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How big was the Universe 13 billion years ago?

  1. Feb 28, 2013 #1
    How big was the Universe 13 billion years ago??

    If we look from the Earth, in opposite directions, at objects that are 13 billion LY away, they are 26 billion LY apart.

    We are seeing them as/where they were 13 billion years ago, so they must have been 26 billion LY apart then.

    This cannot mean that, 13 billion years ago, the Universe was, at the very least, 26 billion LY in diameter. How do I even start to explain this to someone who seems to expect me to know, simply because I post on a science forum?
     
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  3. Feb 28, 2013 #2

    tiny-tim

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    Hi Endervhar! :smile:

    Explain them as trains, they started very close to you, and now they're 13 billion LY away in opposite directions.

    So what? :wink:
     
  4. Feb 28, 2013 #3
    Re: How big was the Universe 13 billion years ago??

    Its difficult to figure out what your asking. It sounds like your asking how two objects can be 26 billion LY apart 13 billion years ago. Today the universe is 93 billion LY across. This is not to say this is the edge of the universe. Its the edge of the observable universe today.

    How do we see a Universe so much larger than its age. This is due to expansion. In the sticky threads above there is a description of the balloon
    analogy. It has a decent explaination
     
  5. Feb 28, 2013 #4
    Re: How big was the Universe 13 billion years ago??

    The short answer is no one knows the size of the universe now so we cant say what it was in the past either. If it's infinite now, then it was so in the past.
    A source of confusion is the many different types of distance measure used in cosmology, here is a short guide:
    http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Astronomical_distance.html
    and here is a more detailed explanation:
    http://www.publish.csiro.au/?act=view_file&file_id=AS03040.pdf
     
  6. Feb 28, 2013 #5

    marcus

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    Re: How big was the Universe 13 billion years ago??

    Endervhar, you are asking about the OBSERVABLE universe, distances now, and in the past, to material that we can now see (or could in principle, with more advanced instruments, see). that's a fine sort of question! When you learn how to read it, this table can help you.

    Look at the top row. It says the most ancient light we can see came from hydrogen whose distance THEN from us was 42 million lightyears and that matter is NOW 45.7 billion lightyears (45.7 Gly) from here.

    It says that it emitted the light in Year 378,000. That is what 0.000378 Gy means.

    Quite possibly you have no trouble at all reading the table and interpreting half the numbers in the top row. The calculator that generated the table is easy to use and has info popups that explain whatever entries you want explanation for. I chose the table to have 30 rows, but you can get it to recalculate with more or fewer rows, and change other stuff ad lib:

    [tex]{\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}}[/tex] [tex]{\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\\ \hline856.422&0.001168&0.000566&0.000940&45.550&0.053&0.072&0.001\\ \hline672.897&0.001486&0.000842&0.001381&45.341&0.067&0.091&0.002\\ \hline528.701&0.001891&0.001247&0.002020&45.101&0.085&0.115&0.003\\ \hline415.404&0.002407&0.001839&0.002944&44.825&0.108&0.146&0.004\\ \hline326.387&0.003064&0.002700&0.004279&44.509&0.136&0.185&0.007\\ \hline256.445&0.003899&0.003951&0.006205&44.150&0.172&0.234&0.010\\ \hline201.491&0.004963&0.005761&0.008979&43.740&0.217&0.296&0.015\\ \hline158.313&0.006317&0.008379&0.012973&43.275&0.273&0.373&0.021\\ \hline124.388&0.008039&0.012159&0.018720&42.747&0.344&0.471&0.032\\ \hline97.732&0.010232&0.017610&0.026985&42.149&0.431&0.593&0.046\\ \hline76.789&0.013023&0.025465&0.038867&41.472&0.540&0.746&0.068\\ \hline60.334&0.016574&0.036773&0.055945&40.706&0.675&0.937&0.099\\ \hline47.405&0.021095&0.053047&0.080484&39.840&0.840&1.174&0.144\\ \hline37.246&0.026848&0.076452&0.115738&38.861&1.043&1.468&0.210\\ \hline29.265&0.034171&0.110103&0.166377&37.755&1.290&1.830&0.305\\ \hline22.993&0.043491&0.158470&0.239106&36.507&1.588&2.275&0.442\\ \hline18.066&0.055352&0.227971&0.343537&35.097&1.943&2.818&0.641\\ \hline14.195&0.070449&0.327812&0.493442&33.506&2.360&3.474&0.927\\ \hline11.153&0.089663&0.471192&0.708498&31.711&2.843&4.261&1.341\\ \hline8.763&0.114117&0.677001&1.016667&29.686&3.388&5.192&1.938\\ \hline6.885&0.145241&0.972188&1.457265&27.404&3.980&6.276&2.798\\ \hline5.410&0.184854&1.394848&2.084258&24.837&4.591&7.513&4.036\\ \hline4.250&0.235270&1.998124&2.968150&21.958&5.166&8.885&5.814\\ \hline3.340&0.299437&2.853772&4.190977&18.748&5.614&10.347&8.361\\ \hline2.624&0.381105&4.052600&5.822089&15.215&5.798&11.823&11.988\\ \hline2.062&0.485047&5.694902&7.857010&11.408&5.534&13.201&17.104\\ \hline1.620&0.617337&7.861899&10.128494&7.459&4.605&14.363&24.207\\ \hline1.273&0.785708&10.571513&12.291156&3.574&2.808&15.228&33.862\\ \hline1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686\\ \hline\end{array}}[/tex]
    Time now (at S=1) or present age in billion years: 13.75330. 'T' in billion years (Gy) and 'D' in billion light years (Gly)
    ==========
    The 0.042 Gly in the top row "Distance then" column is what I was interpreting as 42 million lightyears. The source of the cosmic microwave background (hydrogen then in the form of glowing hot partly ionized gas) was then much closer of course. Over a thousandfold closer than the same material is today. We see it as it was (namely hot gas) but now the same material is not at the same distance, of course.

