Specific Relative Angular Momentum

In astrodynamics specific relative angular momentum (\mathbf{h}\,\!) of orbiting body (m_2\,\!) relative to central body (m_1\,\!) is the relative angular momentum of m_2\,\! per unit mass. Specific relative angular momentum plays a pivotal role in definition of orbit equations.
Specific relative angular momentum (\mathbf{h}\,\!)is defined as cross product of position vector and velocity vector of m_2\,\!:
\mathbf{h}=\mathbf{r}\times \mathbf{v}\,\!
where: Under standard assumptions for a orbiting body in a trajectory around central body at any given time the \mathbf{h}\,\! vector is perpendicular to the osculating orbital plane defined by orbital position and velocity vectors. The magnitude of \mathbf{h}\,\! is denoted as h\,\!:
h=\left|\mathbf{h}\right|\,\!
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 2\pi ab /(2\pi\sqrt{a^3/\mu}) = b \sqrt{\mu/a}, which is \sqrt{a(1-e^2)\mu}. The units of \mathbf{h}\,\! are km2s-1.

 

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