Geodesy and the Summer Solstice
The Earth at the start of the 4 (astronomical) seasons as seen from the north and ignoring the atmosphere (no clouds, no twilight).
Today is the Summer Solstice, the longest day of the year (in the Northern Hemisphere). Because Earth’s axis of rotation is tilted about 23.4 degrees relative to its orbit around the sun, this means that the different parts of the Earth receive the amount of light based on the position of the earth in its orbit around the sun. This tilt causes the earth’s seasons - From March to September, the Northern Hemisphere tilts more toward the sun, creating spring and summer, while in the Southern Hemisphere it’s fall and winter.
At two moments each year—called solstices—the Earth's axis is tilted most closely toward the sun. The hemisphere tilted most toward the sun experiences the longest day, while the hemisphere tilted away from the sun sees its longest night. During the Northern Hemisphere’s summer solstice—which always falls around June 21—the Southern Hemisphere gets its winter solstice.[1]
Did you know that the Summer Solstice helped an ancient scientist produce the earliest accurate estimate of the circumference of the earth?
Eratosthenes
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Eratosthenes teaching in Alexandria by Bernardo Strozzi (1635)
Back in about 250 BC, a Greek polymath named Eratosthenes wanted to see if he could refine Aristotle’s earlier estimate that the distance around the Earth was about 45,500 miles.
He was the perfect person to address this question. Eratosthenes was born in the flourishing city of Cyrene in northeast Libya in 276 BC. He received a typical Greek education, encompassing physical skills, social discourse as well as reading, writing, arithmetic, poetry, and music, then moved to Athens to study Stoicism, Plato, poetry and history. His poetic and research works caught the attention of King Ptolemy III who appointed him head of the Library at Alexandria, Egypt in 245 BC where he remained for the rest of his life.
The Library at Alexandria
The Library of Alexandria, 19th-century artistic rendering by German artist O. Von Corven, based partially on the archaeological evidence available at that time
The library at Alexandria was founded by the order of King Ptolemy I in 295 BC to equip “his library with the writings of all men as far as they were worth serious attention.” A key resource in the library was the works of Aristotle, and books from around the world were soon added to the collection. The King bought copies of the works of Athenian philosophers to add to the collection, and they reportedly searched every ship that sailed into the harbor of Alexandria. If a book was found, it was taken to the library for a decision as to whether to return it or to confiscate it and replace it with a copy made on the spot (with an adequate compensation to the owner).[2]
As head of this well-funded and growing library, Eratosthenes made it his mission to further mankind’s knowledge, and he had the intellect and the resources to do it.
Geodesy
To do this, he started with this formula for a sphere where (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.
Illustration from NOAA. The History of Geodesy. National Ocean Service website.
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.
Eratosthenes' calculations were based on two assumptions. The first was that Syene lay on the Tropic of Cancer (where the sun is directly overhead and leaves no shadow). 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.
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.[3]
Later, Eratosthenes also calculated the earth’s distance from and sun and the moon, he theorized that the earth’s orbit was elliptical and proposed a leap year every four years to keep calendars accurate; created the sieve of Eratosthenes, an ancient algorithm for finding all prime numbers up to any given limit, and wrote a large number of scientific, historical and philosophical works, many of which were lost over the centuries during the course of war.[4]
Today, we know the circumference of the earth is 24,855 miles – at the equator. However, from the North Pole to the South Pole, the circumference is smaller, at 24,860 miles, showing that the earth is not completely spherical.
Technology provides precision
The precise shape of the earth remains incredibly important today, because surveying measurements are all based on specific positions on the surface of the earth. Fortunately, 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, Global Positioning System (GPS) satellites allow scientists to measure changes in the Earth's surface to the centimeter.[3]
Berntsen is proud to support the work of the surveyors and engineers who require quality and precision in their professions. From quality metal markers to Connected RFID, Berntsen delivers the precision reliability surveyors rely on.