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Aristarchus defined the basic structure of the universe, doing remarkably well considering the tools he had. He may have defined more, except we don't have any of his original writings other than those about measuring the sizes and distances of the Sun and Moon. Let's take a look at some other observations he and other scholars of his time made.
From our viewpoint, the sky looks like a rotating sphere with us at the center (if you don't examine things too closely).
As viewed from the Mediterranean area
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Polaris was not "the North Star" 2,000 years ago but was about 10 degrees from the celestial pole; the celestial pole was closer to Kochab (Beta Ursae Minoris, the second-brightest star in Ursa Minor) at the time. Ancient mariners used the entire constellation of Ursa Minor, known as the "Little Bear" or the "Wagon of Heaven," to roughly orient themselves. Kochab and Pherkad (Beta and Gamma Ursae Minoris, respectively) acted as pointers to the celestial north pole, much as the "pointer stars" of the Big Dipper point to Polaris.
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Looking to the south, stars make a low arc as they traverse the sky, rising in the south-southeast and setting in the south-southwest. Some stars barely peek above the horizon close to due south.
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As you travel north, the entire celestial sphere (what appears to be a black sphere of the night sky splashed with stars) appears to rotate to the south. A scholar would likely conclude that if you walk north until the celestial sphere rotates by one degree, you have actually walked one degree around the circumference of the Earth. If only you counted your paces as you walked north that one degree. Then, you would know how many paces made up one 360th of the Earth's circumference.
That's exactly what some people did: count their paces to measure distance. These people were called bematists and specialized in measuring distances. Bematists accompanied armies, caravans, merchants, etc., to measure the distances between cities and waypoints. They were so accurate that modern scholars think they must have used primitive odometers such as those described by Hero of Alexandria, despite no mention of such.
Eratosthenes was a Greek scholar and Chief Librarian at the Library of Alexandria around 200 BC. One of his fields was what we today call geography. As the librarian, he had access to much of the world's extant knowledge. This included the distances between major cities and waypoints, etc. This allowed Eratosthenes to make one of the first maps of the known world that somewhat accurately portrayed the relative locations of cities, seashores, rivers, and mountains. Eratosthenes was the first geographer to use lines on his maps representing parallels and meridians, what we today usually call latitude (parallel) and longitude (meridian) lines.
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Eratosthenes used his resources to measure the circumference of the Earth. He may not have been the first to do this, as it was not a particularly difficult thing for a scholar to do. However, like Aristarchus, he got his name in print for doing it, so he gets the credit.
He needed to measure the altitude (the angle above the horizon) of a fixed celestial object, travel a known distance directly toward or away from that object, and then measure the altitude again. The problem is that everything in the sky is moving, so the target would move between measurements. But what about the celestial north pole? It doesn't move as the sky rotates. The most logical thing to do would be to measure the altitude of the celestial north pole at a suitable starting point, then walk directly toward the pole until the altitude increased by one degree. By counting his paces, he would know the exact distance represented by one degree around the Earth's circumference. Multiply that by 360, and you have the circumference of the Earth—Bob's your uncle.
Unfortunately, sighting the celestial north pole to a fraction of a degree isn't straightforward today and was even more challenging in Eratosthenes' time. Polaris is nearly a degree from the celestial north pole, so you can't sight directly on it. In Eratosthenes' time, Polaris was about 10 degrees from the celestial north pole (and thus was not named Polaris at the time); the celestial north pole was just a dark spot in the sky with nothing visual to sight on. Instruments existed that could measure the altitude of stars, and techniques existed to determine one's latitude using those measurements. Navigators had tables telling them their latitude (which equals the altitude of the celestial north pole from that location) by measuring the altitude of certain stars at their culmination (their highest point above the southern horizon). So, there was really nothing holding ancient scholars back from measuring the Earth's circumference. Someone just needed to do the legwork to get sufficiently precise measurements. Eratosthenes could have carted suitable instruments around the desert to measure the celestial north pole's altitude. However, maybe he could cheat and keep his walking sandals in the closet.
Alexandria is on the south shore of the Mediterranean Sea, on the western Nile Delta. Eratosthenes needed to measure the altitude of the celestial north pole in Alexandria, then go due south a known distance (going north into the Mediterranean Sea would get his feet wet) and measure it again. The difference between the two measurements would yield the distance traveled as a fraction of the Earth's circumference. All he needed was a location at a known distance due south, at which he already knew the altitude of the celestial north pole. Then, he wouldn't need to leave the comfort of his library.
Eratosthenes was in luck. He already knew that the city of Syene was due south of Alexandria (see his map above). That distance had already been measured by bematists and recorded as 5,000 stadia (about 788 kilometers). All he needed was a trusted measurement of the altitude of the celestial pole from Syene, which he apparently lacked.
Fortunately, Eratosthenes still didn't have to saddle up his camel. Syene was famous for the fact that at high noon, on the day of the summer solstice (the day the Sun reached its northernmost point in the sky), the Sun was so directly overhead that vertical pillars and walls cast no shadows. The sun could also be seen reflecting directly from the water in deep wells (actually, the reflection of one's head blocked the reflection of the Sun, since the geometry put them in a straight line). This meant that in Syene, at high noon on the day of the summer solstice, the Sun's altitude was 90 degrees. Eratosthenes just had to wait for high noon on the day of the summer solstice and measure the Altitude of the Sun in Alexandria. This would give the same result as measuring the altitude of the celestial north pole from the same locations.
