Tap image to zoom. What is the size and shape of Earth? 804 km x 50 = 40,200 km. The yellow lines were straight line distances from Capernaum to mountains on the east or west side of the lake shores opposite Capernaum where it was presumed Jesus set out with his disciples to go to a remote place apart from the village of Capernaum to teach and then feed his audience. moving on perfect spheres or in ! In Greek times a stadion varied from 200 to 210 modern yards (182 to 192 meters), so his computed circumference was somewhere between 28,400 and 29,800 modern statute miles (45,700 and 47,960 kilometers), 14 to 19 percent greater than the current value of 24,874 statute miles (40,030 kilometers). Well, we believe that the unit of the "stadium" was about 0.15 km. Then, convert stadia to kilometers. The distance between the two cities was about 5,000 stadia (500 mi), and Eratosthenes concluded that if one-fiftieth of the circumference was 5,000 stadia, then the full circle was 250,000 stadia (25,000 mi) or 40,000 km. Whose was the most sophisticated geocentric model? And for any of you ancient Greeks out there, 5,000 stadia x 50 = 250,000 stadia. _____ Convert Eratosthenes’ calculation (in stadia) for the circumference of the Earth to kilometers: (Remember to convert from meters to kilometers in your calculation) _____ 7/360 × (circum. So radius is: 40000km = 6366km 2π Very close to today’s value of 6378 km! His result, 250,000 stadia (or about 46,250 km), is surprisingly close to modern measurements of the circumference of the Earth (about 40,024 km). Product Image Feedback. So either way that estimate is pretty good considering the level of technology at the time. Multiply X 50, you get the circumference of the Earth: 800 km X 50 = 40,000 km. I think this new Redfern oval stand seats around 5000. The distance between Alexandria and Syene was measured in stadia. He then deduced that the distance from Syene to Alexandria, or 5,000 stadia, must be equal to one fiftieth of the circumference of the earth. 5000 stadia ~ 800km. The stadion or stade (plural = stadia) was a common distance unit of the time. Always check the results; rounding errors may occur. The distance between Alexandria and Syene was measured in stadia. 7/360 × (circum. In most of the world, it is the most common unit for measuring distance between places. 1 metre is equal to 0.0054054054054054 stadium, or 0.001 kilometers. 1 std = 0.185 km. It was known that the distance between Alexandria and Aswan was 5,000 stadia or 800 kilometers (approximately 500 miles). But, there is just one problem: we don’t know whether he used the common, Olympic stadium or another one, which equals to 1/6th of a km. 8046.72 Kilometers (km) Visit 5000 Kilometers to Miles Conversion. Eratosthenes knew the distance between Syene and Alexandria: 5000 stadia (a stage of 160 m). However, not everybody used a stadion of the same length. distance ! ... Now, it’s quite tricky to interpret Eratosthenes’s answer of 250000 stadia and convert it into kilometers for a comparison. Note this proportion: 7°/360° ~ 5000 stadia/circumference of Earth in stadia 7 360 = 5000 x X = 5000 ∗ 360 7 =257,142.85 From geometry, we know that SP = r and SE = 1. It was known that the distance between Alexandria and Aswan was 5,000 stadia or 800 kilometers (approximately 500 miles). There were several different stadia in use, and the experts do not know which one Eratosthenes used. Earth) = 5000 stadia stadia Measurements: Syene to Alexandria distance ≈ 5000 stadia angle = 7° km He concluded that the meridian arc distance from Alexandria to Syene (5000 stadia, about 800 km) must therefore be 1/50 of the total circumference of the Earth (40,000 km). Miles : A mile is a most popular measurement unit of length, equal to most commonly 5,280 feet (1,760 yards, or about 1,609 meters). CODELOCKS. Eratosthenes of Cyrene (276-194 BC) Finding Earth’s Circumference January 21, 2013 Math 250 Eratosthenes’ Method Results of Eratosthenes Knowing also that the arc of an angle this size was 1/50 of a circle, and that the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. 5,000 stadia are approximately 8-900 kilometres. terrestrial arc traveled by the camels (5000 stadia, subtended by an equal angle a at the center of the earth) must be the fiftieth part of the earth's circumference. Thus the circumference can be estimated by multiplying the distance between the two cities, 5000 stadia, by 50, equaling 250,000 stadia. geocentric model" • Heavens must be “perfect”: Objects! Yes, you are all right, stadia with a capacity below 5k are all much too small … Knowing that the distance between cities is 5000 stadia. Today Ancient Astronomy Competing Cosmologies Geocentric vs. Heliocentric Ptolemy vs. copernicus Retrograde Motion Phases of Venus Galileo FIRST HOMEWORK DUE 5 miles to km = 8.04672 km His records show that the distance was found to be 5,000 stadia. Eratosthenes. There are 2.54 centimeters in an inch. Then, it was just a matter of multiplying that by 50 to get an estimate of 250000 stadia for the Earth’s circumference. Earth's circumference is therefore 50 5000, or 250,000 stadia. The modern value of Earth's circumference is 40,100 km. Hint: Convert 1/6t km to a decimal.] •This yields for the radius of the Earth R = 39,789 stadia •Converting to kilometers gives the result R = 6,366 km since there are 0.16 km/stadium o o 360 7.2 2 5000 stadia = πR Earth’s Radius •The calculation yields for the Earth’s radius 39,789 stadia, or 6,366 km •Modern satellite observations give 6,378 km, which is extremely The distance between Alexandria and Syene was thought to be 5000 stadia, which equates with either 880 km (Olympic stade), or 925 km (Italian/Ptolemaic stade). By multiplying 5,000 by 50, Eratosthenes estimated Earth's circumference at 250,000 stadia. The distance of the city of Alexandria from Syene, Egypt, was 5000 stadia. CL5000 Item # 49XR42; Mfr. Examples include mm, stadium to barleycorn metres squared, grams, moles, feet per second, and many more! There is little doubt that Eratosthenes got this figure directly from his earlier map of the known world [].]. Use the formula a … All Eratosthenes had to do was multiply 800 times 50, which equals 40,000 kilometers, just 75 kilometers less than the actual circumference of … Since this angle was 1/50 of a circle, and the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. A stadium was a length unit in antiquity. This gives the radius = 7,361 km, close to the modern value = 6371 km. Keymat: Mfr No. 42,000 km Greek Astronomy Underpinnings of the Greek geocentric model: • Earth at the center of the universe • Heavens must be “perfect”: Objects moving on perfect spheres
At Alexandria, about 5,000 stadia north … He calculated the circumference of Earth as 50 times the distance between Syene and Alexandria Earth) = 5000 stadia Measurements: Syene to Alexandria distance ≈ 5000 stadia angle = 7° Plato Aristotle How did the Greeks explain planetary motion? actual circumference of the earth. A stadia is an ancient Greek unit of length, based on the length of a typical sports stadium. For other uses, see Stadion (disambiguation). A foot is a unit of length equal to exactly 12 inches or 0.3048 meters. distance between Alexandria and Syene cities. 5,000 stadia 1 50 of circum-ference 7.2° = Syene a Sun m R polar = 6356.8 km R equatorial = 6378.1 km radius R is 2πR. Type in your own numbers in the form to convert the units! (5,000 stadia = 800 km). JESUS FEEDING THE 5,000 NEAR THE SHORE OF LAKE TIBERIUS. It is an oblate spheroid. Thus 1 ° of circumference gave 5000/7 = 714 stades and 360 ° of circumference gave 5000/7 x 360 = 250 000 stades, that is to say 40 000 km. Compare your (Eratosthenes') answer At Syene, the midday Sun casts no shadow to this. The distance between Syene and Alexandria was estimated by travellers as 5000 stadia (788 to 925 kms - See accuaracy below), the stadium or stade being the typical unit of measurement used by the Greeks at the time. If Eratosthenes used one length for the stadion, his answer was really, really good. (The stadia is an ancient unit of length equal to about 1/10 of a mile.) The Earth is about 40 thousand kilometers (about 24,860 miles) around. From geometry then, 7.2o 360o Earth's circumference 5000 stadia = => circumference is 250,000 stadia, or 40,000 km. The well would reflect the sunlight at about 90 degree on the first day of summer. For the cloud video-gaming service, see Google Stadia. 1 miles to km = 1.60934 km. Eratosthenes' estimate …
