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Due to the very slow pole motion of the Earth, the Celestial Ephemeris Pole (CEP, or celestial pole) does not stay still on the surface of the Earth.The Celestial Ephemeris Pole is calculated from observation data, and is averaged, so it differs from the instantaneous rotation axis by quasi-diurnal terms, which are as small as under 0.01" (see [6]).
These reference planes include: the observer's horizon, the galactic equator (defined by the rotation of the Milky Way), the celestial equator (defined by Earth's rotation), the plane of the ecliptic (defined by Earth's orbit around the Sun), and the plane of the earth terminator (normal to the instantaneous direction to the Sun).
To change the formulas for passive rotations (or find reverse active rotation), transpose the matrices (then each matrix transforms the initial coordinates of a vector remaining fixed to the coordinates of the same vector measured in the rotated reference system; same rotation axis, same angles, but now the coordinate system rotates, rather ...
To calculate the azimuth of the Sun or a star given its declination and hour angle at a specific location, modify the formula for a spherical Earth. Replace φ 2 with declination and longitude difference with hour angle, and change the sign (since the hour angle is positive westward instead of east). [citation needed]
In two dimensions, only a single angle is needed to specify a rotation about the origin – the angle of rotation that specifies an element of the circle group (also known as U(1)). The rotation is acting to rotate an object counterclockwise through an angle θ about the origin; see below for details.
For example, the elevation and azimuth angles of e suffice to locate it in any particular Cartesian coordinate frame. By Rodrigues' rotation formula, the angle and axis determine a transformation that rotates three-dimensional vectors. The rotation occurs in the sense prescribed by the right-hand rule.
Angle on the bow is the angle made by the ship's course and the line of sight (see Figure 1). The angle on the bow was usually estimated based on the observational experience of the observer. In some cases, the observers improved their estimation abilities by practicing against ship models mounted on a "lazy Susan". [15]
Earth's rotation axis moves with respect to the fixed stars (inertial space); the components of this motion are precession and nutation. It also moves with respect to Earth's crust; this is called polar motion. Precession is a rotation of Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies.