# Our ideas on v_rec/c column added to J's calculator

1. Apr 14, 2013

### marcus

Jorrie obviously doesn't have to adopt any of our suggestions in building his tabular (cosmic history) calculator. It's his project and he's doing all the work. But he's said in several threads that he would like reactions/suggestions from us (and he may have used them in some cases.)

Maybe PF is a good environment for developing teach/learn tools like this. Maybe it would be constructive if people wanted to respond with whatever your thoughts are about his adding a 9th column about RECESSION SPEED history of a representative galaxy which today is at Hubble distance.

1. Should there be a 9th column at all? The table is getting fairly wide already. The calculator is intended to appeal to beginners so they can get familiar with standard model cosmology at a quantitative (not merely verbal) level. So one concern is not to overwhelm beginners with "too much all at once".

2. If there is to be a 9th column, should it be about recession speed?
Have a look at the calculator. What would you like to see in the 9th column? What other kind of information could there be besides what is already in the first 8 columns?

Here are the first 8, they seem essential to me. Do they to you? These are all things I would want to have handy and not be always having to calculate or go to Ned Wright's one-shot calculator for.
Do you disagree? Would you reallocate any of the first 8 columns?

stretch factor (i.e. redshift+1)
scale factor
Time
Hubble radius at that time
Distance now
Distance then (at that time)
cosmic event horizon at that time
radius of observable region at that time (i.e. particle horizon)

3. Suppose a 9th column is adjoined to these and suppose it is going to be about the recession speed of some representative galaxy. What sample galaxy do you pick? What Jorrie is proposing, and has implemented already in his version 9 (link in his sig) is the sample galaxy should be one that today is at today's Hubble distance Rnow or Ro.

That has the advantage that this distance Rnow is one of the 3 model parameters that are input to the model. (when you open the calculator you can either use the default Rnow=14 Gly or whatever, or you can type in some other parameter. It is part of the set-up. So that distance is "around". It serves as a kind of unit or reference scale.

Should one be able to adjust this? Or should one keep it simple and just use Rnow?

Should the column heading say "recession speed" e.g. vrec
or should it say vrec/c because it is giving recession speed as a multiple of the speed of light
or should it say Rnowda/dT, because that is what it is, mathematically (although that would not always say "recession speed" to every user)?

Still undecided about some of this. Like to know your thoughts on it. Have to go, back soon.

2. Apr 14, 2013

### Mordred

I am in two schools of thought on this.

1) One of the common misunderstandings of recessive velocity is that it represents a galaxies inertia rather than merely expansion
Also most laymen posting on expansion or redshift are not familiar with the distance relation of recessive velocity.
Another columm might help better show that relation.

2) In my other school of thought recessive velocity is easy to determine via a simple calculation with the columms already existing stretch factor and distance column.

A 9th column may be easier to relate the recessive velocity relation, it certainly couldn't hurt I don't think it will increase the complexity of the calculator.

I would suggest adding an instruction manual containing the formulas used in the calculator as link on the calculator webpage. Have that file as a downloadable rather than have the new user search the various forum articles for how to use it.

3. Apr 14, 2013

### marcus

Yes to both! Very helpful to point these two things out.

1. Indeed recession speed is not like ordinary motion, nobody gets anywhere and relative positions don't change saving that everybody is farther apart. So it is really best thought of as the change in separation between Cmb STATIONARY observers. (We neglect any random individual motion thru space by the two galaxies.) Everything is in relation to Cmb rest, the soup of uniform ancient light from the uniform ancient matter. We have to make this clear all the time! that could be explained in one of the "tooltips" (the blue info buttons) or in some text right below the table where some other things are already explained, like how to go back in time and have the table be from a different time perspective...
Anyway, recession speed has to be explained, as you say.

2. Yes. what is easy to determine is recession speed for GALAXIES ON THE LIGHTCONE that we are today receiving light from. You can find recession speed at time of emission and also at present moment

Dthen/Rthen = vrec(then)

Dnow/Rnow = vrec (now)

But every time you pick a different S-epoch you are getting a different place on the lightcone and a different galaxy. What we don't have (this is part of Jorrie's point) is a history where you follow one single galaxy and track it's speed over the whole history of expansion.

Even before the galaxy condensed and was a galaxy, back when it was just some diffuse matter, part of a hot cloud of gas, it and the space around it had a recession speed away from us (or from our matter at the time). the idea is pick a single representative, at some sample distance, and track it.