    I'd suggest you bookmark the link to the calculator:
    http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
    It's a good learning tool. It makes tables showing the history of the cosmos, where you can specify the range of the table (the start and end) and the number of steps. To get a table with 30 rows you specify 29 steps. that is what I did to make this one. And I specified that the bottom row of the table should be S=1, which is to say the present day. Otherwise I just used the default settings.
     
    Last edited: Feb 28, 2013
  7. Mar 1, 2013 #6
    Re: How big was the Universe 13 billion years ago??

    Thanks folks. Quite a lot to wade through, there, might need to sign up for a maths course to stand a chance of getting my head round some of it, :)

    I think I may have given the wrong impression originally. The OP was actually the first part of a two part question that I was still trying to formulate in my head.

    I have recast that first bit, just to check whether I am asking a question that makes any sense, before (perhaps) progressing to the next bit.

    Two objects are measured as being 13 billion ly from Earth, in opposite directions.

    The light from these objects has taken 13 billion years to reach Earth; thus they are now observed as being in the positions they occupied 13 billion years ago.

    These objects are currently observed as being 26 billion ly apart. Obviously they no longer occupy these positions, because 13 billion years of expansion will have moved them.

    However, it appears that they must have been 26 billion ly apart 13 billion years ago.

    Is the reasoning sound, so far?
     
  8. Mar 1, 2013 #7

    Bandersnatch

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    Re: How big was the Universe 13 billion years ago??

    Unfortunately, the answer is no.

    The light from the farthest objects we see now travelled for 13,7 billion years - that bit is true.

    edit:
    [strike]But it covered more than 13,7 billion light years, due to the stretching of space as it went.[/strike]
    O.k., this was badly put. It's not that it covered more, it's that the point of origin moved away due to the stretching of space as the light travelled, so it's now much farther than 13,7 bln ly.
    end_edit

    Furthermore, at the moment of emission, the source was 42 million years away.

    These numbers all emerge naturally when you consider what it means to have the space expand.

    Here's how I'd explain it to somebody using analogies:

    Imagine that you're walking through expanding space.

    You start at 100 paces away from your target, you make 1 pace per second, and each second all the distances are increased by 1%.

    After making the first step you are 99 paces away from your target, and then the distances stretch by 1%(it's easier to think of it this way, but obviously it all happens simultaionously).
    So, in effect, after 1 second of travel, you are 99,99 paces away.
    You make another step, taking you to 98,99 paces away, and the space stretches by 1%, so you end up 99,9799 paces away.
    And so on.

    It should be obvious to see that getting to your destination will take much, much more than 100 seconds. That's pretty much why the light that was originally emitted at 42 million ly is only getting to us now.

    Another intereting observation to make is that if you were to start at 101 paces away, then you will never reach your destination, as after each step the stretching of space takes you back to 101 paces away. And, obviously, anything initially farther than that will in effect move away despite walking at the same, steady speed of 1 pace per second.
    This means that there is a distance beyond which we may never, ever, see. At this particular moment, if you could measure the distances as they are right now, the farthest point from which we will ever receive light lies 16,5 billion ly away. Of course, by the time the light arrives, the original emitter will have moved way farther than that.

