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The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.
The orbital angular momentum of light (OAM) is the component of angular momentum of a light beam that is dependent on the field spatial distribution, and not on the polarization. OAM can be split into two types. The internal OAM is an origin-independent angular momentum of a light beam that can be associated with a helical or twisted wavefront.
In celestial mechanics, the specific relative angular momentum (often denoted or ) of a body is the angular momentum of that body divided by its mass. [1] In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum , divided by the mass of the body in question.
The specific angular momentum of any conic orbit, h, is constant, and is equal to the product of radius and velocity at periapsis. At any other point in the orbit, it is equal to: [ 13 ] h = r v cos φ , {\displaystyle h=rv\cos \varphi ,} where φ is the flight path angle measured from the local horizontal (perpendicular to r .)
The total angular momentum of light consists of two components, both of which act in a different way on a massive colloidal particle inserted into the beam. The spin component causes the particle to spin around its axis, while the other component, known as orbital angular momentum (OAM), causes the particle to rotate around the axis of the beam.
Under standard assumptions of the conservation of angular momentum the flight path angle satisfies the equation: [6] = where: is the specific relative angular momentum of the orbit, is the orbital speed of the orbiting body,
If the eccentricity equals 1, then the orbit equation becomes: = + where: is the radial distance of the orbiting body from the mass center of the central body, is specific angular momentum of the orbiting body,
For an elliptic orbit, the specific orbital energy equation, when combined with conservation of specific angular momentum at one of the orbit's apsides, simplifies to: [2] = where = (+) is the standard gravitational parameter;