Specific relative angular momentum
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In astrodynamics, the specific relative angular momentum of an orbiting body with respect to a central body is the relative angular momentum of the first body per unit mass. Specific relative angular momentum plays a pivotal role in definition of orbit equations.
Specific relative angular momentum, represented by the symbol 
, is defined as the cross product of the position vector 
and velocity vector 
of the orbiting body relative to the central body:
where:
- is the orbital position vector of the orbiting body relative to the central body,
- is the orbital velocity vector of the orbiting body relative to the central body,
is the linear momentum of the orbiting body relative to the central body,
is the mass of the orbiting body, and
is the relative angular momentum of the orbiting body with respect to the central body.
Under standard assumptions for an orbiting body in a trajectory around central body at any given time the vector is perpendicular to the osculating orbital plane defined by orbital position and velocity vectors.
The magnitude of is denoted as 
:
For an elliptical orbit, it is twice the area per unit time swept out, hence twice the area of the ellipse divided by the orbital period, hence 
, which is 
.
The units of are m2s-1.
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