1.0 Principle of the SGC System
The principle of the SGC system is to be a self contained galactic
four dimensional inertial coordinate system. The SGC system can
resolve a multitude of interstellar navigational problems while always
maintaining an easy reference to the zero coordinates of a current Earth.
SGC coordinates are given in spatial X,Y,Z
and T (time). The SGC system offers a connecting reference
to the accepted, existing readings for Right Ascension and declination.
The SGC system will use galactic Right Ascension and galactic declination
readings for all course settings between any two objects.
The SGC system can differentiate from positions of stars
viewed from other locations and the actual positions of the stars. This
feature allows for easier automatic computation of stellar locations viewed
from positions other than our solar system. In addition, SGC Coordinates
can be used to track positional changes of any moving body.
The SGC system resolves the ambiguity of other inertial
coordinate systems because the statistical character of the values of the
coordinates are not limited by errors in observation from multiple viewpoints.
As improved measurements of stellar distances and motions are made, adjustments
may be added to each star's motion in SGC coordinates. Such improvements
will also agree automatically with all other observed views of the star
within the SGC coordinate boundary. This achieves a true coordinate
system independent from place of observation.
Due to the complicated nature of this paper, I have added a overview
at the beginning of each chapter. The reader should be able to get a fair
understanding by reading only these sections which can be found above the
SGC divider below.
1.1 SGC Coordinate System - General Rules
The SGC system is heliocentric (origin being the solar system's
barycenter), right handed (coordinates progress clockwise as seen from
Earth looking up at the galactic pole Z coordinate). This matches
the direction of movement of the Right Ascension value, growing larger
in an easterly direction as viewed from Earth.
SGC values are given in X, Y, Z spatial
coordinates and a T - Time Coordinate. These values allow precise
three dimensional charting of stars and their movements over a period of
time. The various types of values are:
Stellar positions referred to as points - without SGC coordinates.
Sometimes it will be easier to refer to stars simply as a point. This could
mean that the coordinates are unknown or were already stated in previous
formulae. Such steller positions will be referred to as any single capital
bold letter, D while previous or future positions of this particular
star will be referred to as; D1,
Apparent coordinates refer to the star as viewed from another location.
(Strictly speaking, this will always be the case unless one is viewing
the star from the it's surface). Apparent coordinates will be referred
to using either no subscript number or a single subscript number; X,
T or X1, Y1,
Z1 and T1.
Apparent coordinates may also be prefaced with the
location of the viewpoint. This is required when there are multiple viewpoints
in an example. This is covered in detail in 6.1.1.
Real coordinates refer to the actual true position of the star at
the star's location. These coordinates discount all effects of positional
shifting due to the speed of light limit. Real coordinates will be referred
to using a subscript letter r; Xr,
Zr and Tr.
Distances will be referred to as a three letter abbreviation in
bold such as ASD (Apparent Stellar Distance) or within a formula
sometimes referred to as the first distance d1, the second
distance d2, etc.
Segments or arcs between to coordinate points may be referred to
with their end points under a line. The segment defined as the line between
the position for 0,0,0, E1 and it's a point along a Z
axis Z1 would then be shown as the segment:
Angles used in formulae will be usually designated as an italizied
letter, such as a, or Greek letter, such as .
Occasionally, to make the graphs less cluttered, an angle may be referred
to in the text by the three points that define it. In the example graph
1.1.2, D1MD2 describe the angle near point M,
shown in the red arc. In some graphs in this paper, angles may be referred
to in this fashion without showing an arc or name.
Angles used for positional orientation - Galactic declination and Galactic
Right Ascension. (see sections 1.2 and 1.3 below for
more details.) Eamples of such angles are:
Gd = The apparent galactic declination of a star.
Gd1 = The apparent galactic declination of a star after
Gdr = The real galactic declination of a star.
Gr = The apparent galactic Right Ascension of a star.
Gr1 = The apparent galactic Right Ascension of a star after
Grr = The real galactic declination of a star.
The SGC system keeps agreement between all Apparent and Real coordinates,
that is to say, these two types of coordinates are part of the same system
and simply show the star's position with different time coordinates. The
SGC system can only show a star in two different spatial coordinates
if the time coordinate is different. Conversely, for any one time coordinate,
the star will have one set of spatial coordinates. The SGC system
does not allow for any star to be in more than one place at any one time
coordinate, regardless from where it is observed.
1.2 SGC - Galactic declination - defined
The values of declination based on Earth Polar (d) are transferred
to declination based on galatic polar. (The defintion of apparent galactic
declination can be found in section 2.2
and real galactic declination defined is in section 5.3.)
The SGC system will state galactic declination differently than
the Earth polar declination as follows:
Straight up to galactic polar Z axis will be 0°
This change from the standard Earth Polar declination of the north pole
= +90°, equator = 0° and south pole = -90° has been done to
simplify calculations. It is my belief that the positive and negative declination
values for Earth polar have been traditionally used because of the nature
of earthbound astronomical observations, the northern hemisphere having
an extreamly limited view of the southern sky and vice versa. Since this
problem would not exist in outer space, removing the plus and minus values
and replacing them with 0° to 180° will remove the need to recalculate
angles above 90° to negative values.
The galactic equator will be 90°
The galactic south pole will be 180°
Note: Galactic declination Gd will be given in decimal
rather than using minutes and seconds of an arc.
1.3 SGC - Galactic Right Ascension - definedThe SGC galactic
Right Ascension will be calculated from the current Right Ascension of
a star based on the Earth Polar. The galactic Right Ascension will be given
in degrees rather than hours and minutes. This will help facilitate calculations
with the SGC system. The possible values will be; including 0°
but less than 360°.
Note: Galactic Right Ascension Gr will be given
in decimal rather than using minutes and seconds of an arc.
1.4 SGC - Formulae and Examples - methods used
The following paper will show the details of the SGC system. I have
chosen to make solutions in spherical trigonometry rather than matrices
so examples may be more easily shown in a graph. In some cases this has
added artificial variables to the formulae, but, I believe, that this will
make the concepts of the SGC system easier to understand. (I would
welcome any comments from those who prefer working in matrices, as to how
I might otherwise present this paper.)
1.5 SGC - Standards and Abbreviations
All names and values will be italicized or referred to in abbreviated form
using two or three capital letters, or for angles, italizied Greek letters.
The Appendix has a complete list of all terms used including alternate
names commonly used.
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Last updated: October 3, 2002 |