Print a history of the universe you'd like to share

[marcus]

I'm interested in the history tables other PF members are getting as they try out Jorrie's online tabulator. What's your current favorite? So this is to invite folks to use the LaTex feature to get a version of your table you can print in a post in this thread. Which values of the Hubbletimes do you prefer using? These days I'm always using 14.4 and 17.3 Gy, with S=3400 marking matter-radiation equality.

Your table can be short or long. Sometimes a very brief table can be effective in showing some historical feature clearly. Here's an example where I set "steps" = 1 and checked the box to include S=1, the exact present.
So then I just ticked the "LaTex" button, said "calculate" and copypasted the LaTex expression that resulted into this post:
$${\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline1090.000&0.000917&0.000373&0.000628&45.332&0.042&0.057&0.001\\ \hline1.000&1.000000&13.787206&14.399932&0.000&0.000&16.472&46.279\\ \hline0.040&25.000000&68.366857&17.299636&-15.809&-395.235&17.300&1551.841\\ \hline\end{array}}$$
It's a brief history of the universe from year 373,000 to year 68 billion

It shows the recession speed (back then) of the matter that emitted the CMB radiation we are now receiving--namely the speed was 0.042/0.000628 times the speed of light.

And it shows the present day recession speed of that same matter, namely 45.33/14.4 times the speed of light.

It also shows both the (cosmic event) horizon distance and the Hubble radius converging in the remote future to the same 17.3 billion lightyear length.

You might construct a sample history that includes other and more interesting features and one not limited to three lines. I'd like to see what results folks have come up with, and hope they will share.

 

[Jorrie]

I still prefer to stick to the WMAP9 max likelihood values, because they seem to be based on a lot of data, gathered over a long period.
$${\scriptsize \begin{array}{|c|c|c|c|c|c|c|}\hline Y_{now} (Gy) & Y_{inf} (Gy) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline14&16.5&3280&69.86&0.72&0.28\\ \hline\end{array}}$$ $${\scriptsize \begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline1090.000&0.000917&0.000378&0.000637&45.731&0.042&0.056&0.001\\ \hline541.606&0.001846&0.001200&0.001945&45.126&0.083&0.113&0.003\\ \hline269.117&0.003716&0.003662&0.005761&44.225&0.164&0.223&0.009\\ \hline133.721&0.007478&0.010876&0.016772&42.912&0.321&0.439&0.028\\ \hline66.444&0.015050&0.031751&0.048364&41.023&0.617&0.855&0.085\\ \hline33.015&0.030289&0.091754&0.138771&38.325&1.161&1.640&0.253\\ \hline16.405&0.060958&0.263633&0.397095&34.484&2.102&3.066&0.743\\ \hline8.151&0.122680&0.754694&1.132801&29.030&3.561&5.501&2.164\\ \hline4.050&0.246896&2.146402&3.182937&21.343&5.269&9.172&6.254\\ \hline2.013&0.496887&5.887073&8.078066&11.017&5.474&13.329&17.716\\ \hline1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686\\ \hline0.725&1.379730&18.510100&15.398913&-4.071&-5.618&16.192&70.012\\ \hline0.525&1.903654&23.586586&16.053616&-7.214&-13.733&16.359&102.579\\ \hline0.381&2.626528&28.804384&16.325686&-9.556&-25.100&16.418&147.685\\ \hline0.276&3.623898&34.079335&16.432954&-11.273&-40.853&16.433&209.986\\ \hline0.200&5.000000&39.376581&16.474344&-12.523&-62.615&16.474&295.973\\ \hline0.145&6.898648&44.682397&16.490176&-13.430&-92.651&16.490&414.622\\ \hline0.105&9.518270&49.991486&16.496208&-14.088&-134.096&16.496&578.329\\ \hline0.076&13.132639&55.301823&16.498497&-14.565&-191.281&16.498&804.203\\ \hline0.055&18.119492&60.612636&16.499361&-14.911&-270.181&16.499&1115.847\\ \hline0.040&25.000000&65.923630&16.499682&-15.162&-379.041&16.500&1545.833\\ \hline\end{array}}$$
I like the above S range, because it shows some values around the time when stars and galaxies began to form. I use the smaller TexScript font, because I normally use split-screen views. It should also work better on mobile devices.

 

[marcus]

I like the range that Jorrie just tabulated because it covers what we are mostly focused on, history since S=1090 the origin of the Microwave Background. And it goes far enough into the future to give a fair idea. You can see both the Cosmic Event Horizon (column 7, D_hor, and the Hubble radius (column 4 interpreted in lightyears), converging to the same eventual longterm value. (This length is a concrete form of the cosmological constant, one of the three controlling parameters of the model.)

I think I'll try extending that range back in time a ways, to another important time-mark. The moment of matter-radiation equality S_eq is an impressive thing to imagine, so folks might want to look at histories including that. Offhand I can't say how many degrees Kelvin it would be---something around 10,000 K.
The density of radiation so great that in mass-equivalent it equals the matter density.

