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One Degree Latitude, Longitude: How Many Miles?


Date: 04/02/2002 at 09:18:42
From: Nick
Subject: Longitude, latitude

In the states of Kansas and Oklahoma, approximately how many miles are 
there in one degree of longitude and one degree of latitude?


Date: 04/02/2002 at 09:30:42
From: Doctor Mitteldorf
Subject: Re: Longitude, latitude

A degree of latitude is the same all over the earth.  It is 1/360 of 
the circumference of the earth, and you can look up the radius of the 
earth at this Web site, then multiply by 2pi:   

   Earth: Geodetic and Geophysical Data - JPL/SSD
   http://ssd.jpl.nasa.gov/phys_props_earth.html   

[Disclaimer:  The geoid is an ellipsoidal form, so a degree of latitude centered on the equator is not the same length as one degree of longitude 
along the equator.  The difference is small enough to ignore for many 
applications, however.  Thanks to James Jacobs for pointing this out.]

Degrees of longitude are the same size as latitude at the equator, but 
they get smaller and smaller as you go toward the pole. At the pole, 
the size of a degree of longitude becomes zero.

The relation between latitude and the size of a degree of longitude is
called a "cosine" function, from trigonometry.  The latitude of 
Oklahoma is about 34 degrees north, and the cosine of that angle is 
0.83.  This means that adegree of longitude in Oklahoma is about 0.83 
times as great as a degree of latitude.

- Doctor Mitteldorf, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
Middle School Geometry
Middle School Higher-Dimensional Geometry
Middle School Terms/Units of Measurement

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