A coordinate system the axes of which are fixed with respect to the Earth. Because the Earth not rigid but (a) is imperfectly elastic and (b) moving irregularly in all its parts, the above definition is inadequate for specifying a unique, time-invariant system. A valid definition would be, for example, a coordinate system the axes of which are parallel to those of another coordinate system defined as follows: (a) a rectangular Cartesian coordinate system in three-space, with the three axes fixed with respect to each other, is defined; (b) two of the axes lie in a plane passing through three given points in the Earth (one of these points is usually the Earth's centre of mass), and one of these axes passes through two of the points; (c) the direction of the third axis with respect to the plane is specified; (d) a (possibly curvilinear), time invariant coordinate system is specified by a transformation from the Cartesian coordinate system to this second one; and (e) the Earth-fixed coordinate system is then defined by parallelism with respect to the second coordinate system. However, the fact that all parts of the Earth are probably in motion with respect to each other makes it unlikely that one Earth-fixed coordinate system, however precisely defined, will serve all needs. Passing through two given points in the Earth (one of these points is usually taken as the Earth's centre of mass).