Matter density is now about .23 nanojoules per cubic meter, (dark plus ordinary) and according to the Planck report we can take S_eq=3400. So matter density at that epoch would be
0.23*3400^3 = 9,039,920,000 nanojoules, or simply 9 joules per cubic meter.
So at S_eq the average energy content of space is effectively TWICE that, a cubic meter contains 9 joules (energy equivalent) of dark and ordinary matter, plus 9 joules of light!
The blue-ish white light of a star hotter than the sun, with surface temp around 10 thousand kelvin.

By the time the microwave background light is released (S=1090) the light will be cooler, down around 3000 kelvin and more orange-ish. So it's different, and comes a few tens of thousands of years later. Let's try to get both these epochs in a cosmos history.

Someone else might have better luck doing this. I decided to start at S=3497 and work down to the present S=1 in fourteen steps. Then for no good reason, or for balance, I threw in fourteen more steps into the future. That roughly matches the future extent in Jorrie's table right before this.
So we are starting with approximate matter-radiation equality, with radiation having a slight advantage (it gains over matter as you increase S and go further back into the past.)
$${\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&T_{Hub}(Gy)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline3497.000&0.000286&0.000049&0.000088&45.889&0.013&0.018&0.000\\ \hline1952.426&0.000512&0.000137&0.000240&45.665&0.023&0.032&0.000\\ \hline1090.068&0.000917&0.000373&0.000628&45.332&0.042&0.057&0.001\\ \hline608.600&0.001643&0.000979&0.001594&44.853&0.074&0.101&0.002\\ \hline339.790&0.002943&0.002496&0.003956&44.184&0.130&0.179&0.006\\ \hline189.710&0.005271&0.006227&0.009679&43.263&0.228&0.315&0.016\\ \hline105.918&0.009441&0.015308&0.023476&42.013&0.397&0.552&0.040\\ \hline59.135&0.016910&0.037265&0.056654&40.324&0.682&0.961&0.100\\ \hline33.016&0.030288&0.090154&0.136315&38.052&1.153&1.652&0.249\\ \hline18.433&0.054249&0.217276&0.327405&35.003&1.899&2.793&0.611\\ \hline10.292&0.097166&0.522326&0.785080&30.918&3.004&4.606&1.491\\ \hline5.746&0.174035&1.252308&1.874004&25.459&4.431&7.300&3.621\\ \hline3.208&0.311715&2.977647&4.373552&18.248&5.688&10.827&8.733\\ \hline1.791&0.558314&6.817194&9.184499&9.243&5.160&14.365&20.670\\ \hline1.000&1.000000&13.787206&14.399932&0.000&0.000&16.472&46.279\\ \hline0.558&1.791105&22.979870&16.668930&-6.933&-12.418&17.112&95.282\\ \hline0.462&2.162190&26.145389&16.932672&-8.543&-18.473&17.175&118.505\\ \hline0.383&2.610157&29.349561&17.088281&-9.894&-25.825&17.209&146.582\\ \hline0.317&3.150935&32.576361&17.178665&-11.021&-34.726&17.224&180.501\\ \hline0.263&3.803752&35.816245&17.230684&-11.958&-45.485&17.231&221.463\\ \hline0.218&4.591822&39.063639&17.260461&-12.736&-58.482&17.260&270.919\\ \hline0.180&5.543165&42.315326&17.277455&-13.381&-74.176&17.277&330.626\\ \hline0.149&6.691609&45.569461&17.287135&-13.917&-93.124&17.287&402.707\\ \hline0.124&8.077991&48.824990&17.292642&-14.360&-116.000&17.293&489.722\\ \hline0.103&9.751605&52.081312&17.295773&-14.727&-143.616&17.296&594.767\\ \hline0.085&11.771963&55.338086&17.297551&-15.032&-176.955&17.298&721.575\\ \hline0.070&14.210903&58.595116&17.298560&-15.284&-217.200&17.299&874.657\\ \hline0.058&17.155147&61.852292&17.299132&-15.493&-265.784&17.299&1059.454\\ \hline0.048&20.709386&65.109551&17.299455&-15.666&-324.434&17.299&1282.538\\ \hline0.040&25.000000&68.366857&17.299636&-15.809&-395.235&17.300&1551.841\\ \hline\end{array}}$$

Now we can see the time-progression. Matter-radiation equal density comes around year 49,000, in ionized gas so dazzling hot that it is effectively opaque. Then in year 373,000 things have expanded and cooled enough (3000 kelvin) for the gas to be effectively transparent. The fog clears and the light we receive today as CMB starts out on its way to us. I'm sure more can be read from the table but the primary aim was to include those two major time-mark moments.

Another thing to notice is that the sixth column D_then is the proper distance outline of our past lightcone. It shows how light directed towards us is initially swept back to a distance of around 5.8 Gly before it begins to make headway. All the sources from which we are receiving light today are on that pear shaped "cone". And the PRESENT DISTANCE of those sources is shown in the fifth column, D. An interesting thing about that column is it shows the now-distance D converging to around 46 Gly as you go back into the past. That distance is what is called the present-day particle horizon, the presentday radius of the observable stuff. And the particle horizon at various epochs has been tabulated in column eight, so you can see that same 46 Gly in the S=1 row.

