Sunday, October 12, 2008

REFERENCE: Orbital Elements

File:Orbit1.svgSix Classic Orbital Elements.
SymbolNameDescription
a
Semi-major axisOrbit size
e
EccentricityOrbit shape
I
Inclination Intersection angle of 2 planes: asteroid and Ecliptic.
Ω
Right Ascension of ascending node. Swivel angle from vernal equinox to ascending node.
ω
Argument of perihelionAngle from ascending node to perihelion
ν
True anomaly Angle from perihelion to object's position
Source: UNDERSTANDING SPACE,
An Introduction to Astronautics;

by Jerry Jon Sellers et al. See page 161, Table 5-3.
REFERENCE PLANE: ECLIPTIC
For the Solar System, the reference plane is usually the Ecliptic, the plane in which the Earth orbits the Sun. 

Above view presumes observation from North of Earth; thus, direction of revolution is Counter Clock-Wise (CCW) around Sol.  

First point of Aries is determined by position of Earth during Vernal Equinox (about March 20).  Over the centuries, this position moves; thus, it used to point to the Aries constellation, but it now points toward Sagittarius.
OTHER SOLAR ORBITS INTERSECT
AXIOM:  In the Solar System, most asteroidal objects must orbit Sol, our sun.  However, most of these orbits are not co-located with Earth's orbit in the Ecliptic; thus, virtually all other Solar orbits are tilted with respect to Earth's orbit, and they must pass through the Ecliptic.  

At one point, the orbit pierces the Ecliptic as object ascends from South to North (Ascending Point ).  At another point, the orbit again pierces the Ecliptic as it descends from North to South (Descending Point ). 

"Line of nodes" connects    with  ☋, the line of intersection between two planes.  TE assumes Sol normally to be on this line between the two nodes.
CLOSEST AND FARTHEST POINTS
A solar orbit has both perihelion, q, nearest distance to Sol, and aphelion, Q, farthest distance from Sol.

AXIOM:  Q and q are seldom equal; thus, the line of nodes is seldom at the center of an orbit.



A typical asteroidal orbit can best be described with six orbital elements which specify its shape and orientation compared to the ecliptic. These elements are briefly described below:
FIRST TWO ORBITAL ELEMENTS
First two elements define the size and shape of the asteroid’s elliptical orbit:
1.     Semimajor axis (a)—longest distance from orbit’s center to any orbital point; it averages perihelion (q) and aphelion (Q) distances, [a = (q+Q)/2].
2.     Eccentricity (e)—measures orbit’s elongation compared to a circle; the quotient of the difference of Q and q by their sum. [e = (Q-q)/(Q+q)].
NEXT TWO ELEMENTS
Next two elements orientate the asteroid's orbital plane with respect to the Solar Ecliptic:
3.     Inclination (i)—angular tilt of the asteroid’s orbital plane with respect to the ecliptic. At the ascending node (), where the orbit passes upward through the reference plane, inclination (0° to 90°) measures from the ecliptic to the orbital plane.
4.     Longitude of the ascending node (Ω) —enables us to precisely place the orbit’s ascending node () (where orbit’s path passes upward through the Solar ecliptic).  Ω is an angle, measured counterclockwise (CCW) from 0° to 360° on the Solar Ecliptic.  It starts from the First Point of Aries ︎ and proceeds to a notional ray from Sol to the ascending node.
FINAL TWO ORBITAL ELEMENTS
Final two elements enable us to find the asteroid’s precise location on its orbit:

5.     Argument of perihelion (ω)—defines the orientation of the elliptical orbit in the orbital plane. ω is an angle from the ascending node to the perihelion (the closest point the orbiting object comes to Sol). It is measured in the direction of motion (most Solar objects travel CCW as observed north of the ecliptic). 
6.     True anomaly (ν or θ)—defines the position of the orbiting body along the ellipse at a specific time.  Of the six elements, this is the only variable; it changes value as object travels throughout its orbit; five other elements stay virtually constant.

For much more on orbital basics.





VOLUME 0: ELEVATIONAL
VOLUME I: ASTEROIDAL
VOLUME II: INTERPLANETARY
VOLUME III: INTERSTELLAR




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