If as Neville and Paul say the Ecliptic axis is a real object and not a subjective mathmatical/geometrical projection, may I ask which ecliptic of the many the solar system has, including the invariable ecliptic plane is the real one, and please tell me what makes it real. ? Philip. Laws. Axis of rotation. In mathematics: a.. Coordinate axis, in mathematics, physics and engineering b.. Axis of rotation, or axis of symmetry, in geometry-related contexts A rotation is a movement of an object in a circular motion. A two-dimensional object rotates around a center (or point) of rotation. A three-dimensional object rotates around a line called an axis. If the axis of rotation is within the body, the body is said to rotate upon itself, or spin—which implies relative speed and perhaps free-movement with angular momentum. A circular motion about an external point, e.g. the Earth about the Sun, is called an orbit or more properly an orbital revolution. Mathematically, a rotation is, unlike a translation, a rigid body movement which keeps a point fixed. This definition applies to rotations within both two and three dimensions (in a plane and in space, respectively.) A rotation in three-dimensional space keeps an entire line fixed, i.e. a rotation in three-dimensional space is a rotation around an axis. This follows from Euler's rotation theorem. In kinematics, Euler's rotation theorem states that, in three-dimensional space, any displacement of a rigid body such that a point on the rigid body remains fixed, is equivalent to a rotation about a fixed axis through that point. The theorem is named after Leonhard Euler. In mathematical terms, this is a statement that, in 3D space, any two coordinate systems with a common origin are related by a rotation about some fixed axis. This also means that the product of two rotation matrices is again a rotation matrix. A (non-identity) rotation matrix has a real eigenvalue which is equal to unity. The eigenvector corresponding to this eigenvalue is the axis of rotation connecting the two systems. All rigid body movements are rotations, translations, or combinations of the two. If a rotation around a point or axis is followed by a second rotation around the same point/axis, a third rotation results. The reverse (inverse) of a rotation is also a rotation. Thus, the rotations around a point/axis form a group. However, a rotation around a point or axis and a rotation around a different point/axis may result in something other than a rotation, e.g. a translation. The principal axes of rotation in space Rotations around the x, y and z axes are called principal rotations. Rotation around any axis can be performed by taking a rotation around the x axis, followed by a rotation around the y axis, and followed by a rotation around the z axis. That is to say, any spatial rotation can be decomposed into a combination of principal rotations.