Just a consistency check: the present distance of the farthest stuff we can see (or could see if space had been transparent enough to let the light thru) has to be not only listed as D_par the particle horizon in the S=1 row but also shown as the limit as you go up the D_now fifth column into the past.

For a recent (Fall 2012) estimate of temp at Seq see http://homepages.spa.umn.edu/~llrw/a5022_f12.html
in particular page 11 of Early Universe Thermal History notes:
http://homepages.spa.umn.edu/~llrw/a5022/f12/EarlyU.pdf

 

[marcus]

I seem to recall one or more PF-ers have been gently kidding me for being such an enthusiast about the progressive improvement of this cosmic tabulator, and it's quite true: I think it's the greatest thing since sliced bread. And I'll argue that it really is.

This has to do with language: the English language versus the languages of geometry, namely charts, graphs, tables, equations. The universe is a physical geometric thing so it does not work well to talk and think about it at a merely verbal level. But 99% of people don't talk and think with equations. So we need ways to visualize what's going on with the geometry using graphs and tables.

A oneshot calculator like Ned Wright's does not give you the "gestalt"---a sense of the whole, or of a process, with stuff happening at changing rates and converging to other stuff etc etc.

The tabular calculator we have here is almost the only one on the internet. It is such an obviously good idea that I expect it will be copied or reinvented by other people.

So I really advise people here to get some practice with it. And comment to Jorrie about it because your input might improve it. And take part in this development.

And here's a new version that Jorrie just put online sometime in the past 12 hours:
http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo8.html
I'm trying its LaTex function for the first time. The idea of the particular table I've decided to print in this post is not to go way back in time but only go back to around the time the first stars and galaxies appeared. This way we get a little bit more detail and smoothness in the light cone curve, because the steps are not so spread out.

The D_then column is what gives you the proper distance outline of the past lightcone. It actually shows you the worldline of a ray of light on its way to us from something that emitted it around year 400 million. It shows how the light was initially swept back until it was 5.8 billion lightyears from us and then began to make headway towards us--the lightcone is pear-shaped. You can see that in the sixth column of the table.

The new version, TabCosmo8, is controlled by 3 parameters: the two main ones being the "now" and the "eventual future" Hubble radii, denoted R_now and R_∞. Number-wise it's the same as TabCosmo7. (R expressed Gly is the same number as T_Hub expressed in Gy, but the Hubble radius may be more familiar to people and thus more user-friendly.)

The Hubble radius at any given epoch is the distance which is expanding exactly at speed c. Other distances expand proportionally. So it is a good intuitive/visual handle on the fractional expansion rate. See what you think. I chose to go from S=12 up to the present S=1 in 13 steps. S=12 marks the epoch when distances are 1/12 their present size (earliest galaxies date from around then.)

$${\begin{array}{|c|c|c|c|c|c|c|}\hline R_{now} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline14.4&17.3&3400&67.92&0.693&0.307\\ \hline\end{array}}$$ $${\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)\\ \hline12.000&0.083&0.415&0.624&32.112&2.676&4.050&1.179\\ \hline9.912&0.101&0.553&0.831&30.612&3.088&4.752&1.579\\ \hline8.188&0.122&0.736&1.106&28.961&3.537&5.551&2.113\\ \hline6.763&0.148&0.981&1.471&27.146&4.014&6.452&2.827\\ \hline5.586&0.179&1.306&1.954&25.153&4.503&7.454&3.779\\ \hline4.614&0.217&1.738&2.590&22.969&4.978&8.551&5.048\\ \hline3.812&0.262&2.309&3.421&20.581&5.400&9.725&6.738\\ \hline3.148&0.318&3.061&4.490&17.983&5.712&10.949&8.983\\ \hline2.601&0.385&4.043&5.832&15.181&5.837&12.177&11.953\\ \hline2.148&0.466&5.308&7.448&12.198&5.678&13.353&15.859\\ \hline1.774&0.564&6.904&9.278&9.088&5.122&14.414&20.952\\ \hline1.466&0.682&8.859&11.176&5.940&4.053&15.302&27.513\\ \hline1.211&0.826&11.168&12.943&2.867&2.368&15.986&35.847\\ \hline1.000&1.000&13.787&14.400&0.000&0.000&16.472&46.279\\ \hline0.826&1.211&16.648&15.475&-2.616&-3.167&16.793&59.176\\ \hline0.654&1.528&20.359&16.316&-5.348&-8.172&17.022&78.870\\ \hline0.518&1.929&24.220&16.789&-7.600&-14.660&17.142&103.899\\ \hline0.411&2.435&28.163&17.040&-9.423&-22.943&17.199&135.586\\ \hline0.325&3.073&32.148&17.169&-10.883&-33.447&17.223&175.631\\ \hline0.258&3.879&36.155&17.235&-12.046&-46.731&17.235&226.204\\ \hline0.204&4.897&40.173&17.267&-12.970&-63.511&17.267&290.052\\ \hline0.162&6.181&44.197&17.284&-13.703&-84.698&17.284&370.652\\ \hline0.128&7.802&48.224&17.292&-14.284&-111.444&17.292&472.392\\ \hline0.102&9.848&52.251&17.296&-14.745&-145.207&17.296&600.816\\ \hline0.080&12.431&56.280&17.298&-15.110&-187.825&17.298&762.921\\ \hline0.064&15.691&60.309&17.299&-15.399&-241.620&17.299&967.540\\ \hline0.050&19.806&64.338&17.300&-15.628&-309.523&17.300&1225.822\\ \hline0.040&25.000&68.367&17.300&-15.809&-395.235&17.300&1551.841\\ \hline\end{array}}$$