At Alexandria, about 5,000 stadia north of Syene … The actual distance between Alexandria and modern Aswan is about 843 km. The modern value of Earth’s circumference is 40,100 km. And for any of you ancient Greeks out there, 5,000 stadia x 50 = 250,000 stadia. A centimeter, or centimetre, is a unit of length equal to one hundredth of a meter. 1 metre is equal to 0.00062137119223733 miles, or 0.001 km. Thus, with 2πR The early Greek and Hindu philosophers believed the Earth to be spherical but we now know that polar radius (6356.8 m) is 21 km smaller than the equatorial radius (6378.1 m). 3. The stadion was a distance unit that was often used in ancient times. Ancient Cosmology: A Flat Earth Miletus Alexandria Measurements (known values): Syene to Alexandria is a distance 5,000 stadia. Roll over image to zoom. He established a final value of 700 stadia per degree, which implies a circumference of 252,000 stadia. Based on the circumference formula (listed above) that Eratosthenes used, what is the circumference of the Earth, in stadia? [Kilometers] symbol/abbrevation: (km) How to convert Greek Stadion to Kilometers (std to km)? He also knew from Egyptian surveyors that Syene was roughly $5000$ stadia (around $850 \,\mathrm{km}$) away from Alexandria. 500,000 cm to km conversion. A kilometer, or kilometre, is a unit of length equal to 1,000 meters, or about 0.621 miles. Compare your (Eratosthenes’) answer to this. Earth's circumference is therefore 50 5000, or 250,000 stadia. Incredibly close for this method of measuring! Source: Wikipedia. How he initially obtained this value is a controversial question which may never be answered, but it is doubtful that Eratosthenes actually measured the distance himself []. 40,100 km): Greek stadium ! The modern measurement is 40,070 kilometers. If Eratosthenes used one length for the stadion, his answer was really, really good. [30 pts total] Show your work in the box. How do we convert to kilometers? be 5,000 stadia north of Syene. NASA. Thus, the latter must be 250,000 stadia. Eratosthenes realised that if 7 degrees equals 5000 stadia, then 360 degrees would equal 250,000 stadia. You can view more details on each measurement unit: stadium or kilometers. the distance from Alexandria and Syrene was 5000 stadia or 925 km (today scientists believe 1 Hellenic stadion = 185 m) From Part II, if you use a central angle of 7º12' and d of 925 km, calculate Eratosthenes' value for the Earth's circumference. © 2005 Pearson Education Inc., publishing as Addison-Wesley Yeah, the Ancient Greeks, a bunch of dead white guys, but 2500 years ago they came up with: • Earth at the center of the universe:! Phytagorean theorem. 5000 statida /circumference = 7 degrees 12 minutes/360 degrees. He did so by taking the angle between Alexandria and Syene in Egypt to be 7.0 degrees and the distance between to two to be 5000 stadia. (or 5,000 stadia for Eratosthenes) was 1/50th, multiplication gives you the earth’s circumference: 500 mi. Also, a Greek stadium is 1/6th km. (or 5,000 stadia for Eratosthenes) was 1/50th, multiplication gives you the earth’s circumference: 500 mi. If we take the stadium unit to be 0.16 km, we find that Eratosthenes estimated Earth's circumference to be about 40,000 km. Use this page to learn how to convert between miles and kilometres. That's pretty damn good for something done over 2,000 years ago! We assume you are converting between stadium and kilometre. Convert 5,000 stadia to kilometers. The angle 7°. Earth) = 5000 stadia. Today we know that the circumference of the Earth at the equator is 4.008 x 10 1 Mm. ›› Quick conversion chart of miles to km. area, mass, pressure, and other types. The distance between the cities was known from caravan travelings to be about 5,000 stadia (see notes 2). His result, 250,000 stadia (28,740 miles / 45,984 kilometers), is quite close to modern measurements of 24,860 miles (40,008 kilometers) over the poles. •This yields for the radius of the Earth R = 39,789 stadia •Converting to kilometers gives the result R = 6,366 km since there are 0.16 km/stadium •This is extremely close to the correct value R = 6,378 o o 360 7.2 2 5000 stadia = πR The yellow dot represents Capernaum. Unfortunately, no accurate data has been preserved for converting the units of measurement used by Erastofen into kilometres and, depending on the conversion factor used, the estimate of the accuracy of its measurements may vary. He figured that 7.2° is 1/50th of 360° and argued that Alexandria, therefore, must be 1/50th of the way around the spherical Earth from Syene (Figure 2). What is the size and shape of Earth? The distance between Alexandria and Syene was thought to be 5000 stadia, which equates with either 880 km (Olympic stade), or 925 km (Italian/Ptolemaic stade). At midday when the Sun was at its highest he measured the angle of the