    Additionally, you might notice than the closer your starting point is to 101 paces away, the longer it takes to reach the destination - by a huge factor, reaching infinity as it approaches the limit at 101 paces.
    So there's always some microwave background light you're going to receive, even though it's slowly getting stretched(redshifted) to infinity.
     
    Last edited: Mar 1, 2013
  9. Mar 1, 2013 #8

    marcus

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    Re: How big was the Universe 13 billion years ago??

    But that's not how it works. You're making shaky assumptions.

    Look at the table. It shows the distances back THEN when the objects emitted their light that we are now getting. We do not see objects which were 13 billion lightyears (13 Gly) when the light was emitted. We have never gotten their light.

    We do receive light from objects which are NOW 13 Gly from us. Look in the table in the D column. You can discover how far they were back THEN when they emitted the light. And the table will show you how long the light took to get here.

    Look down the D (the "distance now" column) and you'll find a row for an object which is NOW 12.7 Gly from us. You can see it emitted the light in year 5 billion. The present time is 13.7 billion. So the light took 8.7 billion years to get here.

    [tex]{\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)\\ \hline5.000&0.200000&1.568895&2.340770&23.932&4.786&7.948&4.548\\ \hline4.372&0.228706&1.915830&2.848499&22.312&5.103&8.718&5.571\\ \hline3.824&0.261532&2.337530&3.458116&20.591&5.385&9.519&6.821\\ \hline3.344&0.299070&2.848622&4.183756&18.766&5.612&10.340&8.346\\ \hline2.924&0.341995&3.465480&5.036801&16.839&5.759&11.165&10.202\\ \hline2.557&0.391082&4.205616&6.022104&14.818&5.795&11.977&12.457\\ \hline2.236&0.447214&5.086472&7.132820&12.714&5.686&12.755&15.186\\ \hline1.955&0.511402&6.123474&8.344913&10.548&5.394&13.478&18.474\\ \hline1.710&0.584804&7.327464&9.613886&8.348&4.882&14.126&22.412\\ \hline1.495&0.668740&8.702047&10.877416&6.152&4.114&14.685&27.097\\ \hline1.308&0.764724&10.241950&12.066023&3.999&3.058&15.147&32.633\\ \hline1.144&0.874485&11.932654&13.119328&1.932&1.690&15.513&39.124\\ \hline1.000&1.000000&13.753303&13.999929&0.000&0.000&15.793&46.686\\ \hline\end{array}}[/tex]

    To understand something of the expansion history of the universe doesn't necessarily require highschool math (i.e. algebra, calculus...). You can get some notion if you know ARITHMETIC. A table like this can be especially helpful to people who rely on simple logic and arithmetic. Please use it.
    You asked about an example of an object that is NOW 13 Gly from here. Take 12.7 Gly as close enough.

    Such an object would have been 5.686 Gly from here back then, when it emitted the light.
    We see it as it was in year 5.08 billion (when it emitted the light we're getting).
    The light has taken 8.7 billion years to get here.

    Because of expansion of the distance it has to travel, the light naturally has to take somewhat longer (8.7) than it would with no expansion! It started out when the object was only 5.7 billion lightyears away. So that tells you how long it would have taken without expansion. But the distance increased some while it was traveling. So naturally it takes longer, namely 8.7.

    And when the light arrives, today, in year 13.7 billion, the object is already 12.7 billion lightyears from us! That indicates how long some new light would take to get here if you could freeze the expansion process and wait for it. With expansion stopped it would take 12.7 billion years.

    Hope this helps.
     
    Last edited: Mar 1, 2013
  10. Mar 1, 2013 #9
    Re: How big was the Universe 13 billion years ago??

    Thanks again.

    I think things are getting clearer. I shall give it some thought before deciding if I still need to ask the second part of the question.

    The passage of light through an expanding Universe seems to have much in common with grasping new concepts as one gets older. It takes longer to get there at 72 than it did at 42. :)
     
  11. Mar 1, 2013 #10

    marcus

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    Re: How big was the Universe 13 billion years ago??

    Yes! A very apt comparison! I am 75 and will spare you some of the annoying details you may still have to look forward to:biggrin: The main thing (as we seem both to have discovered) is to be cheerful and keep struggling to understand. Faced with such a beautiful universe, I think it is the only honorable thing to do.
     
    Last edited: Mar 1, 2013
  12. Mar 1, 2013 #11

    marcus

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    Re: How big was the Universe 13 billion years ago??