 

[marcus]

In TabCosmo8 the default parameters are
R_now = 14.4 Gly
R_∞ = 17.3 Gly
S_eq = 3400
I should give a reference for those.

The reference is the March 2013 Planck mission report
http://arxiv.org/pdf/1303.5076v1.pdf
Table 5 on page 22 for the two main ones, and Table 2 on page 11 for matter-radiation equality.

In Table 5, see the rightmost column, labeled "Planck+WP+highL+BAO".
In "WP" the W stands for WMAP
and "highL" stands for SPT and ACT.
So the numbers in that column are based not only on Planck mission data but also on a lot of other data that has been accumulated over a long period of time by other means including WMAP (polarization) and the South Pole Telescope and the galaxy counts of the BAO study.

The choice of the central values given in that column was influenced by the fact that these were what Ned Wright chose to report in his "News of the Universe" when the Planck findings came out.

The rest was just plugging those central values (67.80 and 0.692) into google calculator.

If you go to google and put this in:
"c/(67.80 km/s per Mpc) in light years"
you get 14.4 billion lightyears
actually you get 14.4220222 but I rounded off.
and if you divide 14.4220222 by the square root of 0.692 you get 17.3
So these are the two Hubble radii implicit in the "Planck+WP+SPT+ACT+BAO" numbers.

Planck team published several sets of of basic cosmic parameters in their report
http://arxiv.org/pdf/1303.5076v1.pdf
see for example Table 5 on page 22.

The rightmost column of Table 5 is labeled "Planck+WP+highL+BAO".

That seems to be the set of numbers that Ned Wright chooses to report, for instance:

Ω_Λ = 0.692 ± 0.010
H₀ = 67.80 ± 0.77

I'll quote from Wright's "News of the universe" item where he seems to choose that column as most reliable and gives a concise summary of the numbers.
==quote==
The parameters of the 6-parameter ΛCDM model fit to Planck+WMAP polarization+SPT+ACT+BAO are Ω_Λ = 0.692 ± 0.010; the baryon density = 0.416 ± 0.0045 yoctograms per cubic meter; the cold dark matter density = 2.23 ± 0.032 yoctograms per cubic meter; CDM:baryon density ratio = 5.36 ± 0.10; dark energy density = 3352 ± 125 eV/cc; H₀ = 67.80 ± 0.77 km/sec/Mpc; and the age of the Universe = 13.798 ± 0.037 Gyr. The baryon density is known to 1.1% precision and the cold dark matter density is known to 1.4% precision.
==endquote==

 

[Jorrie]

In TabCosmo8 the default parameters are
R_now = 14.4 Gly
R_∞ = 17.3 Gly
S_eq = 3400

Marcus was such a driving force behind this tabular cosmo-calculator development that he is now honored with a version (8) of his own. This will henceforth be the standard "PF version", with occasional changes approved by Marcus.

I have a slightly different preference for input defaults and output columns, so my sig contains an experimental version (9) with an extra column for da/dT, but with the "older" WMAP9 inputs. Future developments may perhaps bring us some selectable output columns and various sets of input defaults.

I will talk to admin about the possibility of 'hosting' the calculator and its support files somewhere on PF. Private websites are not good permanent homes for utilities. If it cannot be PF, then perhaps some university website may be interested; anybody has connections?

 

[marcus]

Marcus was such a driving force behind this tabular cosmo-calculator development that he is now honored with a version (8) of his own. This will henceforth be the standard "PF version", with occasional changes approved by Marcus.

I have a slightly different preference for input defaults and output columns, so my sig contains an experimental version (9) with an extra column for da/dT, but with the "older" WMAP9 inputs. Future developments may perhaps bring us some selectable output columns and various sets of input defaults.

I will talk to admin about the possibility of 'hosting' the calculator and its support files somewhere on PF. Private websites are not good permanent homes for utilities. If it cannot be PF, then perhaps some university website may be interested; anybody has connections?

This was a really nice gesture, Jorrie. Thanks for putting Version 8 online with the new Planck numbers. I can see the point of holding back because the new numbers may be revised before they settle down.

