Thursday, November 01, 2012

Inclination, the Z factor

The argument of perihelion is the angle between an orbiting body's  perihelion (q, closest point to Sol) and its ascending node. The ascending node is one of two places where an orbiting object passes through the ecliptic, an imaginary plane of Earth's orbit about Sol.As the zero-point for coordinates on the Celestial Sphere,
First Point of Aries is always zero hours Right Ascension
and zero degrees Declination. It is one
of only two points on the Celestial Sphere
where the Ecliptic and the Celestial Equator intersect.
The angle is measured in the orbital plane and in the direction of motion. For specific types of orbits, words such as "perihelion" (for Sun-centered orbits), "perigee" (for Earth-centered orbits), "pericenter" (general), etc. may replace the word "periapsis".
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.

Fig. 1: Diagram of orbital elements, including the argument of periapsis (ω).
Cardinal longitudes

  • Reference longitude (0°); common convention, reference longitude always points to q, perihelion,shortest distance from Sol to the orbit.
  •  L 
  • other L
  •  back to ref



http://astrowww.phys.uvic.ca/~tatum/celmechs/celm10.pdf (pg 23) The next element to yield is the longitude of the ascending node, for the plane intersects the ecliptic at Z = 0 in the line aX + bY = 0, from which we get:

    sin(Ω) = a/(a2 + b2)

     cos(Ω) = -b/(a2 + b2)
Eq. 10.10.9a,b
with no quadrant ambiguity.

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