From eclipses make excellent lines.

Original author: Tyler Nordgren
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How to measure the Earth with shadows


As a child, getting to the coast of Oregon, I often thought: “How wide is the ocean and what is there, beyond the horizon?” Growing up, I turned my eyes to the night sky, and thought about something similar: “How far are the stars, and do they have other planets? ”And although few of us have been traveling around the world, and no one has yet gone into space beyond the moon, we know the answers to some of these questions. Immensity can be measured. And although these huge numbers in everyday life have little meaning, we at least know that we know them.

Imagine what it would be like to live in a world in which it is not: where the feeling of immensity, the certainty of the presence of the inexplicable, would be generally accepted, and the idea of ​​the knowability of the world would be new. Philosopher Anaxagorasborn about 500 BC in the eastern Mediterranean, where the Turkish coast is now located. By that time, philosophy had recently turned to the study of the natural world. Less than a hundred years earlier, Thales of Miletus allegedly predicted a solar eclipse, which ended the war, and proved that our world was predictable, and all events are not just a whim of the gods.

As far as we know, in this world of physical phenomena, Anaxagoras was the first to realize that eclipses occur because one celestial body interferes with the light of another. Such a rejection of the use of gods and dragons as causes of eclipses was in itself revolutionary, but Anaxagoras went even further: if solar eclipses occur only because the Earth fell into the shadow of the Moon, he reasoned, then the size of the shadow should tell us information about the size of the Moon . In addition, since the moon covered the sun, the sun must be farther away. Then, so that their apparent size is almost the same, the sun must be larger. It contains the power of scientific thought: measure the size of the shadow running across the Earth, and you will learn that the Moon must be at least as big as this shadow, and the Sun even more. Mysticism did not give such opportunities:

February 17, 478 BC the shadow of a ring-shaped eclipse spread over the Mediterranean Sea and crossed the Greek islands and the Peloponnese peninsula, creating a “ring of fire” in the sky that was visible for almost six minutes. Anaxagoras, living in Athens, would be in the midline of the eclipse, but in six minutes he could not measure the size of the shadow on his own. But in a fit of genius, he found the answer to this question: he just went down to the shore and asked the arriving sailors what they had seen. At that time, Athens was the center of commerce for all ships from all over the eastern Mediterranean. If the sailors saw a ring of fire in the sky, they would remember where they were at that moment. The location of all those who saw and did not see this sight, suggested the size of the shadow falling on the sea. So, just reaching the local port, Anaxagoras measured the moon.

We have no evidence of Anaxagoras himself about what he came to, but we have records of his followers. Five hundred years later, the Roman historian Plutarch wrote: "Anaxagoras says that the moon is no less than the size of the Peloponnese." Hippolytus of Rome , a Christian priest of the 3rd century, wrote in his " Exposure to All Heresies, " which, according to Anaxagora, "The Sun exceeds Peloponnesus in size." The story of Anaxagoras, which stands on the beach and measures the size of the moon, is the story of all astronomy. Our species is tied to our world (at best, to our solar system). But from this position we need to look at the entire Universe, on whose shores we stand. To do this, we need to study eclipses, passages (when something small passes in front of something large) and cover(when something big passes in front of something small). Astronomy in particular made possible the shadows encompassing the stars.

Standing on the sky, let's take a walk through our Universe, starting with the world we see during the day and to the stars visible at night. At every step we will find out where we are and how far we have gone. What is the easiest way to measure distances? We can walk. We measure distance in feet [in USA only - approx. perev.], and it is not surprising that the foot is approximately equal to the size of the foot [foot - foot, foot. Measure length about 30.5 cm - approx. trans.]. What distance can a person measure in steps? In the Mediterranean of the III century BC. the Bematiststhere were people who could walk in constant and precise steps, for which they received money. One could hire such a person to accurately measure large distances. The Bematists used along the Nile River, which during the spills erased all signs marking the boundaries of the fields. The Bematists were particularly well suited for traveling the large, flat, devoid of characteristic features of the landscapes along the Nile, south of Alexandria to Aswan, the distance between which they estimated at 5000 stages (approximately 835 km, depending on the exact definition of the stage). We know this distance because around 240 BC. Eratosthenes of Kirensk , the chief librarian of Alexandria, used him to find the size of the world .

Eratosthenes learned that on the day of the summer solstice, the noonday sun shines directly into the well in Aswan and casts no shadow. He knew that in Alexandria this does not happen on any day, so one of two things must be true: either the Earth is flat, and the Sun is very close to it (just like a cloud hanging above one city, it seems to be south of another), or the Sun is very far away, and the Earth is round. The answer to this question could be obtained by examining the moon during a lunar eclipse. Aristotle, 100 years earlier, noted that during each lunar eclipse, the shadow of the Earth looks like a circle. No matter in which part of the sky the eclipse occurred, the shadow of the moon never changed. The only figure looking the same from all sides was the sphere.

Since the Earth's shadow has already confirmed that the Earth is round, the only explanation for the differences in the length of the shadows from the Sun in Aswan and Alexandria was the curvature of the Earth. From the difference between the shadows and the distance between them, the circumference of the earth was calculated.

Here's how it works: Imagine that some day in Hawaii you will notice that your shadow is right under your feet, and flagpoles do not cast shadows at all. You look up and see that the sun is at its zenith, at the highest point of the sky. Hawaiians call it Lahai Afternoon, after the city on the island of Maui, where this phenomenon occurs twice a year. You immediately call a friend from Puerto Rico, who is not impressed with this message. At that moment, he looks at the beautiful sunset, during which the sun touches the Caribbean waters on the horizon. At this moment, you see the Sun at a distance of 90 degrees from each other - that is, exactly a quarter of a circle. So you must be a quarter of the circumference of the earth apart. Measure the distance between you, multiply by four and you get the circumference of the Earth.

This is exactly what Eratosthenes did. At that moment, when the sun was directly above his head, and the shadows disappeared in Aswan, he measured the length of the shadows in Alexandria and concluded that the sun had changed its position by 7.2 degrees. This difference meant that the two cities were 1/50 (7.2 / 360) of the earth’s circumference from each other. And since the distance between them, walked on foot, was 5,000 stages, then, judged Eratosthenes, the whole Earth must be 250,000 stages in a circle. Depending on the exact length of the stage, the size of the circumference of the Earth could differ by only 2% from today's known value. But more important than this accuracy was the very idea that it was possible.

Tyler Nordgren is an astronomer and adjunct professor of physics at the University of Redland.

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