Eratosthene In Rome Italy

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Eratosthene experiment in Scuola Secondaria di 1' grado G.G.Belli
Rome
Italy

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Eratosthene In Rome Italy

  1. 1. Measuring the radius of the Earth THE ERASTOSTHENES’ METHOD Scuola Media Statale “G.G. Belli” - Rome Class 2H Teacher: Leonarda Fucili 22 September 2009
  2. 2. The conditions <ul><li>The class : 7 th level – students aged 12 </li></ul><ul><li>Time : the Autumn equinox, a few days after the beginning of the school year </li></ul><ul><li>Activities : measuring the altitude of the sun at noon and estimating the distance Rome/equator </li></ul><ul><li>Uncertainties for our Earth radius value: after the first result we tried to reduce the approximation </li></ul><ul><li>Documentation : by photos and reports </li></ul>
  3. 4. The location : ROME the astronomical terrace of our school 41° 54’ 57’’N 12° 27’ 52’’E
  4. 5. The time Autumn Equinox: 22 September 2009 C lock time for local noon will be at 13.03 <ul><li>Equation of time = - 07min 09sec </li></ul><ul><li>Due to our longitude, our local noon will be 2,5 degrees x 4 min = + 10 min later than the clock time = +10 min </li></ul><ul><li>Taking into account the summer time = +1h </li></ul><ul><li>12 - 7 min + 10 min + 1h = 13.03 </li></ul>
  5. 6. Eratosthenes’ Method
  6. 7. The experimenters
  7. 8. The method h Sun’s ray Shadow length on the horizontal plane IT IS THE SAME TRIANGLE !!!
  8. 9. ON THE EQUINOX at MIDDAY Altitude of the sun Latitude
  9. 10. Measuring the altitude of the sun : the instruments
  10. 11. Waiting for the local noon
  11. 12. About 1 hour before the local noon
  12. 13. Local NOON Altitude of the Sun about 48 degrees
  13. 14. Altitude of the sun = 48 degrees Latitude = 42 degs
  14. 15. 1. Distance Rome – Equator (Libreville, Gabon) SCALE 1: 30.000.000 1 cm = 300 Km 16,3 cm = about 4800 Km
  15. 16. 2. Distance Rome – Equator = about 5000Km
  16. 17. 3. Distance Rome – Equator GOOGLE EARTH 4.628,94 KM
  17. 18. Distance Rome – Equator <ul><li>We consider the average </li></ul><ul><li>between the previous values: </li></ul><ul><li>about </li></ul><ul><li>4800 Km </li></ul>
  18. 19. THE RATIO Sun’s parallel rays Equator Rome Rome/equator distance = about 4800 Km 42 ° 42 ° 42 ° 360 ° meridian
  19. 20. THE CALCULATION (approximation in latitude: 1 degree) 360 degs 42 degs = About 4800 Km x X = circumference of the Earth = about 41.142 Km
  20. 21. Reducing uncertainties for our Earth radius value   Local Latitude : 41° 54’ 57’’N Distance Rome/ Equator: 4.628,94 KM 360 ° : 41° 54’ 57’’N = 1.296.000” : 150.897” = 8,588 4.628,94 KM x 8,588 = 39.756 Km
  21. 22. Required pre-knowledge <ul><li>Ratio and proportions </li></ul><ul><li>Scales </li></ul><ul><li>Angles </li></ul><ul><li>Numbers and measures </li></ul><ul><li>Decimal and sexagesimal measure systems </li></ul><ul><li>Sphere and its sections: geometrical proprieties </li></ul><ul><li>Calculations with degrees, primes, seconds </li></ul><ul><li>Uncertainties and errors </li></ul><ul><li>Astronomical concepts and language: local meridian, clock time and local noon, equation of time, equinox, equator, latitude, longitude, altitude of the sun, gnomon, zenith, zenithal angle </li></ul>

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