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The History of Geodesy

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Eratosthenes method of calculating the Earths' circumference.

An illustration of how Eratosthenes actually calculated the circumference of the Earth. Click on the image for larger view.

Throughout history, the shape of the Earth has been debated by scientists and philosophers. By 500 B.C. most scholars thought the Earth was completely spherical. The Greek philosopher Aristotle (384-322 B.C.) is credited as the first person to try and calculate the size of the Earth by determining its circumference (the length around the equator) He estimated this distance to be 400,000 stades (a stadia is a Greek measurement equaling about 600 feet). With one mile equal to 5,280 feet, Aristotle calculated the distance around the Earth to be about 45,500 miles (Smith, 1988).

Around 250 B.C., another Greek philosopher, Eratosthenes, measured the circumference of the Earth using the following equation:

(360° ÷ θ) x (s)

In this calculation, (s) is the distance between two points that lie north and south of each other on the surface of the Earth. If you were to draw a line from each of these points to the center of the Earth, the angle formed between them would be θ.

Obviously, Eratosthenes could not go to the center of the Earth, so he got the angle measurement using the rays of the sun. At noon on the longest day of the year, the summer solstice, the sun shone directly into a deep well at Syene (which is now Aswan, Egypt), casting no shadow.

View of Earth with Alexandria and Syene marked.

Eratosthenes calculations were based on the assumption that Syene lay on the Tropic of Cancer and that Alexandria lay directly north of Syene on exactly the same line of longitude. Click on the image for larger view.

At the same time in Alexandria, Egypt, he found that the sun cast a shadow equivalent to about 1/50th of a circle or 7.12°. Eratosthenes combined this measurement with the distance between Syene and Alexandria, about 4,400 stades.

If we plug these numbers into the above equation, we get: (360°÷ 7.12°) which equals 50; and 50 x 4,400 equals 220,000 stades, or about 25,000 miles. The accepted measurement of the Earth's circumference today is about 24,855 miles (Smith, 1988). Given the simple tools and technology that Eratosthenes had at his disposal over 2,000 years ago, his calculations were quite remarkable.

As technology developed, scientists and surveyors began to use different techniques to measure distance. In the 16th and 17th centuries, triangulation started to be used widely. Triangulation is a method of determining the position of a fixed point by measuring the angles to it from two other fixed points that are a known distance apart. Triangulation formed the basis for many national surveys. By the end of the 19th century, major triangulation networks covered the United States, India, Great Britain, and large parts of Europe.

Evolving concept of the Earth

The concept of the shape of the Earth has changed dramatically over time as science and technology have continued to advance. Click on the image for larger view.

At the end of the 16th century, the Royal Society in London and the L'Academie Royale des Sciences in Paris were founded. Soon they became locked in a battle to determine the shape of the Earth. The French argued that the Earth was prolate, or shaped like an egg. The English, using Sir Isaac Newton's universal theory of gravity and the knowledge that the Earth spun around its axis, thought that the Earth was oblate, or flattened at the poles. To prove their idea, the Academy in Paris staged two expeditions, one to Peru (now Ecuador) at the equator, and the other to the border of Sweden and Finland in the northern hemisphere. Their objective was to measure the north-south curvature of the Earth at each location's latitude and determine whose concept of the Earth's shape was correct. The Academy's efforts proved that Newton was right. The Earth is flattened into the shape of an oblate sphere (Smith, 1988).

During the last 100 years, geodesy and its applications have advanced tremendously. The 20th century brought space-based technology, making geodetic measurements extremely precise. Today, NAVSTAR Global Positioning System satellites allow scientists to measure changes in the Earth's surface to the centimeter.

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