SGC Table of Contents

Shuster Galactic Coordinate (SGC) System

A four coordinate spatial / time system defining interstellar space, direction of travel and precise locations of stars, other interstellar objects and vehicles.


(Please do ask if you need an older Excel version of the spreadsheets)

  1. This SGC paper, which are all the web pages (self extracting zip file for Windows) (441 KB)
  2. This SGC paper plus the spreadsheets, both SGC Tri-Coordinate Calculator and SGC Interstellar distance spreadsheet (self extracting zip file for Windows) (597 KB)
  3. The SGC Tri-Coordinate Calculator (Non zipped - Excel 97 .xls spreadsheet for Mac or Windows) (140 KB)
  4. The SGC Interstellar distance spreadsheet (Non zipped - Excel 97 .xls spreadsheet for Mac or Windows) (241 KB)



Spreadsheets

The Excel 97 spreadsheets links are available only with the downloaded version (when you order # 2 above), which you may request for free by sending an .  To conserve space, the online version does not include the spreadsheets.


The links below work either online, or with the downloaded version.

Title Page

Links to a stellar database, 2d charts, 3D charts and a VRML world of the local stars.

 
What is SGC?
 
• Just the 3D Graph of the local stars
 

1.0 Principal of the SGC System

1.1 SGC Coordinate System - General Rules
 
• Formula 1.1.1: Example of a segment notated | formula_only
• Graph 1.1.2: A triangle showing how an angle may be defined | graph_only
1.2 SGC - Galactic declination - defined
 
1.3 SGC - Galactic Right Ascension - defined

1.4 SGC - Formulae and Examples - methods used

1.5 SGC - Standards and Abbreviations

 

2.0 SGC Tri-Coordinates

3.0 The Time Coordinate

• Illustration 3.0.1: Showing T-Coordinate changes depending on viewpoint | illustration_only

 
  • 3.1 Waypoints and the T-Coordinate

  •  
    • Illustration 3.1.1: Trip to Sirius via Alpha Centauri (illustration_only)

     

    4.0 Galactic Proper Motion

    • Table 4.0.1: Showing data for Galactic Proper Motion
     • Illustration 4.0.2: Showing the difference between Earth polar and galactic polar | illustration_only
     • Graph 4.0.3: Sample stellar positions showing the direction of Proper Motion based on both Earth Polar and Galactic Polar. | graph_only


    4.1 Formulae to find the stellar angle of Proper Motion based on galactic polar
     

    • Formulae 4.1.1: Finding the galactic angle of Proper Motion
    • Formula 4.1.2: Finding the cosine of angle v, the angle between the Earth Pole and the Galactic pole | formula_only
    • Formula 4.1.3 & 4.1.4: Attempts to find the galactic angle of Proper Motion.
    • Formulae 4.1.5 & 4.1.6: Attempts to find the galactic angle of Proper Motion when it appears greater than 360 degrees
    • Table 4.1.7: Showing all solutions to resolve galactic angle of Proper Motion

    5.0 Annual Shifts

    5.1 Formulae to find the Annual Shifts
      • Table 5.1.1: Information needed to calculate Annual Shifts
    • Graph 5.1.2: Showing data required to resolve Annual Shifts | graph_only
    • Table 5.1.3: Formulae to resolve galactic Right Ascension and galactic declination change of a star after 1 year for all possible values of the angle of galactic Proper Motion (Graphs showing example solutions for galactic declination are included)
    • Graph 5.1.4: showing one possible solution for resolving change in galactic Right Ascension after 1 year | graph_only


    5.2 Distance of Annual Shifts
     

    • Formula 5.2.1: Distance from the SGC center to the star (ASD1 ) after one year of movement
    • Formulae 5.2.2: Finding Annual Shifts (XAS, YAS, ZAS and TAS) from SGC coordinates changes


    5.3 Real Position Values
     

     • Formulae 5.3.1: Find the real position values of a star.
     • Formulae 5.3.2: Find the real distance to a star.

