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Eratosthene In Birmingham United Kingdom
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Eratosthene In Birmingham United Kingdom

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Eratosthene experiment in King Edward VI High School For Girls

Eratosthene experiment in King Edward VI High School For Girls
Birmingham United Kingdom

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Eratosthene In Birmingham United Kingdom Eratosthene In Birmingham United Kingdom Presentation Transcript

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  • The Partner Schools
    • Lycee General et Technologique Charlie Chaplin Lyon FRANCE
    • (11 to 18 state school 1700 pupils)
        • Scuola Secondaria 1O grado G.G. Belli Roma ITALY
        • (11 to 14 state school 800 pupils)
  • The Partner Schools
    • King Edward VI High School For Girls, England
    • (11 to 18 independent school 550 pupils)
    • Coleguil Technic Mihai Viteazul Oradea ROMANIA
    • (14 to 18 technical college 2000 pupils)
    • Open Schoolgemeenschap Bijlmer Amsterdam NETHERLANDS
    • (12 to 18 state school 1600 pupils)
    • Lycee Francohellenique d Agia Paraskevi Eugene Delacroix (Athens) GREECE
    • (state/ private school 1600 pupils)
    The Partner Schools
    • Scuola Secondaria 1O grado G.G. Belli Roma ITALY
    • (11 to 14 state school 800 pupils)
  • Measuring the radius of the Earth THE ERASTOSTHENES’ METHOD King Edward VI High school For Girls 24 September 2009
  • The experimenters
  • Measuring the altitude of the sun : the instruments
  • Working on the Comenius Project
  • The method!
    • At equinox (September 22) at local noon, the Sun is directly overhead at the equator and a stick casts no shadow.
    • At the latitude of Birmingham, a stick does cast a shadow. By measuring the shadow length and the stick height we can determine the angle of the Sun in the sky.
    • Given the distance between Birmingham and the equator we can then determine the circumference of the Earth (with a tiny bit of trigonometry!) and therefore the Earth’s radius.
  • Eratosthenes’ Method
  • The calculation  degs 360 degs = 4800 km C C = circumference of the Earth  = angle of Sun
  • Distance between Birmingham and the equator
    • Method 1 - using Google Earth
    • Method 2 - using PLANE TRAVEL TIMES and the cruising speed of an airliner!
    • We looked at how long it took a plane to fly from Birmingham UK to Nairobi (Kenya) which is close to the equator. A plane travels at an average cruise speed of around (960 ± 40) km/h and takes around 10 ± 1 hour to travel from the UK to Nairobi. This gives the distance to the equator of (9600 ± 1400) km
    • Nairobi has a longitude of 49 degrees E so the distance from Birmingham (2 degrees W) will be greater than say the distance to Accra (Ghana) which is also on the equator but on the same line of longitude. We have probably underestimated the uncertainty (error) that this method gives for the distance!!
  • Finding the circumference and radius of the Earth
            • L = (571 ± 20) mm
            • H = (424 ± 10) mm C = d x 360 / 
            •  = 53 ± 3°
    • d = (5 808 ± 111) km (Google Earth) d = (9600 ± 1400) km (Plane travel times)
    • C = 5 808 x 360 = 39 451 km C = 9600 x 360 / 53 = 65 208 km
    • 53
    • C max = 5 919 x 360 = 42 617 km C max =11000 x 360 / 50 = 79 200 km
    • 50
    • C min = 5 697 x 360 =3 6624 km C min = 8200 x 360 / 56 = 52 714 km
    • 56
    • Therefore C = (39 500 ± 3 000) km Therefore C = (65 000 ± 13 000) km
    • C = 2  R where R = radius of Earth C = 2  R where R = radius of Earth Therefore R = (6280 ± 480) km Therefore R = (10 000 ± 2000) km
    • Circumference results Radius results
    • Birmingham C = (39 500 ± 3 000) km (Google Earth) R = (6 280 ± 480 ) km
    • C = (65 000 ± 13 000) km (Plane travel times) R = 10 000 ± 2 000) km
    • Lyon C = 39 700 km R = 6 320 km
    • Athens C = 40 443 km R = 6 440 km
    • Rome C = 41 142 km R = 6 547 km
    • Accepted value for radius = 6 354 km (measured through pole)
    • 6 378 km (measured through equator)
  • The time Autumn Equinox: 22 September 2009 C lock time for local noon will be at 13.01
    • Equation of time = - 07min 09sec
    • Due to our longitude (1.9 degrees West, our local noon will be 1.9 degrees x 4 min = + 7.6 min later than the clock time
    • Taking into account the summer time = +1h
    • 12 - 7 min + 8 min + 1h = 13.01
  • Finding the circumference of a melon using Eratosthenes’ method From our measurements, we found the circumference (C) of the melon to be 24.2cm, however the actual circumference was 48.1cm. Experimental uncertainty To find the experimental uncertainty, we first worked out how accurate our measurements were e.g. to the nearest centimetre. We then divided this number by the actual measurement and multiplied this by 100. We added all the uncertainties together to find the total. Our experimental uncertainty is 55%.
    • Our method
    • Push two cocktail sticks of equal height into the melon and measure the height of (H), and distance (d), between them.
    • Shine a torch directly above one stick, so that it creates no shadow.
    • Measure the length (L) of the shadow cast by the other stick
    • Use the tangent of the triangle created by the shadow and the stick to find the angle the light is hitting the stick at (  ).
    • Use the equation  = d to find the 360 C
    • circumference of the melon.
    d H Melon L Light rays Sticks Shadow a
  •