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Specific relative angular momentum

 

 
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Specific relative angular momentum
 
 
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In astrodynamicsAstrodynamics Overview

Astrodynamics is the study of the motion of rockets, missiles, and space vehicles, as determined from Sir Isaac Newton's law...
, the specific relative angular momentum of an orbiting bodyOrbiting body

In astrodynamics, an orbiting body is a body that orbits central body....
 with respect to a central bodyCentral body

In astrodynamics a central body is a body that is being orbited by orbiting body....
 is the relative angular momentumRelative angular momentum

In astrodynamics relative angular momentum of orbiting body relative to central body is the moment of's relative linear mome...
 of the first body per unitUnits of measurement

The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early...
 massMass

Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to....
. Specific relative angular momentum plays a pivotal role in definition of orbit equationFacts About Orbit equation

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying ...
s.

Definition

Specific relative angular momentum, represented by the symbol , is defined as the cross productCross product

In mathematics, the cross product is a binary operation on vectors in a three-dimensional Euclidean space....
 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 massMass

    Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to....
     of the orbiting body, and
  • is the relative angular momentumRelative angular momentum

    In astrodynamics relative angular momentum of orbiting body relative to central body is the moment of's relative linear mome...
     of the orbiting body with respect to the central body.


The units of are m2s-1.

Under standard assumptionsStandard assumptions in astrodynamics Overview

For most of the problems in astrodynamics involving two bodies and standard assumptions are usually the following:...
 for an orbiting bodyOrbiting body

In astrodynamics, an orbiting body is a body that orbits central body....
 in a trajectory around central bodyCentral body

In astrodynamics a central body is a body that is being orbited by orbiting body....
 at any given time the vector is perpendicular to the osculating orbital plane defined by orbital position  and velocity vectors.

As usual in physics, the magnitudeMagnitude (mathematics)

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of th...
 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 from the central mass to the orbiting body: this area is that referred to by Kepler's second law of planetary motion.

Since the area of the entire ellipse of the orbit is swept out in one orbital periodOrbital period

The orbital period is the time it takes a planet to make one full orbit....
, is equal to twice the area of the ellipse divided by the orbital period, giving the equation

.

where
  • is semi-major axisSemi-major axis

    In geometry, the term semi-major axis is used to describe the dimensions of ellipses and hyperbolae. ...
  • is semi-minor axisSemi-minor axis

    In geometry, the semi-minor axis is a line segment associated with most conic sections....
  • is standard gravitational parameterStandard gravitational parameter

    In astrodynamics, the standard gravitational parameter of a celestial body is the product of the gravitational constant an...


See also

  • Kepler's laws of planetary motionKepler's laws of planetary motion

    Johannes Kepler's primary contributions to astronomy/astrophysics were his three laws of planetary motion....
  • Planetary orbitPlanetary orbit

    In physics, an orbit is the path that an object makes around another object while under the influence of a source of centrip...