What Jorrie has come up with is to choose matter which is at comoving distance Rnow, whatever the user has for that, like say 14 Gly.
And then the recession speed is given by this formula:
vrec (T) = Rnow da/dT

You know that a(T) is normalized to equal one: a(now) = 1. the scale factor is a dimensionless number meaning no units, a pure number.
The recession history of any galaxy is given by its distance now multiplied by a(T).
So its recession SPEED history is given by its distance now multiplied by da/dT.

So if you decide to watch a galaxy whose distance now from us is Rnow
then the distance history will be Rnowa(T)
and the recession speed history will be Rnowda/dT.

If you look at the calculator version 9, I think that is how the column is labeled.

Now you can also calculate this for yourself! As long as we are using Gly for distance and Gy for time it is simply a(T)Rnow/R(T).
On a one-shot basis that would be easy enough for the user to calculate. For a particular epoch S you just take the scalefactor in that row of the table, and multiply by sample now distance (taken to be Rnow) and divide by the Hubble radius in that row of the table.

But the pedagogical purpose of the table calculator is to let you see the GESTALT, the shape of history, at a glance. without doing a lot of individual calculations all down the line, which you could do. Wouldn't it be nice to immediately SEE the recession speed start very large back in early days, and then get less and less, and then around year 7 billion start picking up and get faster and faster---and see it exceed the speed of light, at a certain point? And so on.

It's something to think about. Might be worth devoting a column.

Last edited: Apr 14, 2013
4. Apr 14, 2013

### Mordred

Yeah I agree an extra column may be worth it.
Tooltips are handy for the " How to use the calculater"
What I feel is needed is a link to an expanation of the physics behind the calculator. What terms such as scale factor means for 1 example. Our target audience includes those that do not know what common terms or what redshift means. So a handy physics article correlated with the calculator usage would probably generate usage. Incude in said article example exercises.

Lol I particularly enjoy that the calc works well from my phone. :P

edit: Its quite possible to adapt the article I have written and often post to that. I'm willing to work on a rewritten version with the calculator usage. I would need assistance on suggestions etc however.

Last edited: Apr 14, 2013
5. Apr 15, 2013

### Jorrie

I have a link at the bottom of the calculator that points to a post on the "model" used, which is just a bare set of equations really. I agree that we can do with a brief "user manual" and perhaps a tutorial. I am out of town and hence short of time, but you guys can start suggesting ideas and we can consolidate them into one attachment, maybe?

6. Apr 15, 2013

### Mordred

Sure I can start an article, I'll try to make it far shorter than my last article though lol. Although once I have a rough draft Ill start a seperate thread.

The OP question on recessive speed still needs consideration

Last edited: Apr 15, 2013
7. Apr 15, 2013

### marcus

Here's what, to me, seems like the main outstanding question in the OP.
Here's how it might look with a column heading like "sample v_c" or simply "v_c"

$${\begin{array}{|c|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14&16.5&3280&69.86&0.72&0.28\\ \hline \end{array}}$$ $${\begin{array}{|r|r|r|r|r|r|r|} \hline S=z+1&a=1/S&T (Gy)&R (Gly)&D (Gly)&D_{then}(Gly)&D_{hor}(Gly)&D_{par}(Gly)&v_{rec}\\ \hline 1090.000&0.000917&0.000378&0.000637&45.731&0.042&0.056&0.001&20.164\\ \hline 541.606&0.001846&0.001200&0.001945&45.126&0.083&0.113&0.003&13.292\\ \hline 269.117&0.003716&0.003662&0.005761&44.225&0.164&0.223&0.009&9.029\\ \hline 133.721&0.007478&0.010876&0.016772&42.912&0.321&0.439&0.028&6.242\\ \hline 66.444&0.015050&0.031751&0.048364&41.023&0.617&0.855&0.085&4.357\\ \hline 33.015&0.030289&0.091754&0.138771&38.325&1.161&1.640&0.253&3.056\\ \hline 16.405&0.060958&0.263633&0.397095&34.484&2.102&3.066&0.743&2.149\\ \hline 8.151&0.122680&0.754694&1.132801&29.030&3.561&5.501&2.164&1.516\\ \hline 4.050&0.246896&2.146402&3.182937&21.343&5.269&9.172&6.254&1.086\\ \hline 2.013&0.496887&5.887073&8.078066&11.017&5.474&13.329&17.716&0.861\\ \hline 1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686&1.000\\ \hline 0.725&1.379730&18.510100&15.398913&-4.071&-5.618&16.192&70.012&1.254\\ \hline 0.525&1.903654&23.586586&16.053616&-7.214&-13.733&16.359&102.579&1.660\\ \hline 0.381&2.626528&28.804384&16.325686&-9.556&-25.100&16.418&147.685&2.252\\ \hline 0.276&3.623898&34.079335&16.432954&-11.273&-40.853&16.433&209.986&3.087\\ \hline 0.200&5.000000&39.376581&16.474344&-12.523&-62.615&16.474&295.973&4.249\\ \hline 0.145&6.898648&44.682397&16.490176&-13.430&-92.651&16.490&414.622&5.857\\ \hline 0.105&9.518270&49.991486&16.496208&-14.088&-134.096&16.496&578.329&8.078\\ \hline 0.076&13.132639&55.301823&16.498497&-14.565&-191.281&16.498&804.203&11.144\\ \hline 0.055&18.119492&60.612636&16.499361&-14.911&-270.181&16.499&1115.847&15.375\\ \hline 0.040&25.000000&65.923630&16.499682&-15.162&-379.041&16.500&1545.833&21.213\\ \hline \end{array}}$$
Time now (at S=1) or present age in billion years: 13.753301
'T' in billion years (Gy) and 'D' in billion light years (Gly), sample recession speed history of matter now at distance R0, shown as multiples of the speed of light

