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## Look 88 billion years into future with the A20 tabular calculator

 Quote by Jorrie Marcus, the latter two values are correct as defined for the calculator, but they may need a little more explanation...
I am just so pleased with this calculator! It's versatile like a swiss jackknife, you can do a lot of things with.

And that leads to opportunities to explain more stuff, like what you just did. For instance the idea of proper distance (distance at a certain moment with expansion stopped).

Also I guess I should be restrained and not try to bring in TOO MUCH. Introduce concepts slowly. But it's tempting to also mention the idea of the COMOVING DISTANCE which is simply Dnow. The comov. distance of some matter is a way of tagging the matter with a serial number that never changes. So it can be useful. By convention it is the now distance (as of today).

When I did those simple calculations before, conceptually I was working in comoving distance, and then at the end, converting to proper distance at "recombination time" simply by dividing by 1090. That is always how one converts comoving distance to distance at the moment the CMB flash was emitted.

==quote==
... suggested earlier, you know that the two distances we need are 2.9 and 4.4
those are the addition distances the light has to travel to get to the people in Years 17 and 19 billion who are going to receive it. But it already traveled 45.9 by the time it got to us. (In Dnow terms.)

(45.9+2.9) billion/1090 = 44.8 million
(45.9+4.4) billion/1090 = 46.1 million
==endquote==

I guess I am actually talking to people who might be reading (not to you Jorrie). You have to click on the "A27" link and put in something like
upper=1
lower=.6
step=.1
and actually see that for those Years the Dnow distances 2.9 and 4.4

So after the light has covered a comov. distance of 45.9, and has passed the way station (us) and is racing on towards the people who are to receive it in Year 17 billion,
then how far, in comov. terms, does it have to travel?

Well it is just as if we sent them a message today--a flash of a different color to travel neck and neck all the way to them. And the comov. distance from us to them is 2.9

So to get the total comov. diet you just add 45.9 and 2.9. That is the comov. dist between them and the source matter of the CMB which they will see in Year 17 billion.

Now since it is the comov. distance you just have to divide by 1090, and bingo.

Jorrie forgive me if I'm revealing too much enthusiasm, but AFAIK this is unique. I don't know of any online cosmo calculator that has future as well as past, and none of the others give the Event Horizon. In fact they don't do half the things this one does. There's only one other I've seen that tabulates. (A recent one by someone at Oxford in the UK, as I recall.)
The trouble is we have a distribution bottleneck. More beginning astronomy students should get to use it. I don't know how to get the word out. Maybe there are some active academics here at PF who would be willing to pass the link along to colleagues in the astronomy department.

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 None of the columns seem to have the 41 Million light years distance in there.
edit: oops, did not realize we have a page two...and two more posts befoe this. [We shall have to slow Marcus down as in "Curb that enthusiasm." as he is posting faster than I am reading [LOL]....

If I understand what I am looking at in the chart, 41/42 mly is way,way off to the right, via the purple curve, 'distance then'..

As I recall that is about 380,000 years after the big bang and a redshift of about 1090.

[The chart uses S =1+z, and only goes to S =10, redshift of z = 9. ]

In fact I started to try to calculate the distance at z =10, and never found a simple formula....I suspect that's why we have the calculator....

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 Quote by Naty1 edit: oops, did not realize we have a page two...and two more posts befoe this. [We shall have to slow Marcus down as in "Curb that enthusiasm." as he is posting faster than I am reading [LOL].... If I understand what I am looking at in the chart, 41/42 mly is way,way off to the right, via the purple curve, 'distance then'.. As I recall that is about 380,000 years after the big bang and a redshift of about 1090. [The chart uses S =1+z, and only goes to S =10, redshift of z = 9. ] In fact I started to try to calculate the distance at z =10, and never found a simple formula....I suspect that's why we have the calculator....
It's great you are using the calculator, I find it really "empowering" (as they say).

As you know, and most other readers as well, YOU decide the range that the table covers. for example if you want it to cover all of history since the CMB flash (which gets stretch 1090) and if you want the table to have 10 downsteps from there to the present (i.e. 11 rows) then you put in:

upper=1090
lower=1
step= -10

You can also make it show more, or fewer, decimal places in the answers. So it can give more precision in some columns and round off in other columns. You just type the number of decimal places you want the answer to have, in that column, in the box at the head of the column.

