Expressing Latitude and Longitude As Linear Units
On the GRS80 or WGS84 spheroid at sea level at the equator, one latitudinal second measures 30.715 metres, one latitudinal minute is 1843 metres and one latitudinal degree is 110.6 kilometres. The circles of longitude, meridians, meet at the geographical poles, with the west-east width of a second naturally decreasing as latitude increases. On the equator at sea level, one longitudinal second measures 30.92 metres, a longitudinal minute is 1855 metres and a longitudinal degree is 111.3 kilometres. At 30° a longitudinal second is 26.76 metres, at Greenwich (51° 28' 38" N) 19.22 metres, and at 60° it is 15.42 metres.
On the WGS84 spheroid, the length in meters of a degree of latitude at latitude φ (that is, the distance along a north-south line from latitude (φ - 0.5) degrees to (φ + 0.5) degrees) is about
(Those coefficients can be improved, but as they stand the distance they give is correct within a centimeter.)
To estimate the length of a longitudinal degree at latitude we can assume a spherical Earth (to get the width per minute and second, divide by 60 and 3600, respectively):
where Earth's average meridional radius is 6,367,449 m. Since the Earth isn't spherical that result can be off by several tenths of a percent; a better approximation of a longitudinal degree at latitude is
where Earth's equatorial radius equals 6,378,137 m and ; for the GRS80 and WGS84 spheroids, b/a calculates to be 0.99664719. ( is known as the parametric or reduced latitude). Aside from rounding, this is the exact distance along a parallel of latitude; getting the distance along the shortest route will be more work, but those two distances are always within 0.6 meter of each other if the two points are one degree of longitude apart.
| Latitude | Town | Degree | Minute | Second | ±0.0001° |
|---|---|---|---|---|---|
| 60° | Saint Petersburg | 55.65 km | 0.927 km | 15.42 m | 5.56 m |
| 51° 28' 38" N | Greenwich | 69.29 km | 1.155 km | 19.24 m | 6.93 m |
| 45° | Bordeaux | 78.7 km | 1.31 km | 21.86 m | 7.87 m |
| 30° | New Orleans | 96.39 km | 1.61 km | 26.77 m | 9.63 m |
| 0° | Quito | 111.3 km | 1.855 km | 30.92 m | 11.13 m |
Read more about this topic: Geographic Coordinate System
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