Last edited: Apr 15, 2013
8. Apr 15, 2013

### Mordred

I'm leaning towards Vrec/c. Makes it clearer that it is recessive velocity/speed of light. If the user manual is written well enough we can show some of the terminology and concepts. With some of the corresponding calculations you have posted above.

9. Apr 15, 2013

### Mordred

I was looking at the tooltips, some good info under them. Might be an idea to look at them a little closer to make it easier for laymen understanding. It could help in aiding understanding. Thats just one idea however. I think one of the problems that prevent greater usage is lack of knowing what values means what. You have dealt with a lot of posters in regards to the Calculator what are some of the problems you've encountered Marcus?

10. Apr 15, 2013

### marcus

Have a look at this higher resolution version! I told the Calculator to give 28 steps down from S=1090 to S=1 and then 28 more to S=.04. That is the range was 1090 to .04 and the S=1 box was checked.

It says that over its whole history the sample galaxy achieves a MINIMUM recession speed in around year 7.7 billion.
Everybody else would achieve their minimum at the same time. The sample galaxy is chosen to have its distance NOW from us be 14.0 Gly. The actual minimum would be proportional to that choice of now distance. In this case it is 0.852.

The slowest the galaxy is ever receding from us (in the whole course of its history) is 85% of the speed of light.
$${\begin{array}{|c|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14&16.5&3280&69.86&0.72&0.28\\ \hline \end{array}}$$ $${\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)&v_{rec}\\ \hline 1090.000&0.000917&0.000378&0.000637&45.731&0.042&0.056&0.001&20.164\\ \hline 849.077&0.001178&0.000574&0.000953&45.543&0.054&0.072&0.001&17.299\\ \hline 661.405&0.001512&0.000866&0.001419&45.325&0.069&0.092&0.002&14.917\\ \hline 515.214&0.001941&0.001301&0.002103&45.073&0.087&0.118&0.003&12.919\\ \hline 401.336&0.002492&0.001943&0.003106&44.782&0.112&0.151&0.005&11.230\\ \hline 312.629&0.003199&0.002891&0.004574&44.448&0.142&0.193&0.007&9.791\\ \hline 243.528&0.004106&0.004284&0.006717&44.066&0.181&0.246&0.011&8.558\\ \hline 189.701&0.005271&0.006328&0.009846&43.629&0.230&0.313&0.016&7.496\\ \hline 147.771&0.006767&0.009322&0.014408&43.131&0.292&0.399&0.024&6.576\\ \hline 115.109&0.008687&0.013699&0.021057&42.563&0.370&0.507&0.036&5.776\\ \hline 89.667&0.011152&0.020093&0.030744&41.917&0.467&0.644&0.053&5.079\\ \hline 69.848&0.014317&0.029424&0.044849&41.182&0.590&0.816&0.079&4.469\\ \hline 54.409&0.018379&0.043031&0.065385&40.348&0.742&1.032&0.116&3.935\\ \hline 42.383&0.023594&0.062863&0.095274&39.400&0.930&1.303&0.172&3.467\\ \hline 33.015&0.030289&0.091754&0.138771&38.325&1.161&1.640&0.253&3.056\\ \hline 25.718&0.038884&0.133830&0.202060&37.105&1.443&2.057&0.372&2.694\\ \hline 20.033&0.049917&0.195082&0.294128&35.722&1.783&2.572&0.547&2.376\\ \hline 15.605&0.064080&0.284235&0.428027&34.154&2.189&3.202&0.802&2.096\\ \hline 12.156&0.082263&0.413945&0.622664&32.377&2.663&3.964&1.176&1.850\\ \hline 9.469&0.105605&0.602597&0.905329&30.363&3.207&4.876&1.722&1.633\\ \hline 7.376&0.135570&0.876751&1.315024&28.084&3.807&5.950&2.520&1.443\\ \hline 