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Specific relative angular momentum

 

 
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Specific relative angular momentum
 
 
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In astrodynamics
Astrodynamics

Orbital mechanics or astrodynamics is the application of celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft....
, the specific relative angular momentum of an orbiting body
Orbiting body

In astrodynamics, an orbiting body is a body that orbits central body . Under standard assumptions in astrodynamics:* it is less massive than the central body by several orders of magnitude ....
 with respect to a central body
Central body

In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
 is the relative angular momentum
Relative angular momentum

In astrodynamics, the relative angular momentum of an orbiting body relative to a central body is the moment of 's relative linear momentum:...
 of the first body per unit
Units of measurement

The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day....
 mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
. Specific relative angular momentum plays a pivotal role in definition of orbit equation
Orbit equation

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








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In astrodynamics
Astrodynamics

Orbital mechanics or astrodynamics is the application of celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft....
, the specific relative angular momentum of an orbiting body
Orbiting body

In astrodynamics, an orbiting body is a body that orbits central body . Under standard assumptions in astrodynamics:* it is less massive than the central body by several orders of magnitude ....
 with respect to a central body
Central body

In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
 is the relative angular momentum
Relative angular momentum

In astrodynamics, the relative angular momentum of an orbiting body relative to a central body is the moment of 's relative linear momentum:...
 of the first body per unit
Units of measurement

The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day....
 mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
. Specific relative angular momentum plays a pivotal role in definition of orbit equation
Orbit equation

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

Definition

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

In mathematics, the cross product is a binary operation on two vector s in a three-dimensional Euclidean space that results in another vector which is orthogonal to the plane containing the two input vectors....
 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 mass
    Mass

    In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
     of the orbiting body, and
  • is the relative angular momentum
    Relative angular momentum

    In astrodynamics, the relative angular momentum of an orbiting body relative to a central body is the moment of 's relative linear momentum:...
     of the orbiting body with respect to the central body.


The units of are m2s-1.

Under standard assumptions
Standard assumptions in astrodynamics

For most of the problems in astrodynamics involving two bodies and standard assumptions in astrodynamics are usually the following:*A1: and are the only objects in the universe and thus influence of other objects is disregarded,...
 for an orbiting body
Orbiting body

In astrodynamics, an orbiting body is a body that orbits central body . Under standard assumptions in astrodynamics:* it is less massive than the central body by several orders of magnitude ....
 in a trajectory around central body
Central body

In astrodynamics a central body is a body that is being orbited by an orbiting body . Under standard assumptions in astrodynamics:* it is more massive than the orbiting body by several orders of magnitude ,...
 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 magnitude
Magnitude (mathematics)

The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs....
 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 period
Orbital period

The orbital Periodicity is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars....
, is equal to twice the area of the ellipse divided by the orbital period, giving the equation

.

where
  • is semi-major axis
    Semi-major axis

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

    In geometry, the semi-minor axis is a line segment associated with most conic sections . One end of the segment is the center of the conic section, and it is at right angles with the semi-major axis....
  • is standard gravitational parameter
    Standard gravitational parameter

    In astrodynamics, the standard gravitational parameter of a celestial body is the product of the gravitational constant and the mass :The units of the standard gravitational parameter are km3s-2...


See also


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

    In astronomy, Kepler's three laws of planetary motion are*"The orbit of every planet is an ellipse with the sun at a Focus ."*"A line joining a planet and the sun sweeps out equal areas during equal intervals of time."...
  • Planetary orbit
    Planetary orbit

    In physics, an orbit is the gravitationally curved path of one object around a point or another body, for example the gravitational orbit of a planet around a star....