units (grad, mil) can be used. Moving clockwise on a 360 degree circle, east has azimuth 90°, south 180°, and west 270°. There are exceptions: some navigation systems use south as the reference vector. Any direction can be the reference vector, as long as it is clearly defined. Quite commonly, azimuths or compass bearings are stated in a system in which either north or south can be the zero, and the angle may be measured clockwise or anticlockwise from the zero. For example, a bearing might be described as "(from) south, (turn) thirty degrees (toward the) east" (the words in brackets are usually omitted), abbreviated "S30°E", which is the bearing 30 degrees in the eastward direction from south, i.e. the bearing 150 degrees clockwise from north. The reference direction, stated first, is always north or south, and the turning direction, stated last, is east or west. The directions are chosen so that the angle, stated between them, is positive, between zero and 90 degrees. If the bearing happens to be exactly in the direction of one of the cardinal points, a different notation, e.g. "due east", is used instead. True north-based azimuths In geodesy We are standing at latitude , longitude zero; we want to find the azimuth from our viewpoint to Point 2 at latitude , longitude L (positive eastward). We can get a fair approximation by assuming the Earth is a sphere, in which case the azimuth α is given by A better approximation assumes the Earth is a slightly-squashed sphere (an oblate spheroid); azimuth then has at least two very slightly different meanings. Normal-section azimuth is the angle measured at our viewpoint by a theodolite whose axis is perpendicular to the surface of the spheroid; geodetic azimuth (or geodesic azimuth) is the angle between north and the ellipsoidal geodesic (the shortest path on the surface of the spheroid from our viewpoint to Point 2). The difference is usually negligible: less than 0.03 arc second for distances less than 100 km. Normal-section azimuth can be calculated as follows: where f is the flattening and e the eccentricity for the chosen spheroid (e.g., for WGS84). If φ1 = 0 then To calculate the azimuth of the sun or a star given its declination and hour angle at our location, we modify the formula for a spherical earth. Replace φ2 with declination and longitude difference with hour angle, and change