Equator 84 (World Geodetic System 1984) which is a standard for use in cartography, geodesy, and satellite navigation including GPS, also has an equatorial radius of 6,378.137 kilometres (3,963.191 mi). For both GRS 80 and WGS 84, this results in a length for the Equator of 40,075.0167 km (24,901.4609 mi). The geographical mile is defined as one arc-minute of the Equator, so it has different values depending on which radius is assumed. For example, by WSG-84, the distance is , while by IAU-2000, it is . This is a difference of less than over the total distance (approximately ). The earth
Mercator 1569 world map 12 by using compass roses on the equator and it is only in Legend 10 that he introduces the Organum Directorium and also addresses the inverse problems: given the initial point and the direction and distance of the second find the latitude and longitude of the second. Mercator's construction is simply an evaluation of the rhumb line distance in terms of the latitude difference and the azimuth as If the latitude difference is expressed in arc minutes then the distance is in nautical miles. In later life Mercator commented that the principles of his map had not been understood by