Mathematics

Main: Rotation (mathematics)

All rigid body movements are rotations, translations, or combinations of the two.

A Rotation is simply a progressive radial orientation to a common point. That common point lay within the axis of that motion. The axis is 90 degrees perpendicular to the plane of the motion. If the axis of the rotation lay external of the body in question then the body is said to Orbit. There is no fundamental difference between a “rotation” and a “orbit” and or "spin". The key distinction is simply where the axis of the rotation lay, either within or without a body in question. This distinction is and can be demonstrated in and for both “ridged” and “non ridged” bodies.

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.

In flight dynamics, the principal rotations are known as pitch, roll and yaw (known as Tait-Bryan angles). This terminology is also used in computer graphics.

Astronomy

In astronomy, rotation is a commonly observed phenomenon. Stars, planets and similar bodies all spin around on their axes (the plural of axis). The rotation rate of planets in the solar system was first measured by tracking visual features. Stellar rotation is measured through Doppler shift or by tracking active surface features.

This rotation induces a centrifugal acceleration in the reference frame of the Earth which slightly counteracts the effect of gravity the closer one is to the equator. One effect is that an object weighs slightly less at the equator. Another is that the Earth is slightly deformed into an oblate spheroid.

Another consequence of the rotation of a planet is the phenomenon of precession. Like a gyroscope, the overall effect is a slight "wobble" in the movement of the axis of a planet. Currently the tilt of the Earth's axis to its orbital plane (obliquity of the ecliptic) is 23.45 degrees, but this angle changes slowly (over thousands of years). (See also Precession of the equinoxes and Pole star.)

Rotation and revolution

Main: Orbital revolution