I find I'm now wanting to beg another favor. I've gotten to like the 9th column. There should really be a version 9P with the Planck model parameters.

I would be nice if some other PF folk would try printing. Texscript option really looks better than the original LaTex

 

[marcus]

BTW I checked half a dozen past and future rows of version 9 to verify that the sample galaxy recession speed is equal to a R₀/R in units of c. It was spot on---this may be how the calculator gets it.

The column heading you've used is compact, a'R_o and it SHOULD be immediately recognizable by beginners as the recession speed of a sample object whose now distance is R_o. I am still not sure which I prefer:

sample v_rec(t) = R_o a'(t) = R_o a(t)/R(t), understood in units of c.

Probably which notation it is matters less than the need to introduce the idea out front and not rely on the new user clicking every info button and having the initiative to learn what column 9 is about. Which notation is not so important but the calculator needs a way to grab the learner's attention and say "Look! this is the recession speed of a sample galaxy! It's one that is only the Hubble distance away from us at present. Look how, already in the past and also in the near future, it has been and will be receding faster than light!"
And introduce them to the column-head notation at that point in such a way that they don't forget what it stands for.

 

[Jorrie]

The column heading you've used is compact, a'R_o and it SHOULD be immediately recognizable by beginners as the recession speed of a sample object whose now distance is R_o. I am still not sure which I prefer:

sample v_rec(t) = R_o a'(t) = R_o a(t)/R(t), understood in units of c.

I'm still traveling until Saturday, so next week will probably see some progress again. I think the header row should become two lines so that the width can be preserved, but it could be more descriptive.

I will upload a version 9P, if you want to stick it into your sig. Looks like the sig limits me to just two lines and I want Tamara Davis' 3-panel expansion diagram there as well.

PS: I've uploaded TabCosmo9P; please check before posting...

BTW, I have used a'R₀ = a(t)R₀/R(t) in the calculator, as you figured.

 

[Mordred]

olol I seem to recall being one of those people that was gently kidding with you on the calculator Marcus hehe. Anyways I fully agree with your assessment of other online calculators. This calculator has numerous features and flexibility that other calculators do not. The charting aspect alone is a major contributor of that not including the textscript posting allowance. By the way the textscript does work on mobile devices. I had need to post an example in another thread and was able to easily copy paste the textscript from my mobile. The mobile I was using is a galaxy so cannot say for Iphones. However thought you should have some feedback on the mobile usage.

 

[marcus]

... By the way the textscript does work on mobile devices. I had need to post an example in another thread and was able to easily copy paste the textscript from my mobile. ...

Can you point me to the post where you used your mobile to copy paste? I'd be curious to see an example of that way of using J's calculator.

 

[Mordred]

tex]{\scriptsize \begin{array}{|c|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}[/tex] $${\scriptsize \begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&a'R_{0}\\ \hline 1090.000&0.000917&0.000373&0.000628&45.332&0.042&0.057&0.001&21.023\\ \hline 697.717&0.001433&0.000783&0.001284&44.981&0.064&0.088&0.002&16.069\\ \hline 446.614&0.002239&0.001614&0.002589&44.525&0.100&0.137&0.004&12.456\\ \hline 285.881&0.003498&0.003279&0.005163&43.940&0.154&0.211&0.008&9.755\\ \hline 182.994&0.005465&0.006586&0.010226&43.197&0.236&0.326&0.017&7.695\\ \hline 117.136&0.008537&0.013116&0.020154&42.256&0.361&0.501&0.034&6.100\\ \hline 74.980&0.013337&0.025961&0.039591&41.073&0.548&0.768&0.069&4.851\\ \hline 47.995&0.020835&0.051163&0.077607&39.586&0.825&1.168&0.139&3.866\\ \hline 30.722&0.032550&0.100523&0.151915&37.722&1.228&1.764&0.278&3.085\\ \hline 19.665&0.050851&0.197090&0.297081&35.387&1.799&2.638&0.553&2.465\\ \hline 12.588&0.079441&0.385843&0.580450&32.466&2.579&3.889&1.096&1.971\\ \hline 8.058&0.124106&0.754374&1.132370&28.815&3.576&5.622&2.166&1.578\\ \hline 5.158&0.193883&1.471786&2.198818&24.265&4.705&7.901&4.265&1.270\\ \hline 3.302&0.302891&2.854586&4.200217&18.648&5.648&10.642&8.365&1.038\\ \hline 2.113&0.473188&5.430718&7.596980&11.936&5.648&13.450&16.244&0.897\\ \hline 1.353&0.739233&9.785991&11.945027&4.635&3.426&15.614&30.774&0.891\\ \hline 0.866&1.154857&15.923791&15.244637&-2.003&-2.313&16.727&55.742&1.091\\ \hline 0.554&1.804162&23.101099&16.681708&-7.000&-12.630&17.115&96.098&1.557\\ \hline 0.355&2.818530&30.663806&17.131127&-10.379&-29.252&17.217&159.650&2.369\\ \hline 0.227&4.403214&38.339851&17.255151&-12.575&-55.371&17.255&259.082&3.675\\ \hline 0.145&6.878868&46.046595&17.288147&-13.987&-96.214&17.288&414.460&5.730\\ \hline 0.093&10.746428&53.761461&17.296852&-14.892&-160.032&17.297&657.207&8.947\\ \hline 0.060&16.788477&61.478462&17.299157&-15.471&-259.734&17.299&1036.440&13.975\\ \hline 0.038&26.227596&69.196023&17.299782&-15.842&-415.492&17.300&1628.891&21.831\\ \hline 0.024&40.973744&76.913904&17.299794&-16.079&-658.824&17.300&2554.443&34.106\\ \hline 0.016&64.010737&84.631650&17.299862&-16.231&-1038.966&17.300&4000.374&53.281\\ \hline 0.010&100.000000&92.349407&17.299900&-16.328&-1632.838&17.300&6259.262&83.237\\ \hline \end{array}}$$

