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)

This SGC paper, which are all the web pages (self extracting zip file
for Windows) (441 KB)

This SGC paper plus the spreadsheets, both SGC TriCoordinate Calculator
and SGC Interstellar distance spreadsheet (self extracting zip file
for Windows) (597 KB)

The SGC TriCoordinate Calculator (Non zipped  Excel 97 .xls spreadsheet
for Mac or Windows) (140 KB)

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.

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

1.1 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

• Illustration 3.0.1: Showing TCoordinate changes
depending on viewpoint  illustration_only
3.1 Waypoints and the TCoordinate
• Illustration 3.1.1: Trip to Sirius via Alpha Centauri
(illustration_only)

• 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
5.1 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.
6.1 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 midmission point to a star  formula_only
• Graph 6.1.5: Showing various points to resolve
midmission navigational problems
 graph_only
• Formula 6.1.6: Find the Apparent Stellar Distance,
(ASD) from a midmission 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 midmission 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 midmission point

• Formulae 6.4.1 and 6.4.2: Given midmission point
and star's X, Y and Z coordinates

• Formula 6.4.3: Find the Real Stellar Distance,
(RSD) between midmission point and star

• Formula 6.4.4: Find the Gr from the midmission
point to the RSP of the star
• Formula 6.4.5: Find the Gd from the midmission
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 midmission 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 midmission point
• Formula 6.4.9: Find the apparent Gr of the
star as viewed from the midmission point
• Formula 6.4.10: Find the apparent Gd of the
star as viewed from the midmission 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
7.1 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

• 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
Last updated: October 3, 2002 