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There's a tutorial wiki for Jorrie's calculator. It needs exercises that beginning learners can do to help them get used to using the calculator.
IF YOU HAVE SOME IDEAS, feel free to make up exercises and propose them. Anybody can suggest material for a textbook. He might not like what you offer, or it might duplicate existing stuff. But it might be helpful. Here's some I thought of today. They might or might not be accepted and go into the tutorial. Comments welcome.
Intergalactic Message Problems
These exercises are all based on one table. It runs from a=0.1 to a=10 in 20 steps, so when you open LightCone, set Supper = 10, Slower=0.1 and Steps=20. Then press calculate. The link is in my signature.
The situation is we discover that there's a laser message coming in from a distant galaxy that says "Please reply immediately!" We analyze the light and determine that the wavelength has been doubled. The peaks and valleys of the wave have been spread out by a factor of two.
We flash our reply immediately. When does it get to them? Or does it ever get to them?
Learners doing the exercises will have generated this table this table, as I just described. The Answers should go at the end of the chapter, but I will put the answer to this first one right after the table. *Spoiler alert*
[tex]{\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (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}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.100&10.00&0.545&0.8196&30.684&3.068&4.717&2.13&3.74\\ \hline 0.126&7.94&0.771&1.1568&28.684&3.611&5.687&1.99&3.12\\ \hline 0.158&6.31&1.089&1.6308&26.444&4.191&6.804&1.84&2.57\\ \hline 0.200&5.01&1.536&2.2939&23.938&4.776&8.066&1.66&2.08\\ \hline 0.251&3.98&2.165&3.2127&21.143&5.311&9.452&1.47&1.65\\ \hline 0.316&3.16&3.041&4.4626&18.045&5.706&10.920&1.25&1.28\\ \hline 0.398&2.51&4.250&6.1052&14.651&5.833&12.396&1.02&0.96\\ \hline 0.501&2.00&5.883&8.1349&11.008&5.517&13.780&0.76&0.68\\ \hline 0.631&1.58&8.015&10.4035&7.226&4.559&14.962&0.50&0.44\\ \hline 0.794&1.26&10.669&12.6018&3.483&2.767&15.863&0.24&0.22\\ \hline 1.000&1.00&13.787&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline 1.259&0.79&17.257&15.6486&3.109&3.914&16.842&0.22&0.25\\ \hline 1.585&0.63&20.956&16.4103&5.731&9.083&17.047&0.40&0.55\\ \hline 1.995&0.50&24.789&16.8364&7.890&15.743&17.153&0.55&0.94\\ \hline 2.512&0.40&28.694&17.0630&9.638&24.210&17.204&0.67&1.42\\ \hline 3.162&0.32&32.638&17.1800&11.040&34.912&17.224&0.77&2.03\\ \hline 3.981&0.25&36.601&17.2395&12.160&48.409&17.240&0.84&2.81\\ \hline 5.012&0.20&40.575&17.2696&13.051&65.411&17.270&0.91&3.79\\ \hline 6.310&0.16&44.553&17.2847&13.760&86.821&17.285&0.96&5.02\\ \hline 7.943&0.13&48.534&17.2923&14.324&113.777&17.292&0.99&6.58\\ \hline 10.000&0.10&52.516&17.2961&14.772&147.715&17.296&1.03&8.54\\ \hline \end{array}}[/tex]
The wavelengths being enlarged by factor of S=2.0 tells us that the galaxy is NOW at distance of 11 Gly. We look down the D column to find where a target's distance is approximately the same. If we flash a message today to a galaxy that is now at distance 11 Gly it will get there in year 32.6 billion. That is, about 19 billion years from now. But yes, it will get there.
The galaxy is within communication range because its distance now (11 Gly) is less than the current value of the horizon distance Dhor = 16.47 Gly. (Look in the S=1 row.)
Incidental intelligence: our return message will be wavestretched by a factor of about 3.16.
IF YOU HAVE SOME IDEAS, feel free to make up exercises and propose them. Anybody can suggest material for a textbook. He might not like what you offer, or it might duplicate existing stuff. But it might be helpful. Here's some I thought of today. They might or might not be accepted and go into the tutorial. Comments welcome.
Intergalactic Message Problems
These exercises are all based on one table. It runs from a=0.1 to a=10 in 20 steps, so when you open LightCone, set Supper = 10, Slower=0.1 and Steps=20. Then press calculate. The link is in my signature.
The situation is we discover that there's a laser message coming in from a distant galaxy that says "Please reply immediately!" We analyze the light and determine that the wavelength has been doubled. The peaks and valleys of the wave have been spread out by a factor of two.
We flash our reply immediately. When does it get to them? Or does it ever get to them?
Learners doing the exercises will have generated this table this table, as I just described. The Answers should go at the end of the chapter, but I will put the answer to this first one right after the table. *Spoiler alert*
[tex]{\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (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}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.100&10.00&0.545&0.8196&30.684&3.068&4.717&2.13&3.74\\ \hline 0.126&7.94&0.771&1.1568&28.684&3.611&5.687&1.99&3.12\\ \hline 0.158&6.31&1.089&1.6308&26.444&4.191&6.804&1.84&2.57\\ \hline 0.200&5.01&1.536&2.2939&23.938&4.776&8.066&1.66&2.08\\ \hline 0.251&3.98&2.165&3.2127&21.143&5.311&9.452&1.47&1.65\\ \hline 0.316&3.16&3.041&4.4626&18.045&5.706&10.920&1.25&1.28\\ \hline 0.398&2.51&4.250&6.1052&14.651&5.833&12.396&1.02&0.96\\ \hline 0.501&2.00&5.883&8.1349&11.008&5.517&13.780&0.76&0.68\\ \hline 0.631&1.58&8.015&10.4035&7.226&4.559&14.962&0.50&0.44\\ \hline 0.794&1.26&10.669&12.6018&3.483&2.767&15.863&0.24&0.22\\ \hline 1.000&1.00&13.787&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline 1.259&0.79&17.257&15.6486&3.109&3.914&16.842&0.22&0.25\\ \hline 1.585&0.63&20.956&16.4103&5.731&9.083&17.047&0.40&0.55\\ \hline 1.995&0.50&24.789&16.8364&7.890&15.743&17.153&0.55&0.94\\ \hline 2.512&0.40&28.694&17.0630&9.638&24.210&17.204&0.67&1.42\\ \hline 3.162&0.32&32.638&17.1800&11.040&34.912&17.224&0.77&2.03\\ \hline 3.981&0.25&36.601&17.2395&12.160&48.409&17.240&0.84&2.81\\ \hline 5.012&0.20&40.575&17.2696&13.051&65.411&17.270&0.91&3.79\\ \hline 6.310&0.16&44.553&17.2847&13.760&86.821&17.285&0.96&5.02\\ \hline 7.943&0.13&48.534&17.2923&14.324&113.777&17.292&0.99&6.58\\ \hline 10.000&0.10&52.516&17.2961&14.772&147.715&17.296&1.03&8.54\\ \hline \end{array}}[/tex]
The wavelengths being enlarged by factor of S=2.0 tells us that the galaxy is NOW at distance of 11 Gly. We look down the D column to find where a target's distance is approximately the same. If we flash a message today to a galaxy that is now at distance 11 Gly it will get there in year 32.6 billion. That is, about 19 billion years from now. But yes, it will get there.
The galaxy is within communication range because its distance now (11 Gly) is less than the current value of the horizon distance Dhor = 16.47 Gly. (Look in the S=1 row.)
Incidental intelligence: our return message will be wavestretched by a factor of about 3.16.
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