet’s surface. The Sun’s rays come in parallel, but because Earth’s surface curves, a ray at Syene comes straight down whereas a ray at Alexandria makes an angle of 7° with the vertical. That means, in effect, that at Alexandria, Earth’s surface has curved away from Syene by 7° of 360°, or 1/50 of a full circle. Thus, the distance between the two cities must be 1/50 the circumference of Earth. (credit: modification of work by NOAA Ocean Service Education)

It is not possible to evaluate precisely the accuracy of Eratosthenes solution because there is doubt about which of the various kinds of Greek stadia he used as his unit of distance. If it was the common Olympic stadium, his result is about 20% too large. According to another interpretation, he used a stadium equal to about 1/6 kilometer, in which case his figure was within 1% of the correct value of 40,000 kilometers. Even if his measurement was not exact, his success at measuring the size of our planet by using only shadows, sunlight, and the power of human thought was one of the greatest intellectual achievements in history.

Hipparchus and precession

Perhaps the greatest astronomer of antiquity was Hipparchus , born in Nicaea in what is present-day Turkey. He erected an observatory on the island of Rhodes around 150 BCE, when the Roman Republic was expanding its influence throughout the Mediterranean region. There he measured, as accurately as possible, the positions of objects in the sky, compiling a pioneering star catalog with about 850 entries. He designated celestial coordinates for each star, specifying its position in the sky, just as we specify the position of a point on Earth by giving its latitude and longitude.

Practice Key Terms 6

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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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