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Posted by Paul Cooper on April 24, 2006, 3:25 am
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>Is there an expression out there for determining the distance around
>the globe, at let's say the tropic of cancer and the tropic of
>capricorn? I know that the radius of the earth is 6371 - is there
>perhaps an expression which relates the circle distance at the tropic
>of cancer/capricorn to the radius or even perhaps the GCD?
>
>I am attempting to determine how the circle distances change as you
>move from the equator to either of the poles.
>
>
>thanks
Well, the radius of the small circle varies according to the cosine of
the latitude, so the length of a line of latitude at a specific
latitude is simply 2*Pi*6371*cos(Latitude), assuming the earth is a
sphere. This is trivial high school trigonometry.
However, the Earth is NOT a sphere - is better approximated as an
oblate spheroid. The major and minor semiaxes of the WGS84 spheroid
(used by satellite navigation and on a global basis the best fit) are
6,378.137 km (equatorial radius) and 6,356.7523 km (polar radius).
(http://en.wikipedia.org/wiki/WGS84 is a useful summary). If you wish
for a reasonably precise value you will have to take it into account.
If (as I suspect) this is for a homework problem, you may get more
credit if you work out the relationship for the spheroid; given the
start here you should be able to do it - some elementary coordinate
geometry will do it (ask yourself what is the X coordinate at a
specific Y on an ellipse; what is Y given the latitude?). However, I
leave this as an exercise for you!
Paul
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