5.746&0.174038&1.274606&1.906448&25.507&4.439&7.190&3.683&1.278\\ \hline 4.476&0.223420&1.850354&2.753067&22.602&5.050&8.581&5.378&1.136\\ \hline 3.487&0.286815&2.678630&3.944165&19.346&5.549&10.082&7.837&1.018\\ \hline 2.716&0.368198&3.856519&5.562897&15.738&5.795&11.615&11.390&0.927\\ \hline 2.116&0.472674&5.494908&7.622994&11.826&5.590&13.062&16.471&0.868\\ \hline 1.648&0.606794&7.688893&9.965115&7.742&4.698&14.289&23.622&0.852\\ \hline 1.284&0.778970&10.465993&12.220152&3.709&2.889&15.203&33.467&0.892\\ \hline 1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686&1.000\\ \hline 0.891&1.121828&15.399028&14.609450&-1.569&-1.760&15.973&54.117&1.075\\ \hline 0.795&1.258499&17.107443&15.092728&-3.007&-3.784&16.109&62.520&1.167\\ \hline 0.708&1.411820&18.864892&15.465571&-4.326&-6.107&16.210&71.999&1.278\\ \hline 0.631&1.583820&20.659762&15.747018&-5.526&-8.753&16.283&82.672&1.408\\ \hline 0.563&1.776774&22.482644&15.955924&-6.614&-11.751&16.335&94.676&1.559\\ \hline 0.502&1.993235&24.326185&16.109024&-7.594&-15.136&16.372&108.163&1.732\\ \hline 0.447&2.236068&26.184795&16.220171&-8.474&-18.949&16.397&123.310&1.930\\ \hline 0.399&2.508485&28.054308&16.300304&-9.264&-23.239&16.413&140.314&2.154\\ \hline 0.355&2.814089&29.931660&16.357787&-9.971&-28.060&16.423&159.398&2.408\\ \hline 0.317&3.156925&31.814627&16.398874&-10.603&-33.473&16.429&180.812&2.695\\ \hline 0.282&3.541528&33.701600&16.428166&-11.168&-39.551&16.431&204.840&3.018\\ \hline 0.252&3.972987&35.591427&16.449011&-11.672&-46.372&16.449&231.798&3.381\\ \hline 0.224&4.457010&37.483284&16.463825&-12.122&-54.027&16.464&262.043&3.790\\ \hline 0.200&5.000000&39.376581&16.474344&-12.523&-62.615&16.474&295.973&4.249\\ \hline 0.178&5.609142&41.270902&16.481809&-12.881&-72.251&16.482&334.039&4.765\\ \hline 0.159&6.292495&43.165948&16.487105&-13.200&-83.061&16.487&376.742&5.343\\ \hline 0.142&7.059099&45.061509&16.490861&-13.485&-95.189&16.491&424.649&5.993\\ \hline 0.126&7.919098&46.957434&16.493525&-13.738&-108.795&16.494&478.392&6.722\\ \hline 0.113&8.883869&48.853618&16.495415&-13.965&-124.059&16.495&538.684&7.540\\ \hline 0.100&9.966177&50.749985&16.496756&-14.166&-141.182&16.497&606.320&8.458\\ \hline 0.089&11.180340&52.646646&16.497543&-14.346&-160.392&16.498&682.197&9.488\\ \hline 0.080&12.542423&54.543235&16.498219&-14.506&-181.943&16.498&767.318&10.643\\ \hline 0.071&14.070446&56.439888&16.498700&-14.649&-206.118&16.499&862.809&11.940\\ \hline 0.063&15.784626&58.336588&16.499043&-14.776&-233.239&16.499&969.934&13.394\\ \hline 0.056&17.707642&60.233320&16.499288&-14.890&-263.665&16.499&1090.110&15.025\\ \hline 0.050&19.864935&62.130075&16.499464&-14.991&-297.796&16.499&1224.926&16.856\\ \hline 0.045&22.285048&64.026847&16.499590&-15.081&-336.087&16.500&1376.167&18.909\\ \hline 0.040&25.000000&65.923630&16.499682&-15.162&-379.041&16.500&1545.833&21.213\\ \hline \end{array}}$$
Time now (at S=1) or present age in billion years: 13.753301
'T' in billion years (Gy) and 'D' in billion light years (Gly), sample recession speed history of matter now at distance R0, shown as multiples of the speed of light
===========================
You can see the speed get down to 0.852 right around year 7.69 billion, and then start picking up again, so that by year 10 billion it is already around 0.892

