## 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.

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)

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.

## 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

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

## 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
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

## 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

## Appendix B - References

Last updated: October 3, 2002  |