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I tried out the new version of Lightcone today
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone3/LightCone.html
It brought to mind, basically just with the default settings, an amazing trek. The one thing I did was open "setup" and get check Vnow and Vthen while X-ing out event horizon, and particle horizon distances. IOW I de-selected columns I didn't need to make more room for the two recession speeds. But that was all, no other changes---then I clicked calculate:
[tex]{\scriptsize \begin{array}{|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}[/tex]
[tex]{\scriptsize \begin{array}{|c|c|} \hline S&a&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 1090.000&0.000917&0.000373&0.000628&45.332&0.042&3.148&66.182\\ \hline 339.773&0.002943&0.002496&0.003956&44.184&0.130&3.068&32.869\\ \hline 105.913&0.009442&0.015309&0.023478&42.012&0.397&2.918&16.895\\ \hline 33.015&0.030289&0.090158&0.136321&38.052&1.153&2.642&8.455\\ \hline 10.291&0.097168&0.522342&0.785104&30.918&3.004&2.147&3.827\\ \hline 3.208&0.311718&2.977691&4.373615&18.248&5.688&1.267&1.301\\ \hline 1.000&1.000000&13.787206&14.399932&0.000&0.000&0.000&0.000\\ \hline 0.312&3.208025&32.884943&17.184900&11.118&35.666&0.772&2.075\\ \hline 0.132&7.580159&47.725063&17.291127&14.219&107.786&0.987&6.234\\ \hline 0.056&17.910960&62.598053&17.299307&15.536&278.256&1.079&16.085\\ \hline 0.024&42.321343&77.473722&17.299802&16.093&681.061&1.118&39.368\\ \hline 0.010&100.000000&92.349407&17.299900&16.328&1632.838&1.134&94.384\\ \hline \end{array}}[/tex]
The story the last line tells is that there is a galaxy which as of today is 16.3 billion ly from us and we send a message to it, a flash of light. The distance to that galaxy is increasing slightly faster than c, namely Vnow 1.13 c. At first it looks like the galaxy is going to get away, the gap is actually widening. But it is not discouraged (being only a simple photon after all) and it persists.
Eventually, when the galaxy is a hundred times farther from us, 1630 billion ly, it catches up!
It reaches the galaxy in year 92 billion, roughly 80 billion years from now, when the galaxy distance to the galaxy is increasing at 94 times the speed of light.
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone3/LightCone.html
It brought to mind, basically just with the default settings, an amazing trek. The one thing I did was open "setup" and get check Vnow and Vthen while X-ing out event horizon, and particle horizon distances. IOW I de-selected columns I didn't need to make more room for the two recession speeds. But that was all, no other changes---then I clicked calculate:
[tex]{\scriptsize \begin{array}{|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}[/tex]
[tex]{\scriptsize \begin{array}{|c|c|} \hline S&a&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 1090.000&0.000917&0.000373&0.000628&45.332&0.042&3.148&66.182\\ \hline 339.773&0.002943&0.002496&0.003956&44.184&0.130&3.068&32.869\\ \hline 105.913&0.009442&0.015309&0.023478&42.012&0.397&2.918&16.895\\ \hline 33.015&0.030289&0.090158&0.136321&38.052&1.153&2.642&8.455\\ \hline 10.291&0.097168&0.522342&0.785104&30.918&3.004&2.147&3.827\\ \hline 3.208&0.311718&2.977691&4.373615&18.248&5.688&1.267&1.301\\ \hline 1.000&1.000000&13.787206&14.399932&0.000&0.000&0.000&0.000\\ \hline 0.312&3.208025&32.884943&17.184900&11.118&35.666&0.772&2.075\\ \hline 0.132&7.580159&47.725063&17.291127&14.219&107.786&0.987&6.234\\ \hline 0.056&17.910960&62.598053&17.299307&15.536&278.256&1.079&16.085\\ \hline 0.024&42.321343&77.473722&17.299802&16.093&681.061&1.118&39.368\\ \hline 0.010&100.000000&92.349407&17.299900&16.328&1632.838&1.134&94.384\\ \hline \end{array}}[/tex]
The story the last line tells is that there is a galaxy which as of today is 16.3 billion ly from us and we send a message to it, a flash of light. The distance to that galaxy is increasing slightly faster than c, namely Vnow 1.13 c. At first it looks like the galaxy is going to get away, the gap is actually widening. But it is not discouraged (being only a simple photon after all) and it persists.
Eventually, when the galaxy is a hundred times farther from us, 1630 billion ly, it catches up!
It reaches the galaxy in year 92 billion, roughly 80 billion years from now, when the galaxy distance to the galaxy is increasing at 94 times the speed of light.
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