And then by year 13.75 billion which is the PRESENT, the sample galaxy recession speed is EXACTLY THE SPEED OF LIGHT. That is by definition because we CHOSE the galaxy to have now distance equal to the current Hubble radius (14.0 Gly) and the Hubble radius at any epoch is defined as the distance which is in that moment increasing at the speed of light.

Mordy, I don't know if this aspect of the table catches your attention but I noticed how much more gradual the increase is, compared to the deceleration in the first 7 billion years.
Back in S=1090 when the ancient light Background was emitted the galaxy was receding at 20 c, and then it only took some 7.7 billion years to slow down to its minimum!
Then speed started rising but so gradually that it takes OVER FIFTY billion years for it to get back to around 20 c, which it was at the start of this segment of history.

It doesn't get back to that earlier level until around year 66 billion.

Last edited: Apr 15, 2013
11. Apr 15, 2013

### Mordred

nice results, I started on a manual, will defintely need help on several areas, examples such as these would make good exercises for the user manual.

The Cosmological Tabular Calculator

The tabular calculator is a versatile tool to understand how the universe expands in the past, present and future. Its flexible nature allows one to examine such factors as distance now, distance in the past, changes in the Hubble rate or constant. The expansion factor given in terms of stretch i.e. how much space-time has expanded.
The calculator was developed to use the Freidmann Lemaitre Robertson Walker metric. This metric is used in the best fit model of LambdaCDM. Where Lambda is the cosmological constant that represents the energy of expansion. That energy is often referred to as Dark energy or vacuum energy. The CDM denotes cold (non relativistic) dark energy.
In order to understand the calculator one needs to understand the terms and symbols used in the calculator.

The Hubble Constant The Hubble “constant” is a constant only in space, not in time, the subscript ‘0’ indicates the value of the Hubble constant today and the Hubble parameter is thought to be decreasing with time. The current accepted value is 69 kilometers/second per mega parsec, or Mpc. The latter being a unit of distance in intergalactic space described above. Any measurement of redshift above the Hubble distance defined as H0 = 4300±400 Mpc will have a recessive velocity of greater than the speed of light. This does not violate GR because a recession velocity is not a relative velocity or an inertial velocity.

this is a rough start there is still lots of work to do on it. I'll probably refer to the FAQ articles on common nature questions.

Edit: just saw your edit lol yeah its nice to see how the recessive velocity results corresponds adding the 9th column defintely helps. Yeah I noticed the significants of that time period, it shows nicely that reccesive velocity /expansion varied during different times.

Last edited: Apr 15, 2013
12. Apr 15, 2013

### Mordred

I'm going to use the Hubble radius definition you just gave in the manual its nice and simplistic

13. Apr 15, 2013

### marcus

Great! Glad to hear it!
One of the nice things we could do in any manual is consistently use the term "cosmological constant" and avoid the phrase "dark energy". There is no evidence as yet that the cosmological constant introduced by Einstein as a CURVATURE constant actually arises from some type of "energy". So the term (which became kind of a buzzword in the early years of the last decade) is potentially confusing and misleading.

The observational evidence that has accumulated over the past 5 years or so is consistent with it being a small constant vacuum curvature, and in the recent cosmology literature that I follow it looks to me as if the experts are tending to prefer the term "cosmological constant". So I would suggest being consistent.
=====================

Something I like very much about the Calculator is that it makes no mention of "Megaparsecs" beyond what is absolutely necessary to connect with the conventional "km/s per Mpc" quantity.
It is very consistent in always using Gly for distance and Gy for time. So that the speed of light has value UNITY. It is 1 Gly/Gy.
This is really convenient in a lot of ways.
The calculator is remarkably clean and convenient--e.g. if you are told that at some past epoch the Hubble time was 12.0 billion years then you immediately know the Hubble radius was 12.0 billion lightyears, and you know that the Hubble expansion rate was 1/120 % per million years.