    Endervhar, I had an idea of how to make that particular table more readable. I just changed the "number of decimal places" down to ONE. (or two)
    Jorrie's calculator lets you decide on the desired level of precision in each column. So this is the same as the earlier table except ROUNDED OFF:

    [tex]{\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)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}[/tex]Time now (at S=1) or present age in billion years: 13.8
    =========================
    So then it is easier to narrate the table. Easier to talk about what it's telling us. Back in year 5.1 billion there was a galaxy at distance 5.7 from us that sent us some light...
    And it took 8.7 billion years to get here, during which time the distance 5.7 had expanded to 12.7.

    Obviously the light had a tough time making it, but it got here. And some of the other light we are getting had an even tougher time of it, a really uphill battle so to speak. You can read off narratives of other light from other rows of the table.

    So far you and I are only using 3 columns of the table: T (the time), D (the galaxy's distance NOW), and Dthen (the galaxy's distance back then when it emitted the light we are getting today).

    If and when you feel like acquiring some of the other columns, so you can include them in other narratives, just indicate an interest in doing that.
     
    Last edited: Mar 1, 2013
  13. Mar 1, 2013 #12
    Re: How big was the Universe 13 billion years ago??

    So far, so good! Some light filters through.

    "...it took 8.7 billion years to get here..."

    Where did that come from?
     
  14. Mar 1, 2013 #13
    Re: How big was the Universe 13 billion years ago??

    Scrap that last question, the light just arrived!
     
  15. Mar 1, 2013 #14

    marcus

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    Re: How big was the Universe 13 billion years ago??

    Good! Now I want to lay out an introduction to the fourth column, for when and if you want to proceed to that. There's no rush (especially for us septuagenarians, we absorb new info at a deliberate pace, when we are ready.)

    At every age in the history of the universe there is a distance that is growing at exactly the speed of light.

    If you are a distance which is LESS than this characteristic one then you are growing at less than the speed of light. If you are a distance which is MORE than this characteristic key distance then you are growing proportionately FASTER. So if you are twice that key distance you must be growing at twice the speed of light: 2c.

    It's very handy for keeping track of the rates that distances are expanding, and it changes over time. A Russian mathematician named Friedmann discovered how to describe the expansion history with an equation that simply tells us how this key quantity evolves over time. It's a really really good handle on expansion, and the history of expansion.

    The third column of the table gives the AGE of the universe from the moment distances began expanding. The fourth column gives you this key distance---or more exactly it gives the time equivalent. You can read it either in Gy (as shown) or in Gly.

    So if and when you get curious about the RATES that distances are expanding at different ages of the universe, you can mull over some narratives involving the fourth column.
    ==================

    Just as an example, looking back at the table:
    suppose it is year 4.2 billion and a galaxy which is 5.8 Gly from here sends some light in our direction.

    (According to the table that light would be destined to arrive here in year 13.8 billion for us to detect.)

    At the time the light was sent, namely year 4.2 billion, how fast was that distance of 5.8 Gly expanding?

    The table says that the key distance (a kind of "speed-threshhold" distance) was 6.0 Gly. So that distance of 5.8 was expanding at NOT QUITE THE SPEED OF LIGHT. We can calculate it: 5.8/6.0 c
     
    Last edited: Mar 1, 2013
  16. Mar 1, 2013 #15

    phyzguy

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    Re: How big was the Universe 13 billion years ago??

    Well said, Marcus!
     
  17. Mar 1, 2013 #16

    marcus

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    Re: How big was the Universe 13 billion years ago??

    Thanks Phyzguy! If you have any experience or pedagogical ideas, or ways of explaining stuff, that you think might help in this thread---eg to get Ender interested and deeper into subject matter--please share them.

    Getting back to the table, there is an ARITHMETIC hurdle to get over. The first row says that at that particular time (year 1.6 billion) distances were growing at the rate of
    1/23 of a percent per million years.

    Another way to say the same thing is that at that particular time (i.e. that row in the table) the distance that was growing at exactly the speed of light was 2.3 billion ly.

    A person ought to be able to work out by simple arithmetic that those two statements are equivalent. In other words

    what is 1/23 % of 2.3 billion ly? that is how much the distance grows in a million years. so if the answer turns out to be a million ly, then that son-of-yardstick is growing at the speed of light.

    That could be obvious, but it's worth remarking because those are two ways we interpret the fourth column of the table (a percentage expansion rate and as the distance growing exactly at speed of light.)

    [tex]{\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)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}[/tex]Time now (at S=1) or present age in billion years: 13.8
    =========================

    BTW Phyzguy, have you tried the calculator yet? If not I hope you will. I keep the link in my signature--it is
    http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
    You get to set the upper and lower limits of the table, and the number of steps. To get the table I have in this thread you set upper = 5, and lower=1, and steps=12. You should get exactly what we have here. And at the top of each column there is a box with the number of decimal places. You can leave it as it is, or bring the number down to 2 or 1 to make table easer to read.
     
