Accelerated Space Trip with Signals On this version of the space trip, the rocket and signals will be animated. The signals will be shown as laser pulses and a sound will be made when they are received. Here I have chosen to let the rocket pilot's proper time schedule be the driving factor for the plots. I have also divided the trip into 6 acceleration phases. These are, consecutively {a,0,-a,-a,0,a} and the times for each leg are {ta,tc,ta,ta,tc,ta}. As you can see, these allow the rocket, if started at zero speed, to return to the start at zero speed. I feel that this acceleration program should provide enough detail for most people. I have placed the right hand vertical axis at an x value of xMax=c*tTotal/2. The reason for this axis placement is that the farthrest that the rocket can go in time tTotal is xMax=c*tTotal/2 even if the entire trip proceeds at the speed of light. The right hand vertical axis shows rocket proper frame times uniformly spaced. The left hand vertical axis shows the earth times spaced uniformly from 0 to the total earth time, as viewed by the rocket when the rocket returns. It's very important to note that the earth's emission rate (observed by its own clock) is generally much less than the rocket's since the total number of pulses emitted by both is the same. If the earth's emission rate were the same as the rocket's, then, for large v/c, there would be no way that I could show all of the earth's pulses. The results will look the same except the reader will have to take into account the difference in scaling of the pulse intevals. On the bottom horizontal axis I show the rocket distance as viewed in the earth frame. On the top horizontal axis I show the rocket distance from start as viewed (as contracted) by the rocket. I think this method of showing the results of a space trip represents the best way that we can present them. It seems to me that the best information that we can gain from the signal receptions is how their frequencies vary as a function of the proper times of the receiving entity. From the animation one sees that, if almost all of any trip that proceeds near the speed of light, earth's rate of reception for the first half of the trip is about one half of the corresponding rocket rate of emission. For the second half of the trip the rocket pulses are received by the earth in a very brief period just before the final return of the rocket. This results from simple geometry since the pulse emission points are moving away from earth at near the speed of light and therefore these pulses have twice as far to go to their receiver. Also from simple geometry, one sees that,that for the first half of the flight, the rocket receives almost no pulses since it is moving away from its emitter at almost the speed of light. By necessity then, during the second half of the flight, the rocket receiver pulse rate is twice the corresponding earth emission rate. If the learner wants to examine the code from a Chrome browser and in Windows, he can press F12 and select "Sources". For a Mac, select View from the menu bar and then select "View Sources" For Safari browser select Develop and then select Show Error Console. http://wickedlysmart.com/hfjsconsole/
Wikipedia:Same graphics as here but without interaction or animation Signal Reception Rate Derivation
a TT TC/TT Ratio Number of Light Pulses Single Step