Determining circle distances with varying latitude

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

Excellent advice from Paul. Also, you might want to check out
http://www.meridianworlddata.com/Distance-Calculation.asp

Carl