 Recognitions: Gold Member Science Advisor Here's a result I just now got, to demo the feature where you control the precision. I set it to show 1 decimal place for the Stretch, 4 for the scalefactor a, 6 for the Year, 4 for the Hubbletime, 1 for Dnow, 4 for Dthen, and 3 decimal places for Dhor the event horizon distance: Code: S a T T_Hub D_now D_then D_hor 1090.0 0.0009 0.000381 0.0006 45.9 0.0421 0.056 981.1 0.0010 0.000455 0.0008 45.8 0.0467 0.063 872.2 0.0011 0.000554 0.0009 45.7 0.0524 0.070 763.3 0.0013 0.000691 0.0011 45.6 0.0598 0.080 654.4 0.0015 0.000889 0.0015 45.5 0.0695 0.093 545.5 0.0018 0.001196 0.0019 45.3 0.0830 0.112 436.6 0.0023 0.001712 0.0027 45.0 0.1032 0.139 327.7 0.0031 0.002704 0.0043 44.7 0.1363 0.184 218.8 0.0046 0.005103 0.0080 44.0 0.2012 0.273 109.9 0.0091 0.014809 0.0227 42.6 0.3875 0.530 1.0 1.0000 13.754712 13.8999 0.0 0.0000 15.622 I checked the calculator's "copy/paste friendly version" box to get a table output in a format that I could copy and paste easily. But the normal output looks better, in the grid designed for it. So try it yourself just set upper=1090, lower=1, step=-10 1090 being the stretch factor for the CMB flash and 1 being the stretch factor for the present (i.e. no change in distances or wavelengths, the identity)

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 Quote by marcus The trouble is we have a distribution bottleneck. More beginning astronomy students should get to use it. I don't know how to get the word out. Maybe there are some active academics here at PF who would be willing to pass the link along to colleagues in the astronomy department.
I've got some feedback that our use of the Hubble times Ynow and Yinf as the primary input parameters are off-putting to some teachers. They say it brings in the idea of the Hubble time too early for beginners and they would like to start with the Omegas; students do not find the Y's in published results, only the Omegas. Some also prefer z rather than S as an input, but this is not really an important issue. Maybe having negative z for the future is more intuitive than our 0 < S < 1?

Actually in my calculator I immediately convert the Ys to Omegas, so apart from the user interface and "front-end", nothing else need to change. I will look into the possibility of a B-model, returning it to the legacy input parameters, giving people a choice.

What do you think?

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 Quote by Naty1 In fact I started to try to calculate the distance at z =10, and never found a simple formula....I suspect that's why we have the calculator....
Yes, if you look at the equations in http://www.physicsforums.com/showpos...3&postcount=29, they all have integrals - hence the need for a numerical integrator...

(Now CosmoLean_A27, no longer A22).

 Mentor Some different scaling for the scale factor entries would be interesting - maybe equidistant logarithm or equidistant scale factor (+optional?). If you want to look at the range of 1090 to 1, for example, you just have a single entry in the stelliferous era, unless you want 100+ lines as output. Entries like (1090, 545, ..., 2, 1) +- rounding errors would be more relevant I think.

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 Quote by mfb Some different scaling for the scale factor entries would be interesting - maybe equidistant logarithm or equidistant scale factor (+optional?). If you want to look at the range of 1090 to 1, for example, you just have a single entry in the stelliferous era, unless you want 100+ lines as output. Entries like (1090, 545, ..., 2, 1) +- rounding errors would be more relevant I think.
Yes, good idea. I will look into that as an option during the next update.

What do you think of working with Hubble time inputs vs. standards density parameters and Hubble constant as input?

 Mentor I think if you want to change those parameters, you usually know how to do that. Density parameters are probably easier to manipulate, however.

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 Quote by mfb Some different scaling for the scale factor entries would be interesting - maybe equidistant logarithm or equidistant scale factor (+optional?). If you want to look at the range of 1090 to 1, for example, you just have a single entry in the stelliferous era, unless you want 100+ lines as output. Entries like (1090, 545, ..., 2, 1) +- rounding errors would be more relevant I think.
I have done a first attempt at an optional nonlinear scaling of the stretch (scale) factor. It divides S by any S_step larger than 1, with 2 probably the most useful. There is a tick box in the latest version, which I have renamed to TabCosmoC1 (for Tabular Cosmological Calculator).

After a bit of forum testing and perhaps tuning, we can make it more visible again.

