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In mathematics, a rotation of axes in two dimensions is a mapping from an xy - Cartesian coordinate system to an x′y′ -Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle . A point P has coordinates ( x, y) with respect to the ...
The Earth-centered, Earth-fixed coordinate system (acronym ECEF ), also known as the geocentric coordinate system, is a cartesian spatial reference system that represents locations in the vicinity of the Earth (including its surface, interior, atmosphere, and surrounding outer space) as X, Y, and Z measurements from its center of mass.
Earth's rotation. Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis, as well as changes in the orientation of the rotation axis in space. Earth rotates eastward, in prograde motion. As viewed from the northern polar star Polaris, Earth turns counterclockwise . The North Pole, also known as the Geographic North ...
The axis of rotation need not go through the body. In general, any rotation can be specified completely by the three angular displacements with respect to the rectangular-coordinate axes x, y, and z. Any change in the position of the rigid body is thus completely described by three translational and three rotational coordinates.
The locations of points in 3D space most conveniently are described by three cartesian or rectangular coordinates, X, Y, and Z. Since the advent of satellite positioning, such coordinate systems are typically geocentric , with the Z-axis aligned to Earth's (conventional or instantaneous) rotation axis.
Rotation matrix. In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix. rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system.
The geographical centre of Earth is the geometric centre of all land surfaces on Earth. Geometrically defined it is the centroid of all land surfaces within the two dimensions of the Geoid surface which approximates the Earth's outer shape. The term centre of minimum distance [1] specifies the concept more precisely as the domain is the sphere ...
The geographic center of the United States is a point approximately 20 mi (32 km) north of Belle Fourche, South Dakota at 44°58′2.07622″N 103°46′17.60283″W. It has been regarded as such by the United States Coast and Geodetic Survey and the U.S. National Geodetic Survey (NGS) since the additions of Alaska and Hawaii to the United ...