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B The League of Extraordinarily BIG Telescopes

  1. Jan 2, 2018 #1

    OmCheeto

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    I just finished up some hypothetical maths, as I saw yesterday that someone else on the internets repeated my repeated assertion that a really big telescope lens would collapse into a black hole.

    I don't think that's correct.

    Now, the original author of the claim, claims to be an Astrophysicist PhD student, so I'm hesitant to correct his maths, as I am notoriously bad at maths.
    But we did come up with the same number for a "spherical" silica telescope:

    248,544,369,352 m Om's Schwarzschild radius
    252,000,000,000 m quarksandcoffee radius​

    My problem was, that telescope lenses are disks, and not spheres.

    Given that I no longer know how to do calculus, I did some very basic maths on the gravitational pull at the edge of a very large and flattish type mirror, and kept coming up with diminishing values for "g" at the edge of my extraordinarily large mirror:

    g = 0.0000000005 m/s^2
    given:
    radius = 130 billion meters
    thickness = 0.001 meters​

    The above radius was based on us extracting all of the silica from the earth's crust (1.4E23 kg of SiO2), as, it seems people like to make mirrors out of glass, even though the working parts of the mirrors are made of aluminium.

    ps. According to my calculations, it would take a quadrillion earth crust's worth of silica to reach the Schwarzschild radius.
     
  2. jcsd
  3. Jan 2, 2018 #2

    PAllen

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    I'm not going to check your calculations, but I am going to tell you the 'best guess' to answer them. The key point for a non-spherical object is the hoop conjecture:

    https://en.wikipedia.org/wiki/Hoop_Conjecture

    So, you need to compute:

    2 M G/ c2

    for the mass of your lens, telescope, or whatever, then check to see that a hoop of circumference 2 π times this will enclose the object in all orientations. If not, there is no reason it must collapse to a BH.
     
  4. Jan 2, 2018 #3

    stefan r

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    A light year is just under 1016meter.

    You can have collapse issues in situations that do not involve black holes. You have 1 mm of glass supporting millions of kilometers of glass. If you reinforce the glass similar to any of the real large telescopes then mass of the supports add a lot more gravity.

    Might be able to spin a series of rings to make a disc. Would be much easier to just have an array of free flying small mirrors. I believe it would be even easier to have free flying telescopes with accurate clocks so they do not have to fly as a lens. You can compile the image from the data they collect. Millions of tiny (1,300km?) lenses could search the universe independently and then aim together when there is a chance that someone found T-Rex.
     
  5. Jan 2, 2018 #4

    OmCheeto

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    Thanks for the pointer!

    And it's good to know that even Kip has had trouble with his maths; "The mathematics to prove the same for objects of all shapes was too difficult for him at that time, but he formulated his hypothesis as the hoop conjecture."

    ps. I'll do the maths after my nap.
     
  6. Jan 2, 2018 #5

    PAllen

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    I should point out that the math has proved too difficult for anyone since, in the sense that the hoop conjecture is still an open problem in GR. However, failure to find any counterexamples has added confidence to it, in the absence of a proof.
     
  7. Jan 3, 2018 #6
  8. Jan 3, 2018 #7

    stefan r

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  9. Jan 3, 2018 #8

    OmCheeto

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    Actually, the seed for this thread was a video by Tom Scott:



    Fascinating!

    From there, I mistakenly read through the comments, and saw someone say; "surely there could be a truly "large enough" telescope eventually, once you pass a certain point wouldn't it just collapse in to a black hole?"

    Which is what I had said previously here at the forum. It would appear that we had both seen the comment at the end of that article:

    Anyway, you’re going to run into a problem here because when you start putting a lot of mass in one spot space starts to curve a lot, and eventually it’s going to collapse into a black hole. For something with the density of glass, which is about 2.5 grams/cc, you’re going to hit this point fairly quickly. In fact, a ball of glass 14 light minutes in radius will have enough concentrated mass to collapse into a black hole.

    Tough luck.

    After my nap, the outcomes of my maths got a bit weirder. Hence, my hesitation to say anything more.
     
  10. Jan 5, 2018 #9
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