 Recognitions: Gold Member Jorrie...this model: cool. Thanks for your efforts.!!
 Mentor Very nice, thanks. Yinf standard is 16.3, but the tooltip gives 16.9 as best fit?
 Recognitions: Gold Member Science Advisor Indeed it is very nice! Here's something I just tried with the nonlinear step box checked. I wanted 20 steps down from 1090 to 1 (from recombination to present) so I put this into google calculator: "1090^.05" and got 1.41863714 That is the 20th root of 1090. So I put in S upper = 1090 S lower = anything less than 1 would do, I happened to put 0.15 step = 1.41863714 (just pasted in from the calculator) Code: S a T T_Hub D_now D_then D_hor 1090.00 0.001 0.000 0.001 45.890 0.042 0.056 768.34 0.001 0.001 0.001 45.617 0.059 0.080 541.61 0.002 0.001 0.002 45.280 0.084 0.112 381.78 0.003 0.002 0.003 44.870 0.118 0.158 269.12 0.004 0.004 0.006 44.373 0.165 0.223 189.70 0.005 0.006 0.010 43.773 0.231 0.313 133.72 0.007 0.011 0.017 43.051 0.322 0.439 94.26 0.011 0.019 0.029 42.186 0.448 0.613 66.44 0.015 0.032 0.049 41.151 0.619 0.855 46.84 0.021 0.054 0.082 39.913 0.852 1.186 33.02 0.030 0.092 0.140 38.436 1.164 1.638 23.27 0.043 0.157 0.236 36.673 1.576 2.248 16.40 0.061 0.265 0.399 34.571 2.107 3.061 11.56 0.086 0.449 0.675 32.066 2.773 4.125 8.15 0.123 0.759 1.140 29.084 3.568 5.486 5.75 0.174 1.282 1.917 25.541 4.445 7.167 4.05 0.247 2.159 3.200 21.353 5.272 9.133 2.86 0.350 3.607 5.224 16.474 5.770 11.247 2.01 0.497 5.913 8.091 10.988 5.460 13.230 1.42 0.705 9.312 11.326 5.272 3.716 14.739 1.00 1.000 13.755 13.900 0.000 0.000 15.622 0.70 1.419 18.895 15.324 -4.341 -6.158 16.025 0.50 2.013 24.378 15.937 -7.598 -15.292 16.178 0.35 2.855 29.998 16.170 -9.954 -28.419 16.225 0.25 4.050 35.670 16.254 -11.630 -47.105 16.254 0.17 5.746 41.360 16.284 -12.816 -73.637 16.284

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 Quote by mfb Yinf standard is 16.3, but the tooltip gives 16.9 as best fit?
Yes, tooltip in error. Thanks for heads-up, will fix.

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 Quote by marcus I wanted 20 steps down from 1090 to 1 (from recombination to present) so I put this into google calculator: "1090^.05" and got 1.41863714
I thought about putting something like this in the calculator, but in order to retain flexibility, it clutters the relatively 'clean' look and feel a little. Maybe I should put it in the accompanying tooltip...

Edit: Done. Also fixed the tooltip mistake.

