Logbook entry

WK1: Returning Home - Galaxy Navigation & Long Range Route Planning

Galaxy Navigation
The Galaxy Map divides the Milky Way into four quadrants with Sol centered at the origin.  Cartesian coordinates are used to navigate the galaxy map with the X and Z axis parallel to the horizontal plane of the galaxy, and the Y axis perpendicular.  The axis are measured in light years.  In general, these coordinates can be ignored as the navigation computer can report your current distance to any selected destination. However, it is useful to know route lengths between points for long range route planning.

Using vector algebra we can determine the distance between two sets of coordinates.  For example Beagle Point is located at -1,111.5625 / -134.21875 / 65,269.75.  My two potential destinations are:

• Stuemeae FG-Y d7561 (Explorer's Anchorage) at 28.6875 / -19.78125 / 25,899.6875
• Colonia (Jaques Station / Animula Spires / The Mosta-Murdoch Raceway) at -9,530.5 / -910.28125 / 19,808.125

By subtracting the destination coordinates from the source coordinates we arrive at the vectors to each destination.  We then calculate the magnitude of that vector using M² = X² + Y² + Z².

For Beagle to Explorer's Anchorage:
C_EA - C_BP = V_BP-EA
[29 / -20 / 25,900] - [-1,112 / -134 / 65,270] = [1,140 / 114 / -39,370]
M_BP-EA² = 1140² + 114² + 39370²
M_BP-EA = 39,387 Ly

Explorer's Anchorage to Colonia:
C_C - C_EA = V_EA-C
[-9,531 / -910 / 19,808] - [29 / -20 / 25,900] = [-9560 / -890 / -6092]
M_EA-C² = 9560² + 890² + 6092²
M_EA-C =  11,371 Ly

For Beagle to Colonia:
C_C - C_BP = V_BP-C
[-9,531 / -910 / 19,808] - [-1,112 / -134 / 65,270] = [-8419 / -776 / -45462]
M_BP-C² = 8419² + 776² + 45462²
M_BP-C = 46,241 Ly

Traveling directly to Colonia will take 46,241Ly instead of 50,758Ly saving 4,517 Ly, or 8.9%. While that appears to be a small improvement given the total distance of the return journey, some of the waypoints during the Distant Worlds expedition were themselves only 5k Ly.   Assuming a modest travel rate of 5,000 Ly per week, we should arrive in Colonia in approximate 9.25 weeks. 

Long Range Route Planning
Calculating the best route and plotting it are two different things entirely.  The navigation computer appears to have a hard limit of 20k Ly, however it often fails to plot routes at much shorter distances.  Best practices is to plot routes at 5k-10k Ly at a time.  To maximize efficiency, we should aim to plot a course as straight as possible to our destination.  That means that each waypoint should lie along the calculated vector.

To calculate waypoint coordinates, we will scale our destination vector to 5k Ly and add our scaled vector to our current coordinates:
C_ScaleFactor = M_Waypoint / M_BP-C
C_ScaleFactor = 5000 / 46241
C_ScaleFactor  = 0.108

V_Waypoint = V_BP-C * C_ScaleFactor
V_Waypoint = [-8,419 / -776 / -45,462] * 0.108
V_Waypoint = [-909 / 84 / -4,910]

C_Waypoint = C_BP + V_Waypoint
C_Waypoint = [29 / -20 / 25,900] + [-909 / 84 / -4,910]
C_Waypoint = [-880 / 64 / 20,990]

Since we are rounding, you will find the the solution above does not provide a perfectly straight line toward our destination, however increasing waypoint distance or performing calculations to six decimal places will provide a more accurate solution.