flattening of the Earth at the poles (about ) and many other details. Planetary coordinate systems use formulations analogous to the geographic coordinate system. In astronomy A series of astronomical coordinate systems are used to measure the elevation angle from different fundamental planes. These reference planes are the observer's horizon, the celestial equator (defined by Earth's rotation), the plane of the ecliptic (defined by Earth's orbit around the Sun), the plane of the earth terminator (normal to the instantaneous direction to the Sun), and the galactic equator (defined by the rotation of the Milky Way). Coordinate system conversions As the spherical coordinate system is only one of many three-dimensional coordinate systems, there exist equations for converting coordinates between the spherical coordinate system and others. Cartesian coordinates The spherical coordinates of a point in the ISO convention (i.e. for physics: radius , inclination , azimuth ) can be obtained from its Cartesian coordinates by the formulae The inverse tangent denoted in must be suitably defined, taking into account the correct quadrant of . See the article on atan2. Alternatively, the conversion can be considered as two sequential rectangular to polar conversions: the first in the Cartesian plane from to , where is the projection of onto the -plane, and the second in the Cartesian -plane from to . The correct quadrants for and are implied by the correctness of the planar rectangular to polar conversions. These formulae assume that the two systems have the same origin, that the spherical reference plane is the Cartesian plane, that is inclination from the direction, and that the azimuth angles are measured from the Cartesian axis (so that the axis has ). If θ measures elevation from the reference plane instead of inclination from the zenith the arccos above becomes an arcsin, and the and below become switched. Conversely, the Cartesian coordinates may be retrieved from the spherical coordinates (radius , inclination , azimuth ), where , , , by Cylindrical coordinates Cylindrical coordinates (axial radius ρ, azimuth φ, elevation z) may be converted into spherical coordinates (central radius r, inclination θ, azimuth φ), by the formulas Conversely, the spherical coordinates may be converted into cylindrical coordinates by the formulae These formulae assume that the two systems have the same origin and same reference plane, measure the azimuth angle in the same senses from the same axis, and that the spherical angle is inclination from