 

[Mordred]

That was a test from my phone of version 9p its a little tricky doing the copy paste from phone but it is possible. A copy textscript button to clipboard would make it far easier for older phones. The only field I modified on that post is the number of steps set to 26

this is the thread where I used it on

https://www.physicsforums.com/showthread.php?t=684006&page=3

this one is an older version I'd have to check which one though

 

[marcus]

That was a test from my phone of version 9p its a little tricky doing the copy paste from phone but it is possible. A copy textscript button to clipboard would make it far easier for older phones. The only field I modified on that post is the number of steps set to 26

Hey great! It's a kick to see someone else using version 9p! Have you tried the "include S=1.000" feature yet. (Knowing you, you almost surely have ) EDIT: yes it's used in your table in post #48 of that "edge of universe" thread.

Jorrie,
thanks for putting version 9p online! This morning I put the link in my signature. Also in my browser screen's bookmark bar to have it even handier. About double line headers, I'd be happy either way. One line, with the header a'R_o would, I think, be sufficiently clear for beginners IF you expanded the sentence that makes units Gy and Gly explicit to say the sample recession speed history (a'R_o) is given in multiples of the speed of light.

That sentence is an important vehicle because unlike the tooltips it is permanently in view.
Ostensibly it merely tells the user about the units used in table, but by casual mention it can alert the user to another important fact or two:
"Times are given in billions of years (Gy), distances in billions of light years, and the recession speed history (a'R_o) of a sample galaxy now at distance R_o from us is given in multiples of the speed of light."

If that sentence catches the newcomer's attention then he/she knows what column 9 is about and can go mouse the info button to learn more.

 

[Mordred]

yes I've used the S-1.000 feature lol

 

[marcus]

this is the thread where I used it on

https://www.physicsforums.com/showthread.php?t=684006&page=3
...

BTW You probably know this already, but in case not, if you ever want a link to the exact post you just click on the post NUMBER in the upper right corner. For example in this case where it says "#48"
That will give you:
https://www.physicsforums.com/showpost.php?p=4351022&postcount=48
which links to an isolated copy of the post. Then, if you want a link to that post in context of the other posts in the thread you look again in the upper right corner where you see the name of the thread (e.g. "Where is the edge...?") and click on that. This will give a link to your post with the table, now in context:
https://www.physicsforums.com/showthread.php?p=4351022#post4351022

 

[Mordred]

No I didn't know that. When I'm on my phone I don't see post numbers or signatures. However i will be handy when I'm on my comp.

Thanks for that tip

 

[marcus]

Mordred, I'd like to know your feeling about this suggested change. You know right above the table, when you first open the page, it says:
==============================
Select table type Standard Office LaTex TexScript ---- Check this box to include S=1.000

S a T (Gy) R (Gly) D (Gly) Dthen DHor Dpar a'R0
1090. 0.000917 0.000373 0.000628 45.332 ...
...
...
===============================
And then right at the bottom of the table it says:
Time now (at S=1) or present age in billion years:13.787200 'T' in billion years (Gy) and 'D' in billion light years (Gly)
To view a different 'Time now', read this info tip: --------->

Suppose Jorrie were to move the sentence about units up to the top so it would look like:

==============================
Select table type Standard Office LaTex TexScript ---- Check this box to include S=1.000
Time now (at S=1) or present age in billion years:13.787200. 'T' in billion years (Gy), 'D' in billion light years (Gly), sample recession speed history (a'R₀) in multiples of c.
S a T (Gy) R (Gly) D (Gly) Dthen DHor Dpar a'R₀
1090. 0.000917 0.000373 0.000628 45.332 ...
...
...
===============================
To view a different 'Time now', read this info tip: --------->

My question is, putting yourself in the place of a newcomer or beginner, does that make any difference. Is it more confusing/off-putting or less? More user-friendly, or less?
EDIT I just saw that you are out and using phone. Probably at work. So now is the wrong time for me to be asking this. But please let me know later whenever it's convenient and you've had time to think about it.

