Longitude - Length of A Degree of Longitude

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

\Delta^1_{\rm LONG}= \frac{\pi}{180}a \cos \phi. \,\!

When the Earth is modelled by an ellipsoid this result must be modified to

\Delta^1_{\rm LONG}= \frac{\pi a\cos\phi}{180(1 - e^2 \sin^2 \phi)^{1/2}}\,,

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
e^2=\frac{a^2-b^2}{a^2}.

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).

Read more about this topic:  Longitude

Famous quotes containing the words length of, length and/or degree:

    “The value of life lies not in the length of days but in the use you make of them; he has lived for a long time who has little lived.”
    —Michel de Montaigne (1533–1592)

    “Twenty-four-hour room service generally refers to the length of time that it takes for the club sandwich to arrive. This is indeed disheartening, particularly when you’ve ordered scrambled eggs.”
    —Fran Lebowitz (b. 1950)

    “Crude men who feel themselves insulted tend to assess the degree of insult as high as possible, and talk about the offense in greatly exaggerated language, only so they can revel to their heart’s content in the aroused feelings of hatred and revenge.”
    —Friedrich Nietzsche (1844–1900)