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Math Help - latitude and longitude question

  1. #1
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    latitude and longitude question

    I'm asked to:

    Explain with the aid of diagrams, how to find the distance, in km, between 2 locations of the same longitude if:
    a) both locations are above the equator.
    b) one location is above the equator and the other is below.

    any of you guys familiar with latitude and longitude?
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  2. #2
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    Get a ball of string (see diagram).

    latitude and longitude question-string.jpg

    Have someone hold one end of the string at the starting point while you walk due south or due north to the other location while holding the ball, letting it out as you go (see diagram).

    latitude and longitude question-string2.jpg

    Measure the string. If it is less than half the longitudinal circumference of the Earth the length of the string is the distance. Otherwise you went the wrong way and need to subtract the length of the string from the longitudinal circumference.

    latitude and longitude question-string3.jpg



    Alternatively you could convert the difference in latitude to radians by multiplying by \frac {\pi}{180} then multiply by the radius of the Earth.

    latitude and longitude question-string4.jpg
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  3. #3
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    Quote Originally Posted by Seza<3 View Post
    Explain with the aid of diagrams, how to find the distance, in km, between 2 locations of the same longitude if:
    a) both locations are above the equator.
    b) one location is above the equator and the other is below.
    Since both places have the same longitude the distance is a part of a great circle.

    1. Calculate the difference of the latitudes. If you write the latitude of a place south of the equator as a negative number this calculation fits both questions, a) and b).

    2. Let R denote the radius of the earth then the distance d is calculated by:

    d = \frac{\pi}{180^\circ} \cdot |\phi_1 - \phi_2| \cdot R
    Attached Thumbnails Attached Thumbnails latitude and longitude question-entfernung_auferde.gif  
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