    Last edited: Mar 2, 2013
  18. Mar 2, 2013 #17

    marcus

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    Re: How big was the Universe 13 billion years ago??

    Since we just turned a page, I'll recopy the table discussed in the previous post, to have it available for reference.
    This is what you get from
    http://www.einsteins-theory-of-relativity-4engineers.com/TabCosmo7.html
    if you set upper = 5, and lower=1, and steps=12. And at the top of each column there is a box where you can change the desired the number of decimal places. You can leave it as it is, or bring the number down to 2 or 1 to make table easer to read.

    [tex]{\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)\\ \hline5.0&0.20&1.6&2.3&23.9&4.8&7.9&4.5\\ \hline4.4&0.23&1.9&2.8&22.3&5.1&8.7&5.6\\ \hline3.8&0.26&2.3&3.5&20.6&5.4&9.5&6.8\\ \hline3.3&0.30&2.8&4.2&18.8&5.6&10.3&8.3\\ \hline2.9&0.34&3.5&5.0&16.8&5.8&11.2&10.2\\ \hline2.6&0.39&4.2&6.0&14.8&5.8&12.0&12.5\\ \hline2.2&0.45&5.1&7.1&12.7&5.7&12.8&15.2\\ \hline2.0&0.51&6.1&8.3&10.5&5.4&13.5&18.5\\ \hline1.7&0.58&7.3&9.6&8.3&4.9&14.1&22.4\\ \hline1.5&0.67&8.7&10.9&6.2&4.1&14.7&27.1\\ \hline1.3&0.76&10.2&12.1&4.0&3.1&15.1&32.6\\ \hline1.1&0.87&11.9&13.1&1.9&1.7&15.5&39.1\\ \hline1.0&1.00&13.8&14.0&0.0&0.0&15.8&46.7\\ \hline\end{array}}[/tex]Time now (at S=1) or present age in billion years: 13.8

    To this sample of a stripped down history table, could we add some "time-line" contextual information? I don't mean on the table itself, but in our posts commenting on it: as a help to assimilation---some famiiar landmarks to help relate to it?

    I was reminded that Deuterium2H posted about when the first rocky planets might have formed. A good guess is around year 4.2 billion: the 6th row of the above table. Here is his post. It's about when the oldest metal-rich stars could have formed.
    https://www.physicsforums.com/showthread.php?p=3105934#post3105934
    It came up just now in the "earliest rocky planet" thread https://www.physicsforums.com/showthread.php?p=4292203#post4292203

    In case anyone is new to the topic, the metal-rich ("Population 1") stars are those enriched in elements heavier than hydrogen and helium---elements such as carbon, silicon, oxygen cooked for them in earlier generations of stars. "Metals" in this context just means anything heavier than helium.

    So as a rough guess the first such stars, and rocky planets, could have been appearing around the era labeled stretch 2.6. The light from galaxies in the process of forming such stars will have been wave-stretched by a factor of S=2.6 on its way to reach us. We will be seeing them as they were in year 4.2 billion, when their distance from here was about 5.8 billion lightyears (if one could have stopped the expansion process and measured it.)

    And the distance in the universe that was expanding at the speed of light, at that time, was 6.0 billion lightyears---which is to say that distances were expanding at a percentage rate of 1/60 of a percent per million years. (See the previous post for discussion of that.)
     
    Last edited: Mar 2, 2013
  19. Mar 2, 2013 #18
    http://www.lanl.gov/science-innovation/science-features/planetary-formation-theory.php

    here is one related article. Marcus if you target the 10% metal percentage mentioned in the above. That may help narrow down the age.
    This is kind of a fun question to answer

    http://www.space.com/17441-universe-heavy-metals-planet-formation.html

    according to the above the conditions needed may be earlier than we think as gas giants also may also require heavy metals
     
    Last edited: Mar 2, 2013
  20. Mar 4, 2013 #19
    Just a note to say that I'm not ignoring the helpful information that has been posted through lack of interest. Last Tue I was discharged after 10 days in hospital with pneumonia. I thought the enforced inactivity would give me a good opportunity to get to grips with this time/distance stuff, but the recovery isn't going as well as hoped, so I'm not doing a lot of effective thinking.

    That's my excuse, and I'm sticking to it!
    I have every intention of getting there eventually.
     
  21. Mar 4, 2013 #20
    Thanks for letting us know and good luck on your recovery
     
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