3.0 The Time Coordinate

The issue of a fourth Time coordinate is easier to understand if you consider that although the speed of light is fast, it still takes many years to traverse interstellar space from one star to another. The light from our nearest neighbor, Alpha and Beta Cenaturi, requires more than 4 years to get to us. Now, most stars move a little in relation to each other. Compared to the distance they are apart, the movement isn't big, but it's there.

If you start thinking in hundreds of light years, and the star is moving, say just 20 miles a second, in relation to us, well, after a several hundred years, it's no longer where it was. In fact, the light, and therefore the position of the star, can be this old just when we look up at a star from Earth. If you are trying to get a coordinate system that works without errors, how can this positional error be resolved? That's where the fourth Time coordinate comes in.

Suppose a mission is planned to Sirius, a double star about 8.6 light years distant. A navigator, Celeste, is appointed to the mission and she is faced with the task of making sure the starship takes the correct course and correct speed at 0.5 c, so it may rendezvous with Sirius in about 17 years.

During Celeste's trip she makes various sightings of her destination star, Sirius and discovers that Sirius is apparently in a different location, depending from where it is observed.

                                                        Illustration 3.0.1

Illustration showing T-Coordinate changes depending on viewpoint

In illustration 3.1 it is July 1, 2020, halfway into the 17 year mission traveling at 0.5c. Celeste is halfway to Sirus or 4.3 light years from Earth and 4.3 light years from Sirus. Her stay on Earth sister, Candice, sees Sirus with a 8.6 light year delay. Celeste, being closer sees it with only a 4.3 year delay.

Since Sirus has a Radial Velocity and is moving, according to this graph, in a downward right direction, Candice sees Sirus at position A although it is really at position C. Candice gives Sirus at position A a SGC T-coordinate of 2020.5 according to the SGC rule;

All stars viewed from Earth have the SGC T-coordinate of the current Earth time.

Celeste sees Sirus at position B because she is closer and the light has only been travelling for 4.3 years. She, however gives Sirus at position B the SGC T-coordinate of 2032.8 according to the SGC rule;

A nice side effect is that the SGC system allows the T-Coordinate to be equal to the ASD value and the Tr-Coordinate to be equal to the RSD value (covered in 5.1). This will play an important role in making it easier to transfer SGC coordinates back to galactic Right Ascension and galactic declination.

3.1 Waypoints and the T-Coordinate
Suppose Celeste makes a detour on the way to Sirius, reaches a waypoint and then alters course. What will happen?
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                                                        Illustration 3.1.1
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In the illustration, 3.1.1, Celeste makes a rather large detour to Alpha and Beta Centauri before turning towards Sirius. As she journeys toward our nearest steller neighbour in the Centauri system, she will be increasing her SGC T coordinate relative to Earth at 0,0,0. However, she will be also increasing her distance to Sirius, which is in the opposite direction. This means that Sirius will appear even further in the past when she looks up at it, than it appears to her stay on Earth sister, Candice. This is exactly the opposite of the earlier example when Celeste flew right at Sirius.
What does this mean to the SGC T coordinate? In such a multiple waypoint situation, the SGC T coordinate alone cannot resolve the enitre navigational problem.
Luckily there are two solutions:
Celeste breaks up the trip into two straight journeys and works with the SGC T coordinate to resolve each leg.
Or; Celeste makes use of additional reference points that define her viewpoint positions. This allows her to resolve all steller sightings in any direction as she travels.

This second, more complex, solution is outlined in 6.1.

Forward to Chapter 4 - Galactic Proper Motion

Backward to Chapter 2 - SGC Tri-Coordinates

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Last updated: June 28, 2014 |

3.0 The Time Coordinate

3.1 Waypoints and the T-Coordinate

Forward to Chapter 4 - Galactic Proper Motion