shadow that the sun formed on the ground, which he measured it to be 7.2°. So either way that estimate is pretty good considering the level of technology at the time. The actual distance between Alexandria and modern Aswan is about 843 km. The exact size of the stadion he used is no longer known (the common Attic stadion was about 185 m), but it is generally believed that Eratosthenes' value corresponds to between 39,690 km and 46,620 km. The well would reflect the sunlight at about 90 degree on the first day of summer. Circumference = 50 x 5000 stadia = 250,000 stadia 250,000 stadia x 185 meters/stadion = 46,250 kilometers. Since 7° is about 1/50 of 360°, the distance between the two cities (5,000 stadia) must be 1/50 of the distance around the meridian. 7/360 x (circum. © 2014 Pearson Education, Inc. Eratosthenes Measures Earth (c. 240 B.C.) The angle between ray and pole=7 degree 1)Convert 7.2 degree to radians,we know radians soradians A= 0.1256 radians 2)Convert 5000 stadia to km 6.36 stadia=1 km 1 stadia=1/6.36km 5000stadia=5000/6.36=786.1… View the full answer ... built in 1911, now moved 30 km away, in Campia Turzii. 5,000 stadia to km. Definition: The stadion (plural: stadia), was an ancient Greek unit of length, based on the length of a typical sports stadium of the time. So he multiplied 5000 by 50 to get 250,000 stadia. How is modern science rooted in ancient astronomy? Who measures the Earth size? Model # KM-5000 UNSPSC # 46171503 Catalog Page # N/A Country of Origin China. 20,000 ft to km conversion. The circumference of the Earth compared to modern value. Since this angle was 1/50 of a circle, and the distance between Syene and Alexandria was 5000 stadia, he multiplied 5000 by 50 to find the earth's circumference. The stadion was a distance unit that was often used in ancient times. Then, since he was aiming for an easy-to-use number, he added 2,000 stadia and got 252,000. Eratosthenes later rounded the circumference of the Earth to 252,000 stadia, most likely just because that number is easily divisible by … Eratosthenes. If we take the stadium unit to be 0.16 km, we find that Eratosthenes estimated Earth's circumference to be about 40,000 km. ference as 50 × 5,000 stadia, or 250,000 stadia. Actual diameter of the Earth (pole to pole) = 40,008 km. Again, you may use the following proportion: I stadia 0.1575 km 5,000 stadia D km (Hint: crossmukiplydivide) Thus, D= km. This comverts to 40,074 km. The SI base unit for length is the metre. He then used the following relation: However, not everybody used a stadion of the same length. The Earth is about 40 thousand kilometers (about 24,860 miles) around. He knows the distance between the two cities is 5000 "stadia". So he calculated the circumference of the earth to be 252,000 stadia. Carl Sagan even says that Eratosthenes paid a man to walk and measure the distance (see the video below). 5000 pedes 1.48 km 4854 ft 0.919 mi 1000 passus or 8 stadia leuga leuca (Gallic) league: 7500 pedes 2.22 km 7281 ft 1.379 mi Except where noted, based on Smith (1851). Note that rounding errors may occur, so always check the results. 4. • Many of our current systems had their roots in the achievements of ancient astronomy • Daily timekeeping How far is 20,000 feet in kilometers? [30 pts total] Show your work in the box. Measurements: Syene to Alexandria . The arc between the two cities was 7 °. From this, he calculated the whole circumference to be 50 x 5000 or 250,000 stadia. How far is 500,000 centimeters in kilometers? From geometry then: 7.2o = 5000 stadia 360o Earth’s circumference => circumference is 250,000 stadia, or 40,000 km. That the distance between Alexandria and Syene is 5000 stades. Because the arc of the angle he measured was 1/50 of a circle, he multiplied 5000 stadia by 50. How close did his figure come to present-day calculations? English and metric equivalents are approximate, converted at 1 pes = 0.9708 English feet and 296 mm respectively. two cities compared in Eratosthenes' determination of earth's circumference. circumference = 250,000 stadia = 46,250 km = 2 p radius. distance ≈ 5000 stadia. So radius is: 40,000 km 2π = 6366 km (very close to modern value, 6378 km!) perfect circles." 804 km x 50 = 40,200 km. It was recorded as 5000 stadia. However, at noon on the same day in the city of Alexandria, which was located 5,000 stadia* to the north of Syene, a shadow could be observed.. 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