Specific angular momentum ( $h$ )

The specific angular momentum is angular momentum per unit mass,

h = r \times v

. For a planar Kepler orbit its magnitude is

h = r^{2} \dot{θ} = μ a (1 - e^{2})

.

Table of contents
- High-eccentricity angular-speed crossover Specific angular momentum
- Periapsis angular speed Specific angular momentum

High-eccentricity angular-speed crossover ( $r_{x} = h / n_{p}$ )

For a nearly radial Kepler orbit with pericentre

q

, specific angular momentum is

h ≃ 2 GMq

. Relative to a circular reference orbit of radius

a_{p}

and mean motion

n_{p}

, the instantaneous azimuthal rate changes from faster to slower at

r_{x} = h / n_{p} ≃ a_{p} (2 q / a_{p})^{1/4}

. In a rotating reference frame the polar angle has a turning point at this radius. The true anomaly there differs from

π

by approximately

2 q / r_{x}

.

Periapsis angular speed ( $\dot{θ}_{peri}$ )

The specific angular momentum of an elliptic Kepler orbit is

h = μ a (1 - e^{2})

. At periapsis,

r = a (1 - e)

, so

\dot{θ}_{peri} = \frac{h}{r ^{2}} = n \frac{1 + e}{( 1 - e ) ^{3/2}} .

The mean motion understates instantaneous angular speed near periapsis. A particle in an exterior mean-motion resonance can briefly overtake the planet in angle despite completing full orbits more slowly.

 Ancestors (6)

 Incoming links (182)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (1)

Specific angular momentum by

Wikipedia Bot  1

Specific angular momentum is a physical quantity that represents the angular momentum of an object per unit mass. It is commonly denoted by the symbol \( h \) or \( \mathbf{l} \), depending on the context. Specific angular momentum is useful in orbital mechanics and dynamics to analyze the motion of bodies in gravitational fields, such as planets, satellites, and spacecraft.

 Read the full article

  See all articles in the same topic Create my own version