Length of A Degree of Longitude
The length of a degree of longitude depends only on the radius of a circle of latitude. For a sphere of radius a the value of the radius at a latitude φ is acosφ and the length of arc for a one degree (or π/180 radians) increment is
When the Earth is modelled by an ellipsoid this result must be modified to
where e, the eccentricity of the ellipsoid, is related to the major and minor axes (the equatorial and polar radii respectively) by
0° | 110.574 km | 111.320 km |
15° | 110.649 km | 107.551 km |
30° | 110.852 km | 96.486 km |
45° | 111.132 km | 78.847 km |
60° | 111.412 km | 55.800 km |
75° | 111.618 km | 28.902 km |
90° | 111.694 km | 0.000 km |
Cos φ decreases from 1 at the equator to zero at the poles, so the length of a degree of longitude decreases likewise. This contrasts with the small (1%) increase in the length of a degree of latitude. The table shows values of both for the WGS84 ellipsoid, where a=6,378,137.0 m and b=6,356,752.3142 m. Note that the distance between two points 1 degree apart on the same circle of latitude, measured along that circle of latitude, is not the shortest (geodesic) distance between those points; the difference is less than 0.6 m. A calculator for any latitude is provided by the U.S. government's National Geospatial-Intelligence Agency (NGA).
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