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:

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°



  • The galactic equator will be 90°



  • The galactic south pole will be 180°
  • 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.

     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.

    Forward to Chapter 2 - SGC Tri-Coordinates

    Title Page for SGC | Table of Contents | The Appendix
    Last updated: October 3, 2002  |