### Inclination, the Z factor

The

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.

Cardinal longitudes

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

with no quadrant ambiguity.

**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.

Cardinal longitudes

**Reference longitude (0°);**common convention, reference longitude always points to q, perihelion,shortest distance from Sol to the orbit.- L
- Q
- 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/√(a

^{2}+ b

^{2})

- cos(Ω) = -b/√(a

^{2}+ b

^{2})

with no quadrant ambiguity.

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