Specific relative angular momentum

See also: Classical central-force problem

The specific relative angular momentum (h) is also known as the areal momentum (defined as the product of mass and areal velocity).

In astrodynamics, the specific relative angular momentum of two orbiting bodies is the vector product of the relative position and the relative velocity. Equivalently, it is the total angular momentum divided by the reduced mass.^[1] Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem.

Contents 1 Definition 2 Elliptical orbit 3 See also 4 References

Definition

Specific relative angular momentum, represented by the symbol , is defined as the cross product of the relative position vector and the relative velocity vector .

where:

• is the relative orbital position vector
• is the relative orbital velocity vector
• is the total angular momentum of the system
• is the reduced mass

The units of are m²s⁻¹.

For unperturbed orbits the vector is always perpendicular to the fixed orbital plane. However, for perturbed orbits the vector is generally not perpendicular to the osculating orbital plane

As usual in physics, the magnitude of the vector quantity is denoted by :

Elliptical orbit

In an elliptical orbit, the specific relative angular momentum is twice the area per unit time swept out by a chord from the primary to the secondary: this area is referred to by Kepler's second law of planetary motion.

Since the area of the entire orbital ellipse is swept out in one orbital period, is equal to twice the area of the ellipse divided by the orbital period, giving the equation

.

where

• is the semi-major axis
• is the semi-minor axis
• is the semi-latus rectum
• is the gravitational constant
• , are the two masses.

See also

• Kepler's laws of planetary motion
• Kepler orbit

Orbits   Orbits General Box Capture Circular Elliptical / Highly elliptical Escape Graveyard Hyperbolic trajectory Inclined / Non-inclined Osculating Parabolic trajectory Parking Synchronous (semi sub) Geocentric Geosynchronous Geostationary Sun-synchronous Low Earth Medium Earth High Earth Molniya Near-equatorial Orbit of the Moon Polar Tundra Two-line elements About other points Areosynchronous Areostationary Halo Lissajous Lunar Heliocentric Heliosynchronous   Parameters Classical  Inclination  Longitude of the ascending node  Eccentricity  Argument of periapsis  Semi-major axis  Mean anomaly at epoch Other  True anomaly  Semi-minor axis  Linear eccentricity  Eccentric anomaly  Mean longitude  True longitude  Orbital period   Maneuvers Bi-elliptic transfer Delta-v budget Geostationary transfer Gravity assist Gravity turn Hohmann transfer Low energy transfer Oberth effect Inclination change Phasing Rendezvous Transposition, docking, and extraction Collision avoidance (spacecraft)   Other orbital mechanics topics Apsis Celestial coordinate system Characteristic energy Direct motion Epoch Ephemeris Equatorial coordinate system Ground track Interplanetary Transport Network Kepler's laws of planetary motion Lagrangian point n-body problem Orbit equation Orbital speed Orbital state vectors Perturbation Retrograde motion Specific orbital energy Specific relative angular momentum List of orbits

References