Navigation at Sea

Abstract

In all but the most exacting applications, such as global oceanic or satellite navigation, the earth may be assumed to be a sphere. Therefore the most appropriate coordinate system to use to define positions on its surface is what would be called in coordinate geometry spherical polar coordinates. The axis of spin is taken to be the polar axis and the plane perpendicular to the axis that passes through the center of the sphere is the equatorial plane. The position of any point on the surface of the sphere is specified with reference to an orthogonal set of lines of latitude and longitude. The lines of longitude, or equivalently, meridians, are great circles that pass through both poles, formed by the intersection of planes passing through the axis and the spherical surface. The lines of equal latitude are formed at the intersection of the spherical surface with circular cones having vertices at the center and drawn around the axis. The angle of a cone at its apex is called the colatitude, that is, 90° minus the latitude, so that if the angle of the cone is 90°, corresponding to the geographical equator, the latitude is 0°. To distinguish between the northern and southern hemispheres the latitude must be specified as N (north) or S (south). Since the longitude lacks any natural zero from which to begin measurement, an arbitrary point was chosen and agreed to by international convention in 1884, namely the meridian passing through the observatory at Greenwich, England. That meridian is called the prime meridian, and a plane through that meridian and the axis divides the globe into two hemispheres the east (E) and west (W). The geographic coordinates are illustrated in Fig. 5.1.