 Recognitions: Gold Member Science Advisor One of the luxuries associated with using the new online Cosmic Tabulator is you can (in seconds) get a whole history of the universe from recombination (the origin of the Background) down to today and on far into the future. I just tried this to see how it would look if I set it to use 30 steps to get from recombination to Now, and then let it do a dozen or so steps beyond that into the future. What I like about this (besides that it is very quick to get once you decide you want to start at S=1090 and get to the present in 30 steps) is that you see in context a lot of the numbers that we are always hearing about--that keep coming up in Cosmo Forum threads. For instance right in the first row you see that the CMB was emitted in year 380,000, by matter that was then 42 million LY away, and is now 45.89 billion LY from us. And you see, from the bottom row, that both the distance to the cosmic event horizon AND the Hubble distance are converging together to 16.3 billion LY. In fact that's what they'll essentially be by year 62 billion. And the Hubble times give you a convenient handle on the expansion rates now, and in the past, and in the future. You can see the present Hubble time (in the S=1 row) is 13.9 billion years---this means distances are increasing by 1/139 of a percent every million years. Far in the future, when the Hubble time is stabilizing at 16.3 billion years, distances will of course be increasing by 1/163 of a percent every million years. Then again, if you check out the row around S=2.5 you'll see that, back around year 4 billion, expansion was considerably faster---around 1/60 of a percent per million years. And the nice thing is you get to see how all these numbers gradually change over time. Code: S a T T_Hub D_now D_then D_hor 1090.0 0.001 0.00038 0.001 45.890 0.042 0.056 863.33 0.001 0.00056 0.001 45.714 0.053 0.071 683.80 0.001 0.00083 0.001 45.512 0.067 0.089 541.60 0.002 0.00121 0.002 45.280 0.084 0.112 428.97 0.002 0.00176 0.003 45.016 0.105 0.141 339.77 0.003 0.00255 0.004 44.715 0.132 0.178 269.11 0.004 0.00369 0.006 44.373 0.165 0.223 213.15 0.005 0.00532 0.008 43.985 0.206 0.280 168.82 0.006 0.00764 0.012 43.547 0.258 0.351 133.72 0.007 0.01095 0.017 43.051 0.322 0.439 105.91 0.009 0.01567 0.024 42.492 0.401 0.549 83.889 0.012 0.02239 0.034 41.861 0.499 0.685 66.444 0.015 0.03196 0.049 41.151 0.619 0.855 52.627 0.019 0.04555 0.069 40.350 0.767 1.064 41.683 0.024 0.06488 0.098 39.449 0.946 1.322 33.015 0.030 0.09233 0.140 38.436 1.164 1.638 26.150 0.038 0.13132 0.198 37.295 1.426 2.024 20.712 0.048 0.18667 0.281 36.013 1.739 2.494 16.405 0.061 0.26525 0.399 34.571 2.107 3.061 12.993 0.077 0.37676 0.567 32.950 2.536 3.739 10.291 0.097 0.53495 0.804 31.129 3.025 4.544 8.151 0.123 0.75926 1.140 29.084 3.568 5.486 6.456 0.155 1.07696 1.613 26.790 4.149 6.571 5.114 0.196 1.52614 2.277 24.220 4.736 7.794 4.050 0.247 2.15887 3.200 21.353 5.272 9.133 3.208 0.312 3.04392 4.454 18.176 5.666 10.540 2.541 0.394 4.26571 6.093 14.701 5.786 11.940 2.013 0.497 5.91316 8.091 10.988 5.460 13.230 1.594 0.627 8.05254 10.269 7.165 4.495 14.305 1.263 0.792 10.6898 12.304 3.428 2.715 15.101 1.000 1.000 13.7547 13.900 0.000 0.000 15.622 0.792 1.263 17.1291 14.965 -3.021 -3.814 15.929 0.627 1.594 20.6981 15.594 -5.540 -8.831 16.095 0.497 2.013 24.3777 15.937 -7.598 -15.292 16.178 0.394 2.541 28.1165 16.117 -9.255 -23.516 16.216 0.312 3.208 31.8857 16.208 -10.578 -33.934 16.230 0.247 4.050 35.6702 16.254 -11.630 -47.105 16.254 0.196 5.114 39.4625 16.277 -12.465 -63.743 16.277 0.155 6.456 43.2586 16.289 -13.127 -84.754 16.289 0.123 8.151 47.0568 16.294 -13.652 -111.28 16.294 0.097 10.291 50.8558 16.297 -14.068 -144.77 16.297 0.077 12.993 54.6553 16.299 -14.397 -187.06 16.299 0.061 16.405 58.4551 16.299 -14.658 -240.46 16.299 0.048 20.712 62.2551 16.300 -14.865 -307.87 16.300 Time now (at S=1) or present age in billion years: 13.7547 Again looking at the bottom row, to give an example of telling yourself stories to interpret the numbers, suppose today we decide to send a message (an intense flash of light) to a galaxy which is NOW 14.865 billion LY from us. there are lots of galaxies like that, most of those we see with a telescope are that far or farther. So imagine we pick out an especially pretty one and decide to send them a message today. How long will the message take to reach them? Well today is year 13.75 billion and the table says the message gets there in year 62.25 billion, so you do the arithmetic. And how far will they be from us when the message actually "catches up" to them and gets there? The table says they will be 20.7 times farther than they are today, and that means they will be at a distance of 307.87 billion LY. I keep the link to the calculator in my signature to have it handy. But here it is, a little more visibly: http://www.einsteins-theory-of-relat...abCosmoC1.html As always, thanks Jorrie. It's neat.