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Chapter 1 What the Shadow Tell Us Chapter 1 What the Shadow Tell us The first timepiece was simply following the progress of the shadow cast by a stationary object as the sun traversed the sky from east to west. This ad-hoc device was replaced by purposely placing a vertical pole in an open field and marking the tip of the shadow at key intervals of the day. In the northern hemisphere, the shadow, anchored to the base of the pole, makes it semi-circle round in a clock-wise direction, like the hour hand of our clocks. Perhaps there is a connection, but this "hand" varies in length being long in the mornings and getting progressively shorter until noon then once more elongating in the evening. If you plotted the tip of the shadow it would determine a straight line somewhat north of the pole. The distance north depends on the season and the latitude. The shadow at its shortest, noon, points true north. The advantages of this clock were that it quite accurate and it never needed rewinding, however it worked only on sunny days, required a relatively large field, very local and it was not portable. Some of these disadvantages were overcome with better designed and more compact sun clocks. The Egyptians invented the first portable timepiece around 1500 B.C. It was a simple device, a long narrow base with five variably spaced marks etched along the length of the base and an elevated bar attached to one end. The base was oriented in a east-west direction. In the morning, the elevated bar would be on the east end of the base, at noon it would be flipped around so that the elevated bar was on the west end. The Egyptians divided the day into 10 hours plus a twilight hour in the morning and the evening. As portable as this device was, it was still very local--noon at one location is noon only on locations along the same meridian. Then came a most significant device, invented in antiquity, highly developed by the Islamic world in the Middle Ages and not replaced by more accurate instruments until the middle of the 17th century, the astrolabe. This key instrument will be treated more thoroughly later in this chapter. The original timepiece is still seen in the form of obelisks. An important variation of the device was the scaphe, a sundial shaped like a hemispherical bowl with a vertical gnomon placed inside. The top of the gnomon was level with the edge of the bowl. He studied the shadow cast by the gnomon through the seasons and came to the conclusion that the earth orbited the sun. The varying lengths of the shadow told him more than just the time of day, he could decipher the season--it was a complete calendar. This characteristic was used very effectively in the design of the Kentucky Vietnam Veterans Memorial. Every veteran has his day of remembrance. Aristarchus of Samos (310 -- 230 BC) was a Greek mathematician who succeeded Euclid. His treatise, "On the Sizes and Distances of the Sun and Moon," is his only work that has survived the ages, all the others we know only what others, mainly Archimedes, say about them. Aristarchus correctly assumed that the moon shone with the reflected light from the sun. With the quarter moon, he formed a right Figure 3: Aristarchus' drawing for calculating distances to triangle and from earth to the sun and the moon. From this figure he estimated the angle estimated that the sun was at least 20 times the distance of the extended from the earth to the moon. sun between the earth and the moon. In the treatise his estimate for the angle was the equivalent of 3º. Of course he was off. Archimedes later used a ½º figure which he attributed to Aristarchus. Perhaps Aristarchus refined his measurement later. It was still off, the actual measurement is about .1 degree. Be that as it may, even with the larger angle he calculated that the sun was at least 20 times further than the moon and that the volume of the sun was 300 times larger than the earth. The sun is much further and larger than he calculated but this was still bigger than was generally believed. This calculation probably triggered the search an alternative to the geocentric model of the universe. It just didn't make sense that a satellite should be so much bigger than the primary. Aristarchus' hypotheses that the stars and the sun were fixed and the earth moved around the sun in a circular orbit never gain traction among his contemporaries. Cleanthes even accused Aristarchus of "an act of impiety." The very concept that the gods did not live at the center of creation was sacrilegious. That are no records that Aristarchus was ever persecuted for impiety but there were other more persuasive arguments against the notion of a solar system. Firstly was the concept of gravity of the time. Everything fell to the center and everything in their experience fell to earth therefore the earth must be the center of the universe. Secondly there was no parallax in viewing the stars. If the earth moved in an orbit, there should be shift in the apparent position of stars when observed from the extreme parts of the orbit. No parallax was detected. Thirdly, and probably the primary reason for rejecting the hypotheses, the geocentric model with epicycles worked better at predicting celestial events than a solar system with circular orbits. His contemporaries scoffed at Aristarchus' response that that there was no parallax because the stars were very far away. Eratosthenes of Cyrene He looked into a well and saw a way to measure the size of the earth. Eratosthenes of Cyrene (275-195 BC), like most of the ancient astronomers, knew the earth was a sphere so when he saw the sun reflect directly back from the bottom of a well at noon on the first day of summer in Syene (Aswan, Egypt) he knew he could measure circumference of the earth by comparing it to the angle to the sun at summer solstice from Alexandria, a known distance almost directly north of Syene assuming that the sun was far enough that the light beams could be considered parallel. Of course this was not a bad assumption since he had already calculated the distances from the earth to the sun and the moon to be 804,000,000 and 780,000 stadia (length of a stadium) respectively. Eratosthenes estimated the distance between the cities to 5000 stadia. The angle of shadow at Alexandria on the summer solstice was about 1/50 the circumference of a circle. With that he calculated that the earth had a circumference of 250000 stadia. The obvious question is how long is a stadia? And, of course, there have been a lot of studies debating the size of stadia in modern measurements. The standard Roman stadium was larger than the Egyptian and they were not sure which standard he used. The estimates range from 150 to 170 meters with 157.2 meters being the most favored. If the favored number is taken, the measurement is remarkably accurate, but even the worst case would give you a far better estimate of the size of the earth than the one Columbus used. Astronomy students at Sonoma State University scheduled to repeat this experiment on Wednesday March 22, 1999, but they have not posted their results. Perhaps the world is flat after all. Eratosthenes made a huge contribution to the body of knowledge even though none of his work, including his treatise, On the measurement of the Earth have survived the ages. What we know about his work we have learned from others like Plato, Theon of Smyrna, Hippocrates and a lot of others. Eratosthenes was quite influential. Though Eratosthenes lived a long time, his death was not natural. He committed suicide by starvation not wanting to continue living blind. The Merkhet The merkhet, invented by the Egyptians, is the earliest known astronomical observing tool. The device consisted of a short, mud-brick circular wall to create a false horizon, a sighting rod and a plumb bob. The observer, in the center, using the sighting rod directed the holder of the plumb bob on the mud-brick wall and marked the position of the sun as it rose at dawn. The extreme points in the sun's migration marked the solstices. This instrument allowed the Egyptians to discover that it took a little over 365 days for the sun to complete its journey. This discovery led to the development of a simplified calendar of twelve 30 day months divided into three seasons, plus an extra 5 days for a total of 365 days. The calendar did not account for the extra quarter day each year. The merkhet was not only useful during the day; it could be used to tell time at night and also determine the true north-south line. To tell time at night, the observer would align a selected star with the plumb-bob. Marks along the wall showed the progress of the star in its nightly trek from east to west. Bisection of the angle between star rise and star set determines the true north-south line. Of course, the device required an open field and the time was local. The Antikythera Mechanism In October 1900 sponge divers discovered an ancient shipwreck off Point Glyphadia on the Greek island of Anyikythera. The ship was loaded with jewelry, statues and other artistic artifacts from early 1st century BC.
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