The History of Geodesy

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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.

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.

Eratosthenes method of calculating the Earths' circumference

This illustration shows how Eratosthenes actually calculated the circumference of the Earth. At noon on the summer solstice, Eratosthenes measured the length of the shadow cast by a column of known height at Alexandria. With these two lengths, he could solve for the angle between them (θ). If the length of the shadow, and height of the column (h) were proportional to the distance between Alexandria and Syene (s=4,400 stades), and the radius of the Earth, then by calculating the angle on the column (θ), he was calculating the same angle formed at the center of the Earth (θ). The equation he used to determine the circumference of the Earth [(360° ÷ θ) x (s)] reflects this theory.

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.

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. Given the simple tools and technology that Eratosthenes had at his disposal over 2,000 years ago, his calculations were quite remarkable.

View of Earth with Alexandria and Syene marked

Eratosthenes' calculations were based on two assumptions. The first was that Syene lay on the Tropic of Cancer. The second assumption was that Alexandria lay due north of Syene on exactly the same line of longitude (the meridian line). At noon during the summer solstice, the rays of the sun always shine directly perpendicular to the Earth's surface, but only on the Tropic of Cancer. If Alexandria was exactly due north of Syene, then Eratosthenes could argue that the key measurements he used — the length of the column's shadow in Alexandria and the distance between Alexandria and Syene — were geographically sound.

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.

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.

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.

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.
Since the days of ancient mythology, scientists and philosophers have debated the shape of Earth. Since about 500 B.C., the idea that the Earth was a perfect sphere has dominated most scientific thinking, even though the concept of a flat Earth may have persisted in some regions for another millenium. Around the end of the 16th century, the idea that the Earth was a perfect sphere evolved into a radical new idea: that the Earth was an imperfect sphere. This new way of thinking was initially divided into two major schools of thought. One believed the Earth was egg-shaped (prolate). The other believed the Earth was flattened at the poles (oblate). The modern concept of a basically oblate Earth was demonstrated to be correct and has spawned many theoretical variations during the last hundred years as geodesy has advanced.

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Last updated:
02/26/21

Author: NOAA

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