    6.0 Using the SGC system to resolve problems in navigation

    6.1 Finding distances from SGC values
     
    • Table 6.1.1: Point Abbreviations: Real and apparent SGC point positions, distances and course angles defined
     • Formula 6.1.2: Hypotenuse rule for 3D coordinates | formula_only
    • Formula 6.1.3: Find the exact arrival time for average velocity | formula_only
    • Formula 6.1.4: Find the Real Stellar Distance, (RSD) from a mid-mission point to a star | formula_only
    • Graph 6.1.5: Showing various points to resolve mid-mission navigational problems
    | graph_only
    • Formula 6.1.6: Find the Apparent Stellar Distance, (ASD) from a mid-mission point to a star | formula_only_part_1 | formula_only_part_2 | formula_only_part_3 | formula_only_part_4
    • Formula 6.1.7: Find the Real Stellar Distance, (RSD) between two stars | formula_only
    • Graph 6.1.8: Showing the the Apparent Stellar Distance, (ASD) between a star and a mid-mission point
    | graph_only
    • Formula 6.1.9: Find the Real Stellar Distance, (RSD), and Apparent SGC coordinates of a star as viewed from a starship | formula_only_Part_1 | formula_only_Part_2 | formula_only_Part_3 | formula_only_Part_4
    • Formula 6.1.10: Find the Apparent Stellar Distance, (ASD) between a starship and a star | formula_only


    6.2 Finding galactic course values from SGC values
     

    • Table 6.2.1: SGC values transferred to Galactic Right Ascension (Gr)
    • Table 6.2.2: SGC values transferred to Galactic declination, (Gd))


    6.3 Example 1 - Find the galactic Right Ascension, (Gr) and the galactic declination, (Gd) of a star viewed from 0,0,0 with only the X, Y and Z coordinates
     

    • Formula 6.3.1: Given star X, Y and Z coordinates
    • Formula 6.3.2: Find the Gr of the star
    • Formula 6.3.3: Find the Gd of the star
    6.4 Example 2 - Find the galactic Right Ascension, (Gr) and the galactic declination, (Gd) for both the Real Stellar Position, (RSP) and the Apparent Stellar Position, (ASP) of a star as viewed from a mid-mission point
     
    • Formulae 6.4.1 and 6.4.2: Given mid-mission point and star's X, Y and Z coordinates
    • Formula 6.4.3: Find the Real Stellar Distance, (RSD) between mid-mission point and star
    • Formula 6.4.4: Find the Gr from the mid-mission point to the RSP of the star
    • Formula 6.4.5: Find the Gd from the mid-mission point to the RSP of the star
    • Formula 6.4.6: To find the apparent X, Y and Z coordinates of the star as viewed from the mid-mission point
    • Formula 6.4.7: Insert example values to formula 6.4.6
    • Formula 6.4.8: Find the ASD of the star as viewed from the mid-mission point
    • Formula 6.4.9: Find the apparent Gr of the star as viewed from the mid-mission point
    • Formula 6.4.10: Find the apparent Gd of the star as viewed from the mid-mission point


    6.5 Example 3 - Find the NPI for a mission to Lalande 25372
     

    • Graph 6.5.1: Showing points and angles needed to find the NPI | graph_only
    • Formulae 6.5.2: Solution to find mission distance and mission time for graph 6.5.1
    • Formulae 6.5.3: Reduction of formulae in 6.5.2 | Formulae_only
    • Formulae 6.5.4: Restating formulae 6.5.2 in SGC values | Formulae_only
    • Formulae 6.5.5: Resolving values for the starship's velocity and the Radial movement of the star | Formulae_only
    • Formulae 6.5.6: Substituting example values to solve formulae 6.5.4 and 6.5.5 | Formulae_only (work in progress)
    • Formulae 6.5.7: Find SGC coordinates for NPI | Formulae_only (work in progress)


    6.6 Summary

    7.0 Estimated Deviations

    7.1 Proper Motion and Radial Velocity
     
    • Table 7.1.1: Apparent Motion of stars as viewed from our Solar System at 0,0,0 over extremely long observation


    7.2 Special cases

    7.3 The problem of the validity of any measurements for deviation in the galactic orbit

    7.4 Using the SGC system to find a galactic orbit
     

    • Formula 7.4.1: Finding a galactic orbital speed of a star using SGC | formula_only
    • Formula 7.4.2: Reduction of 7.4.1 | formula_only


    7.5 Overall Error of Measurement

    8.0 Relativity changes

    • Formula 8.0.1: Showing the bending of the light rays toward the center due to acceleration | formula_only
    • Formula 8.0.2: Einstein's time dilation | formula_only
    • Formula 8.0.3: Einstein's time dilation reduced to T coordinate only | formula_only

    9.0 Changes in Curvature of Space-time

    Appendix A - Acronyms

    Appendix B - References

     

    Last updated: October 3, 2002  |