Accelerated Space Trip 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. In order to clearly see the large ratio of Earth clock rate to rocket clock rate, I have chosen to show rocket times that are proportional to the values of gamma at each rocket time. The left hand vertical axis contains the Earth frame times that correspond to the set of gamma spaced rocket proper times given by the right hand axis. I have connected these times by broken lines of constant time which have slope v/c. 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. I have again shown relative clock rates versus rocket proper time by color coding the values. If the learner wants to examine the code from a Chrome browser and in Windows, he can press F12 and select "Sources".
Minguzzi Paper Aging Ratio Equation Derivation
a TT TC/TT Ratio Show Aging Ratios