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Argument of periapsis

 

 
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Argument of periapsis
 
 
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The argument of periapsis (or argument of perifocus) (?) is the orbital element describing the angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
 of an orbit
ORBit

ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
ing body's periapsis
Apsis

In celestial mechanics, an apsis, plural apsides is the point of greatest or least distance of the elliptical orbit of an object from its center of attraction, which is generally the center of mass of the system....
 (the point of closest approach to the central body), relative to its ascending node (the point where the body crosses the plane of reference
Plane of reference

A term used in celestial mechanics, the plane of reference is the plane by means of which orbital elements are defined. The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longitude of the ascending node....
 from South to North). The angle is measured in the orbital plane
Orbital plane (astronomy)

The orbital plane of an object orbiting another is the geometrical Plane in which the orbit is embedding. Three points in space suffice to define the orbital plane....
 and in the direction of motion. (For specific types of orbits, words such as "perihelion" (for Sun
Sun

The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
-centered orbits), "perigee" (for Earth
Earth

Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
-centered orbits), "pericenter" (general), etc.






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The argument of periapsis (or argument of perifocus) (?) is the orbital element describing the angle
Angle

In geometry and trigonometry, an angle is the figure formed by two Ray sharing a common endpoint, called the vertex of the angle . The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide...
 of an orbit
ORBit

ORBit is a Common Object Request Broker Architecture 2.4 compliant Object Request Broker . It features mature C , C++ and Python bindings, and less developed bindings for Perl, Lisp , Pascal , Ruby , and Tcl....
ing body's periapsis
Apsis

In celestial mechanics, an apsis, plural apsides is the point of greatest or least distance of the elliptical orbit of an object from its center of attraction, which is generally the center of mass of the system....
 (the point of closest approach to the central body), relative to its ascending node (the point where the body crosses the plane of reference
Plane of reference

A term used in celestial mechanics, the plane of reference is the plane by means of which orbital elements are defined. The two main orbital elements that are measured with respect to the plane of reference are the inclination and the longitude of the ascending node....
 from South to North). The angle is measured in the orbital plane
Orbital plane (astronomy)

The orbital plane of an object orbiting another is the geometrical Plane in which the orbit is embedding. Three points in space suffice to define the orbital plane....
 and in the direction of motion. (For specific types of orbits, words such as "perihelion" (for Sun
Sun

The Sun , a G V star, is the star at the center of the Solar System. The Earth and other matter orbit the Sun, which by itself accounts for about 98.6% of the Solar System's mass....
-centered orbits), "perigee" (for Earth
Earth

Earth is the third planet from the Sun. Earth is the largest of the terrestrial planets in the Solar System in diameter, mass and density. It is also referred to as the World and Wiktionary:Terra.Note that by International Astronomical Union convention, the term "Terra" is used for naming extensive land masses, rather...
-centered orbits), "pericenter" (general), etc. may replace the word "periapsis". See apsis
Apsis

In celestial mechanics, an apsis, plural apsides is the point of greatest or least distance of the elliptical orbit of an object from its center of attraction, which is generally the center of mass of the system....
 for more information.)

An argument of periapsis of 0° means that the orbiting body will be at its closest approach to the central body at the same moment that it crosses the plane of reference from South to North. An argument of periapsis of 90° means that the orbiting body will reach periapsis at its northmost distance from the plane of reference.

Adding the argument of periapsis to the longitude of the ascending node
Longitude of the ascending node

The longitude of the ascending node is one of the orbital elements used to specify the orbit of an object in space. It is the angle from a reference direction, called the origin of longitude, to the direction of the ascending node, measured in a reference plane....
 gives the longitude of the periapsis
Longitude of the periapsis

In astrodynamics, the longitude of the periapsis of an orbiting body is the longitude at which the periapsis would occur if the body's inclination were zero....
.




Calculation

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 argument of periapsis ? can be calculated as follows:

where:
  • is the vector pointing towards the ascending node (i.e. the z-component of is zero),
  • is the eccentricity vector
    Eccentricity vector

    In astrodynamics, the eccentricity vector of a conic section orbit is the vector pointing towards the periapsis and with magnitude equal to the orbit's scalar eccentricity ....
     (the vector pointing towards the periapsis).


In the case of equatorial orbits, though the argument is strictly undefined, it is often assumed that:

where:

  • is x-component of the eccentricity vector


In the case of circular orbits it is often assumed that the periapsis is placed at the ascending node and therefore ?=0.

See also

  • Kepler orbit
    Kepler orbit

    In celestial mechanics, a Kepler orbit describes the motion of an orbiting body as an ellipse, parabola, or hyperbola, which forms a two-dimensional orbital plane in three-dimensional space....
    s
  • Orbital node
    Orbital node

    An orbital node is one of the two points where an orbit crosses a plane of reference which it is inclined to. An orbit which is contained in the plane of reference has no nodes....
  • Orbital mechanics


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