8.0 - Relativity changes

This chapter explains why any time dialation effects caused by relativity should not affect the SGC system. These relativistic effects are dependent on each individual mission and dependent on how fast the starship travels. In short, the navigator ignores all time dialation and uses the Current Earth Time to figure SGC values.

Changes of a relativistic nature, pertaining to changes in time intervals are essential to make an accurate mission profile map. The SGC system is basically a free float system based on the Sun's movement as being the state of rest. Therefore all adjustments should be made relative to the Sun and would only apply to each individual mission. For example, a ship travelling at speeds approaching the speed of light, will need to make a large adjustment to the on board clock to return all stellar coordinates to proper SGC values. On the other hand a slower ship travelling at only .01% of the speed of light would hardly need to make any adjustments.

 As an example; Celeste's trip to Sirius would need to travel at an average speed of 9/25th of the speed of light or .36 % in order to reach Sirius, 9 light years away in 25 years. At this high velocity, there will be effects of a relativistic nature that she will note. As the starship approaches Sirius, Celeste observes Sirius to be moving slightly faster than expected. Sirius appears to speed up hastening to the appointed rendezvous. There will be a bending of the light rays toward the center of field of vision. Even it's red shift seems altered. She will also notice a slow down of the playback rate of incoming messages from Earth. The overall mission seems to be proceeding faster and she must arrange for engine shutdown and reignition sooner than expected. She also notices that the efficiency of the engines has suffered due to the high speeds and the relative mass increase.

 Celeste, being a top navigator, knows to watch the Current Earth Time (CET), that is relativistically compensated by the on board computer which senses all velocity changes. She bases her course corrections and navigational sightings on the CET time while the Current Ship Time (CST) runs noticeably slower. When Celeste finally arrives at Sirius, she knows to list the T-coordinate for Sirius based on CET and not CST. The extra time that she saved by a relativistic time dilation was an extra bonus and does not change the SGC coordinates.

 It can be seen that, although relativity compensation must be made on a mission to mission bases, the basic structure of the SGC system remains intact.

 As points of interest, I have included some relativistic formulae below:

An already published formulae showing the bending of the light rays toward the center due to acceleration is:

Formula 8.01
Where v = velocity, c = speed of light,  = rest angle of star,1 = measured angle of star (This angle deviates from the rest angle as a function of the speed of the starship.)

Time dilation may be found by using Einstein's formulae:

Formula 8.02
Where x = the distance travelled, t = non-dilated time, t1 = dilated time, v = velocity of travel, c = speed of light and it is assumed no change in the Y or Z coordinates.

A more simple version showing only the time dilation would be:

Formula 8.03
Where t1, the dilated time, shows the amount of ship time it takes for an equivalent relative time at a location of zero relative velocity. In other words, taking our example Celeste's mission to Sirius; Celeste's one minute of Realative Ship Time, (RST) would be equal to t1 times one minute of her sister Candice's time, who stayed at home on Earth. It can be seen that as Celeste increases velocity to approach the speed of light, c, the formula comes closer to showing 1 over zero or approaches an infinite value for t1, thus making Celeste's minutes, as she approaches the speed of light, drag on to years and centuries compared to her stay on Earth, sister, Candice.

 Just as a matter of interest, the total time dialation for Celeste's mission to Sirius would be 236 days. In other words, at the end of the mission, Celeste's clock would be 236 days less than her stay on Earth sister, Candice.

Forward to Chapter 9 - Changes in Curvature of Spacetime

Backward to Chapter 7 - Estimated Deviations

Table of Contents | The Appendix Last updated: October 3, 2002  |