 

[Mordred]

Yeah I like your suggestion. Thinking in terms of a new user/layman understanding.

Thinking in terms of a sort of familiar layman in terms of redshift terminology.
"are the distances given in angular or radial commoving?
or are they converted to proper distances?

Thinking in terms of "I wish it could do this"
wouldn't it be nice if it had a side bar unit converter or chart.

And wouldn't it be nice to play around with other units.

Not sure how feasible those ideas are in terms of programming but I can see that it may generate interest in the
calculator. Having a unit
converter more so than the
seond suggestion

Another possible wish list item.

Wouldnt it be nice to see how a known emitter luminosity changes due to redshift. Such as a form of standard candle

For a one stop shop calculator I would add "Wouldn't it be nice to play with the flat and curved metrics or other related parameters along with unit conversion and type of distance conversion.

That would be a calculator one would have a hard time putting down.

Lol however as a programmer I know much that's asking lol

 

[Jorrie]

That would be a calculator one would have a hard time putting down.

Lol however as a programmer I know much that's asking lol

The lucky part is that my programmer son is visiting atm. He plans to rewrite the calculator-engine for more flexibility anyway. We will collect all the wishlists and try separating them into beginners and advanced and attempt to make all of them available at some level. Should be ready by next weekend.

 

[Mordred]

I may be able help in that.

On my flashdrive at work I have a small. Exe converter.
I can't recall how it measured up on cosmology units however it can convert pretty much any other unit one can ask for in most fields of study.
Its also very user friendly.

Out of any software based calculators its my all time favourite. Been packing that calculator for close to 12 years.
I can probably zip it and post on Monday.

 

[Jorrie]

The lucky part is that my programmer son is visiting atm. He plans to rewrite the calculator-engine for more flexibility anyway. We will collect all the wishlists and try separating them into beginners and advanced and attempt to make all of them available at some level. Should be ready by next weekend.

I may be able help in that.

On my flashdrive at work I have a small. Exe converter.
I can't recall how it measured up on cosmology units however it can convert pretty much any other unit one can ask for in most fields of study.

Thanks for the offer and interest, especially with a user manual. Your suggestions towards functionality are much appreciated. The users on PF are really the drive behind this specific calculator.

A converter calculator may not be too useful in the context of the TabCosmo calculator though. The 'engine' I was referring to is the internal workings of Tabcosmo - it has become a tad unstructured with the various updates and features added, so a good cleanup, without adding to it, is now required. Then I will consider adding more user choice towards selectable input sets (e.g. beginners, advanced, WMAP, Planck, others...) and customizable output columns.

 

[Mordred]

I fully agree in that approach.
Portions of said facelift will probably affect the writing of the user manual in regards to changes in how the tooltips are written. So its good to understand your current goals on the programming end.

 

[Jorrie]

I fully agree in that approach.
Portions of said facelift will probably affect the writing of the user manual in regards to changes in how the tooltips are written. So its good to understand your current goals on the programming end.

What do you think of eventually creating a Wiki on some reliable Wiki-hosting site for the TabCosmo manual? Wikis have superior functionality for collaboration (e.g. change-tracking with roll-back) and also some multimedia capabilities. With 'eventually' I mean after initial discussions and thrashing out of the ideas on PF.

 

[Mordred]

Its an idea that does have its merits. For the reasons you mentioned above. As well as wiki's volume of users.

 

[Mordred]

found a handy option with excel, when you use the calculator copy all in standard.

then if you have chart option on your excel use paste special html.