Whereas if you had the misfortune to be working in terms of seconds, Megaparsecs, and kilometers, then you wouldn't have immediate no-sweat "arithmetic-less" conversions like that.

My hope is that Jorrie's calculator will be of real pedagogical value by making it easy for beginners to grasp the basic overall shape of expansion cosmology without getting swamped in an intimidating random assortment of units, unnecessary detail, and misleading buzzwords.
======================

What I would suggest is that since a user manual is not the same as a mini-textbook in conventional cosmology, the aim would be to stick very close to the language and conceptual style of the calculator (clean, consistent, economical, simple) and bring in as little as possible outside distraction.

14. Apr 15, 2013

### Mordred

http://hubblesite.org/newscenter/archive/releases/2001/09/image/g/

matches up pretty close to this related article.

Yeah I agree on the above I was thinking of just having a conversion section then sticking with the units used in the calculator. Mostly what I have written thus far is a jotting down of ideas, once I have the ideas jotted down I can format to the claculator terms and units.

The above results you posted does show well with the added recessive velocity column the curvature of the above Pic

Last edited: Apr 15, 2013
15. Apr 15, 2013

### Mordred

16. Apr 15, 2013

### Mordred

Hrrrm interesting the calc works on my phone but on my windows xp pro I get 7 script error messages and have to click no each time to get it to calculate. Then to do another calc I have to refresh page.

wonder what setting on my laptop is causing the prob lol

17. Apr 15, 2013

### marcus

Oh no! This has happened to me with an online one-shot cosmos calculator I used to depend on (Siobhan Morgan's Javascript). I have a different computer from yours and I don't remember the type of error. It simply refused to calculate. I'm fairly clueless computerwise and eventually appealed to a family-member for help. Jorrie may be able to give you some advice.

18. Apr 15, 2013

### Mordred

The simple solution is try a different browser. It will most likely work under firefox. As its an IE browser error. I'll try that tomorrow.

Been playing around with the calc getting more familiar with it.

19. Apr 16, 2013

### Jorrie

I think it is likely to be browser dependent, but the original error may lurk in the script, where it is difficult to find if my browser (F/Fox) does not complain. When home (next week) I will check it with various browsers.

It may help if you also try different browsers, e.g. switch between IE, F/F and Chrome.

20. Apr 16, 2013

### Mordred

Firefox works if it helps my IE on my laptop at work is version 8 its an older version but as its a work computer I don't have much say in it lol

21. Apr 16, 2013

### Jorrie

I have made a small change that seems to solve the problem with IE9; haven't had time to check earlier versions of IE. CTRL-open or CTRL-refresh to make sure it reloads and is not using the old cached version.

PS: I'm not quite comfortable with the header Vrec for the 9th column, because it does not represent the recession speed of an object for the S that the rows represent. As you know it is specific to an object at R0. I feel that the info tip should rather explain what a'R0 means, because that keeps it strictly correct.

Last edited: Apr 16, 2013
22. Apr 16, 2013

### Mordred

I still get the "a script is causing IE to run slower" stop script popups. As long as I click no each time in IE 8 the script runs correctly and completes the foms and calculations which it didn't before.

So its a bit better than before lol, I had this on my home PC with my wifes FB account, thats how I knew it was an IE compatibility related problem as firefox also solved that problem.

I'm still working on the user manual, it should be fairly short as looking at the tooltips a majority of the instructions are alreaday contained in them. Also Marcus pointed out the need for same terminology and units used in the manual as that in the calculator which I agree with.

edit: judging from when the popups occur it seems to be a problem with recognizing the tables themselves. When I click calculate each time it tries to create x number of rows and columns is when the error occurs. may help in tracking it down.

Last edited: Apr 16, 2013
23. Apr 16, 2013

### marcus

That's a good point. It is a "sample Vrec". The recession history of a sample galaxy chosen to be at distance R0 from us at the present time. This provides a pattern or template for all galaxies' recession histories, since it's always the same curve just with the scale adjusted.

