Specific relative angular momentum

Categories: Astrodynamics | Celestial mechanics

In astrodynamics specific relative angular momentum (<math>\mathbf{h}\,\!</math>) of orbiting body (<math>m_2\,\!</math>) relative to central body (<math>m_1\,\!</math>) is the relative angular momentum of <math>m_2\,\!</math> per unit mass. Specific relative angular momentum plays a pivotal role in definition of orbit equations.


Specific relative angular momentum (<math>\mathbf{h}\,\!</math>)is defined as cross product of position vector and velocity vector of <math>m_2\,\!</math>:

<math>\mathbf{h}=\mathbf{r}\times \mathbf{v}\,\!</math>

where:


Under standard assumptions for a orbiting body in a trajectory around central body at any given time the <math>\mathbf{h}\,\!</math> vector is perpendicular to the osculating orbital plane defined by orbital position and velocity vectors.


The magnitude of <math>\mathbf{h}\,\!</math> is denoted as <math>h\,\!</math>:

<math>h=\left|\mathbf{h}\right|\,\!</math>

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 <math>2\pi ab /(2\pi\sqrt{a^3/\mu}) = b \sqrt{\mu/a}</math>, which is <math>\sqrt{a(1-e^2)\mu}</math>.


The units of <math>\mathbf{h}\,\!</math> are km2s-1.