$${\scriptsize \begin{array}{|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.92&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize \begin{array}{|r|r|} \hline S=z+1&a=1/S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&a'R_{0} \\ \hline 1090.000&0.000917&0.000373&0.000628&45.332&0.042&0.057&0.001&21.023\\ \hline 824.004&0.001214&0.000596&0.000986&45.123&0.055&0.075&0.001&17.729\\ \hline 622.920&0.001605&0.000943&0.001537&44.875&0.072&0.099&0.002&15.044\\ \hline 470.907&0.002124&0.001483&0.002383&44.585&0.095&0.130&0.004&12.831\\ \hline 355.990&0.002809&0.002318&0.003681&44.245&0.124&0.171&0.006&10.989\\ \hline 269.117&0.003716&0.003606&0.005666&43.849&0.163&0.224&0.009&9.443\\ \hline 203.444&0.004915&0.005586&0.008699&43.389&0.213&0.294&0.014&8.137\\ \hline 153.797&0.006502&0.008621&0.013327&42.856&0.279&0.386&0.022&7.026\\ \hline 116.265&0.008601&0.013267&0.020383&42.239&0.363&0.505&0.035&6.076\\ \hline 87.893&0.011378&0.020369&0.031137&41.526&0.472&0.660&0.054&5.262\\ \hline 66.444&0.015050&0.031211&0.047518&40.703&0.613&0.861&0.084&4.561\\ \hline 50.229&0.019909&0.047749&0.072463&39.753&0.791&1.120&0.130&3.956\\ \hline 37.972&0.026335&0.072963&0.110441&38.659&1.018&1.452&0.200&3.434\\ \hline 28.705&0.034837&0.111382&0.168249&37.399&1.303&1.877&0.309&2.982\\ \hline 21.700&0.046082&0.169898&0.256221&35.948&1.657&2.416&0.475&2.590\\ \hline 16.405&0.060958&0.258995&0.390062&34.278&2.090&3.095&0.731&2.250\\ \hline 12.401&0.080636&0.394607&0.593593&32.357&2.609&3.939&1.121&1.956\\ \hline 9.375&0.106665&0.600921&0.902799&30.146&3.216&4.974&1.719&1.701\\ \hline 7.087&0.141098&0.914540&1.371531&27.607&3.895&6.222&2.633&1.481\\ \hline 5.358&0.186646&1.390430&2.078601&24.693&4.609&7.686&4.026&1.293\\ \hline 4.050&0.246896&2.109877&3.133394&21.363&5.274&9.345&6.148&1.135\\ \hline 3.062&0.326597&3.188436&4.668210&17.587&5.744&11.128&9.366&1.007\\ \hline 2.315&0.432025&4.776649&6.785555&13.382&5.781&12.904&14.206&0.917\\ \hline 1.750&0.571486&7.034071&9.415811&8.859&5.063&14.485&21.377&0.874\\ \hline 1.323&0.755967&10.055776&12.153347&4.274&3.231&15.695&31.743&0.896\\ \hline 1.000&1.000000&13.787206&14.399932&0.000&0.000&16.472&46.279&1.000\\ \hline 0.756&1.322809&18.036680&15.848777&-3.713&-4.912&16.897&66.111&1.202\\ \hline 0.636&1.572668&20.828978&16.391142&-5.651&-8.887&17.042&81.645&1.382\\ \hline 0.535&1.869723&23.697550&16.741545&-7.325&-13.696&17.130&100.197&1.608\\ \hline 0.450&2.222887&26.614648&16.961015&-8.757&-19.467&17.182&122.307&1.887\\ \hline 0.378&2.642759&29.561671&17.095931&-9.975&-26.361&17.210&148.626&2.226\\ \hline 0.318&3.141938&32.527232&17.177642&-11.005&-34.577&17.224&179.937&2.634\\ \hline 0.268&3.735406&35.503890&17.226808&-11.875&-44.358&17.228&217.174&3.122\\ \hline 0.225&4.440970&38.487213&17.256248&-12.608&-55.993&17.256&261.452&3.706\\ \hline 0.189&5.279806&41.474352&17.273992&-13.226&-69.831&17.274&314.097&4.401\\ \hline 0.159&6.277087&44.464043&17.284457&-13.746&-86.285&17.284&376.689&5.230\\ \hline 0.134&7.462739&47.455154&17.290675&-14.184&-105.848&17.291&451.106&6.215\\ \hline 0.113&8.872344&50.447111&17.294360&-14.552&-129.108&17.294&539.580&7.387\\ \hline 0.095&10.548203&53.439399&17.296709&-14.861&-156.761&17.297&644.766&8.782\\ \hline 0.080&12.540608&56.432159&17.297985&-15.122&-189.638&17.298&769.820&10.440\\ \hline 0.067&14.909350&59.425098&17.298727&-15.341&-228.725&17.299&918.495&12.411\\ \hline 0.056&17.725513&62.418143&17.299150&-15.525&-275.196&17.299&1095.253&14.755\\ \hline 0.047&21.073610&65.411078&17.299556&-15.680&-330.444&17.300&1305.398&17.541\\ \hline 0.040&25.054115&68.404224&17.299677&-15.811&-396.128&17.300&1555.237&20.855\\ \hline 0.034&29.786480&71.397392&17.299730&-15.921&-474.218&17.300&1852.267&24.794\\ \hline 0.028&35.412721&74.390574&17.299744&-16.013&-567.059&17.300&2205.402&29.477\\ \hline 0.024&42.101679&77.383590&17.299906&-16.090&-677.436&17.300&2625.238&35.044\\ \hline 0.020&50.054085&80.376784&17.299882&-16.156&-808.662&17.300&3124.376&41.664\\ \hline 0.017&59.508588&83.369981&17.299849&-16.211&-964.674&17.300&3717.794&49.534\\ \hline 0.014&70.748912&86.363007&17.299984&-16.257&-1150.155&17.300&4423.299&58.889\\ \hline 0.012&84.112372&89.356207&17.299943&-16.296&-1370.670&17.300&5262.065&70.013\\ \hline 0.010&100.000000&92.349407&17.299900&-16.328&-1632.838&17.300&6259.262&83.237\\ \hline \end{array}}$$

anyways you can graph the results that way with Excel however the forum limitation on file size won't let me post it grrrr...

 

[Mordred]

there it accepts larger pdf files lol