24. Apr 16, 2013

### marcus

Jorrie, one possibility would be to make this text more visible, that is now right at the bottom of the table:
==quote==
'T' in billion years (Gy) and 'D' in billion light years (Gly), sample recession speed history of matter now at distance R0, shown as multiples of the speed of light
==endquote==
This would make clear up front what the units are, for time, distance, speed, and so be user-friendly to newcomers who may not be used to Gly for billion light year, and so on.

I redid this table to hit the inflection point more exactly, at year 7.3 billion.
The table is set to have 26 steps from S=1090 to exact present, and another 26 steps to S=.04.
One can see the minimum recession speed comes in the S=1.7 row, around year 7.3 billion. The slowest recession speed ever attained is 0.8516 c.
$${\begin{array}{|c|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{∞} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14&16.5&3280&69.86&0.72&0.28\\ \hline \end{array}}$$ $${\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)&v_{rec}sample\\ \hline 1090.000&0.000917&0.000378&0.000637&45.731&0.042&0.056&0.001&20.1636\\ \hline 832.918&0.001201&0.000592&0.000983&45.527&0.055&0.074&0.001&17.0999\\ \hline 636.471&0.001571&0.000922&0.001508&45.289&0.071&0.096&0.002&14.5867\\ \hline 486.356&0.002056&0.001428&0.002302&45.009&0.093&0.125&0.003&12.5044\\ \hline 371.647&0.002691&0.002197&0.003500&44.684&0.120&0.163&0.005&10.7630\\ \hline 283.992&0.003521&0.003365&0.005304&44.307&0.156&0.212&0.008&9.2950\\ \hline 217.011&0.004608&0.005131&0.008015&43.872&0.202&0.275&0.013&8.0485\\ \hline 165.828&0.006030&0.007798&0.012088&43.369&0.262&0.357&0.020&6.9840\\ \hline 126.717&0.007892&0.011817&0.018200&42.790&0.338&0.462&0.031&6.0704\\ \hline 96.830&0.010327&0.017862&0.027367&42.124&0.435&0.598&0.047&5.2831\\ \hline 73.992&0.013515&0.026948&0.041109&41.360&0.559&0.773&0.072&4.6026\\ \hline 56.541&0.017686&0.040590&0.061703&40.483&0.716&0.996&0.109&4.0129\\ \hline 43.205&0.023145&0.061058&0.092556&39.477&0.914&1.280&0.167&3.5009\\ \hline 33.015&0.030289&0.091754&0.138771&38.325&1.161&1.640&0.253&3.0557\\ \hline 25.228&0.039638&0.137768&0.207983&37.005&1.467&2.093&0.383&2.6682\\ \hline 19.278&0.051872&0.206718&0.311611&35.494&1.841&2.661&0.580&2.3305\\ \hline 14.731&0.067883&0.310005&0.466715&33.764&2.292&3.365&0.876&2.0363\\ \hline 11.257&0.088835&0.464670&0.698717&31.784&2.824&4.228&1.323&1.7800\\ \hline 8.602&0.116254&0.696135&1.045272&29.520&3.432&5.269&1.994&1.5571\\ \hline 6.573&0.152136&1.042148&1.561411&26.934&4.098&6.502&3.003&1.3641\\ \hline 5.023&0.199093&1.558281&2.325166&23.985&4.775&7.922&4.517&1.1988\\ \hline 3.838&0.260543&2.324459&3.439363&20.641&5.378&9.496&6.782&1.0605\\ \hline 2.933&0.340960&3.450250&5.016065&16.884&5.757&11.146&10.156&0.9516\\ \hline 2.241&0.446198&5.070303&7.113058&12.751&5.689&12.742&15.136&0.8782\\ \hline 1.713&0.583918&7.312958&9.599448&8.373&4.889&14.119&22.363&0.8516\\ \hline 1.309&0.764145&10.232782&12.059647&4.011&3.065&15.144&32.599&0.8871\\ \hline 1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686&1.0000\\ \hline 0.764&1.308652&17.700005&15.230903&-3.469&-4.539&16.147&65.616&1.2029\\ \hline 0.682&1.465878&19.447858&15.566734&-4.731&-6.935&16.236&75.350&1.3183\\ \hline 0.609&1.641994&21.229081&15.819561&-5.879&-9.654&16.301&86.289&1.4531\\ \hline 0.544&1.839269&23.035135&16.007122&-6.919&-12.726&16.348&98.568&1.6086\\ \hline 0.485&2.060245&24.859344&16.144845&-7.857&-16.187&16.380&112.342&1.7865\\ \hline 0.433&2.307770&26.697095&16.244907&-8.700&-20.077&16.402&127.785&1.9889\\ \hline 0.387&2.585034&28.544549&16.317231&-9.457&-24.446&16.416&145.094&2.2179\\ \hline 0.345&2.895609&30.399001&16.369270&-10.135&-29.346&16.425&164.489&2.4765\\ \hline 0.308&3.243498&32.258319&16.406749&-10.742&-34.841&16.430&186.221&2.7677\\ \hline 0.275&3.633183&34.121403&16.433445&-11.285&-41.000&16.433&210.567&3.0952\\ \hline 0.246&4.069687&35.987064&16.452507&-11.770&-47.901&16.453&237.840&3.4630\\ \hline 0.219&4.558633&37.854565&16.466097&-12.204&-55.634&16.466&268.393&3.8759\\ \hline 0.196&5.106324&39.723214&16.475939&-12.592&-64.297&16.476&302.617&4.3390\\ \hline 0.175&5.719816&41.592963&16.482824&-12.938&-74.001&16.483&340.955&4.8582\\ \hline 0.156&6.407015&43.463378&16.487715&-13.247&-84.873&16.488&383.899&5.4403\\ \hline 0.139&7.176777&45.334268&16.491186&-13.523&-97.051&16.491&432.003&6.0926\\ \hline 0.124&8.039020&47.205331&16.493809&-13.769&-110.692&16.494&485.887&6.8235\\ \hline 0.111&9.004857&49.076799&16.495546&-13.989&-125.973&16.496&546.245&7.6425\\ \hline 0.099&10.086732&50.948438&16.496771&-14.186&-143.090&16.497&613.854&8.5601\\ \hline 0.089&11.298588&52.820200&16.497630&-14.361&-162.263&16.498&689.587&9.5881\\ \hline 0.079&12.656041&54.691883&16.498394&-14.518&-183.740&16.498&774.418&10.7395\\ \hline 0.071&14.176583&56.563793&16.498808&-14.658&-207.797&16.499&869.442&12.0295\\ \hline 0.063&15.879808&58.435746&16.499091&-14.783&-234.745&16.499&975.882&13.4745\\ \hline 0.056&17.787665&60.307731&16.499279&-14.894&-264.931&16.499&1095.110&15.0932\\ \hline 0.050&19.924739&62.179573&16.499566&-14.994&-298.742&16.500&1228.663&16.9063\\ \hline 0.045&22.318568&64.051596&16.499641&-15.082&-336.617&16.500&1378.261&18.9374\\ \hline 0.040&25.000000&65.923630&16.499682&-15.162&-379.041&16.500&1545.833&21.2125\\ \hline \end{array}}$$Time now (at S=1) or present age in billion years: 13.753301
'T' in billion years (Gy) and 'D' in billion light years (Gly), sample recession speed history of matter now at distance R0, shown as multiples of the speed of light.
===================
In case anyone else is reading, and is interested, the table is set to have 26 steps from S=1090 to exact present, and another 26 steps to S=.04.
You can see the minimum recession speed (rightmost column!) comes in the S=1.7 row, around year 7.3 billion. You can also see that for the sample case we are tracking, where the distance today is 14 Gly, the current Hubble radius, the slowest recession speed ever attained is 0.8516 c. That is about 85% of the speed of light.
At present, because the galaxy is at Hubble radius, the recession speed is exactly c. And as you can also see from the table, in future it will continue to grow.
A galaxy at half the distance (now at 7 Gly instead of 14 Gly) would have a proportionally scaled recession speed history---just divide all the speeds by two! So knowing this one sample history lets us get the recession speeds for objects at other distances as well.

Last edited: Apr 16, 2013
25. Apr 16, 2013

### Mordred

I had a thought last night, not sure if its important enough to have it changed. I was thinking having the row number displayed on the left would help in describing which row one is describing.

However as marcus just demonstrated naming the value on the S columm also works, so like I stated not sure if its worth the page real estate.

Marcus I ran into the same number as the minimal recessive velocity, I was playing with the calc last night trying to obtain the same results as your posts. Was a good training exercise.

Aslo for benefict of those paying attention. when you have the results you wish to display simply click the latex checkbox. this will convert the graph to latex, copy all the latex instruction and paste on the forum.

Last edited: Apr 16, 2013