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Circumference of the earth via latitute mesurement

  1. Mar 18, 2007 #1
    Suppose I know city A is located at latitude 21 degrees exactly and city y is located at latitude 24 degrees exactly. I know the distance between the two cities is 400 kilometers.
    I want to find the circumference of the earth approximately


    How do I do this?

    My feeling is that we
    subtract the two latitudes to find 24-21 = 3 degrees

    so 3 degrees corresponds to roughly 400 kilometers (1)

    so 180 degrees of latitude corresponds roughly to X kilometers (2)

    and I find that x = 24000 kilometers

    is line (1) and (2) correct or should the second line read

    360 degrees of latitude corresponds roughly to X kilometers??

    thanks
     
  2. jcsd
  3. Mar 18, 2007 #2

    Integral

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    That works fine as long as the cities have the same longitude.

    You should use 360deg not 180.
     
    Last edited: Mar 18, 2007
  4. Mar 18, 2007 #3
    Hi. thank you for that. yes the cities are at the same longitude.
    my problem is when i do this calculation with different, more realistic, numbers for latitude and distance than the ones i posted originally.


    i.e the more realistic numbers are 37.977 degrees of latitude
    41.856 degrees of latitude and 430 km is the distance betwee these two cities.


    i get an answer that is exactly a factor of two off from the true circumference of the earth?

    i get about 20000 km

    when it should be 40000 km.
    so that is why i was thinking it should be 360 and not 180 degrees

    so why am i off?

    thanks
     
  5. Mar 18, 2007 #4

    Integral

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    Post your arithemtic.

    I get 40,000km
     
  6. Mar 18, 2007 #5
    oh wait sorry i didnt see your previous post where you said to use 360. thats exactly my question
    why 360?
    arent there 180 degrees of latitude?
    i understand if i use 360 i get the answer.
    but there are 360 of longitude not latitude and we only know the latitudes of the cities?
     
    Last edited: Mar 18, 2007
  7. Mar 18, 2007 #6

    Integral

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    There are 90 degs from equator to pole, that is 1/4 the circumference of the earth, 4*90=360.
     
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