The altitude of the Sun measured at Alexandria at the appointed time was 82.8 degrees. This yielded a difference between Alexandria and Syene of 7.2 degrees or 1/50 of a circle. He multiplied 5,000 stadia by 50 to get the circumference of the Earth as 250,000 stadia. Assuming a stadion of 157.7 meters, Eratosthenes' calculated circumference of the Earth is 39,425 kilometers. The actual mean circumference of the Earth is 40,075 kilometers.
It is logical to assume that Eratosthenes compensated for the distance to the Sun (thought at the time to be closer than it actually is). However, he made no mention of such a correction. The Sun is so distant that assuming its rays are parallel introduces an error of only about 0.01%. Had Eratosthenes compensated for its thought-to-be closer distance, it would have resulted in a greater error. Eratosthenes' solar altitude for Syene was measured crudely but was only about one degree off, Syene being about that far north of the Tropic of Cancer (the latitude where the Sun is directly overhead on the day of the summer solstice). However, Syene was also about three degrees east of Alexandria's meridian (the imaginary north-south line passing through Alexandria). That error approximately canceled his solar altitude error. His final calculation of the circumference of the Earth was only about two percent off.
According to legend, Eratosthenes measured the Sun's altitude using a stick in the sand on the beach near Alexandria. However, the precision of his measurement (stated to the tenth of a degree) implies that he used a more sophisticated instrument, such as a gnomon. A gnomon is a structure that casts a shadow on a surface marked to measure the Sun's altitude or the Sun's angle to determine the time of day (as with the gnomon of a sundial). Eratosthenes' gnomon would have been a rod or pillar permanently set in the ground with a horizontal scale at its base precisely marked to measure the Sun's altitude above the southern horizon.
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As mentioned above, during the summer, the Sun's path is higher above the southern horizon than in the winter. This means one of several things. It could be that either the sun wobbles north and south over the course of the year or the earth does the wobbling. Neither scenario makes sense. However, knowing that the Earth revolves around the Sun, there is a simpler explanation. A spinning object, like the Earth, would be stable in its orientation. Like the gyroscope-based instruments on an airplane that always spin on the same axis regardless of which way the airplane is pointed, the spinning earth should always be oriented in the same direction. This is reinforced by the fact that the celestial north pole, where the earth's axis is pointed, never moves. Although a spinning gyroscope does wobble slowly (precession), a large, slowly spinning object like the Earth takes many years to precess around one circuit (the Earth takes about 26,000 years).
As the Earth orbits the Sun, the path of the Earth makes a circle that describes a plane which is called the orbital plane. If the Earth's axis were perpendicular to its orbital plane, the sun would always be directly above the Earth's equator and would always rise directly in the east and set directly in the west. However, in the summer, the sun rises in the northeast and sets in the northwest, making a high arc as it goes nearly overhead (directly overhead in Syene). In the winter, the Sun rises in the southeast and sets in the southwest, making a low arc far to the south of its summer track. Mid-era astronomers who understood Aristarchus' heliocentric model knew that this was consistent with the Earth's axis being angled to the Earth's orbital plane.
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Eratosthenes is credited with being the first to measure the tilt of the Earth's axis. This is quite simple to determine, but Eratosthenes is credited with being the first to do it. He had measured the Sun's altitude on the summer solstice in Alexandria as 82.8 degrees. All he lacked was the altitude of the Sun in Alexandria on the winter solstice. After a six-month wait, he measured this at 35.8 degrees. By subtracting the Sun's altitude at the winter solstice from the altitude at the summer solstice, he got 47 degrees, twice the Earth's axial tilt. Divide that by two to get the axial tilt of 23.5 degrees. The actual tilt of the earth's axis is 23.44 degrees.
Another achievement of Eratosthenes was recalculating the distance to the Sun. His method is not recorded but was likely a refinement of Aristarchus' method. According to Eusebius of Caesarea, his result was 10,000 times 400 and 80,000 stadia ("of stadia myriads 400 and 80,000"). If interpreted as 804,000,000 stadia (4,000,000 stadia plus 800,000,000 stadia), it comes to 149,000,000 kilometers or 93,000,000 miles. This assumes that the now-unknown length of a stadion was about 185 meters, as some modern scholars attest. However, using terrestrial distances given by Eratosthenes, it appears that his stadion was about 157.7 meters. This would make his distance to the Sun about 127,000,000 kilometers.
Eratosthenes also calculated the size of the Sun as 27 times the size of the Earth. This is surprising because, had he used 127,000,000 kilometers as the distance to the Sun and Aristarchus's relative distance and size of the Moon, he should have calculated the Sun to be 112 times the size of the Earth, which is closer to the actual value of 109 times.
Altitude (as the angle above the horizon)
Axis
Beta (as the designation of the second-brightest star in a constellation)
Celestial equator
Celestial pole
Celestial sphere
Circumpolar
Culmination
Gamma (as the designation of the third-brightest star in a constellation)
Meridian
Orbital plane
Parallel
Precession
Summer solstice
Winter solstice
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