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No Answer in Google

Discussion in 'Fred's House of Pancakes' started by airportkid, Jun 10, 2008.

  1. airportkid

    airportkid Will Fly For Food

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    And it's a simple question: How tall would the tallest possible mountain be?

    Everest (30k ft) is highest above sea level, Mauna Kea (50k ft) is tallest above its base, and a peak in the Andes (20k ft) is furthest from Earth's center. Taking Mauna Kea as the most "rumpled" section of Earth's surface, what's the maximum "rumple" gravity can't flatten?

    Olympus Mons on Mars reaches nearly 90k ft base to peak, but Martian gravity is also less than Earth's. So perhaps Mauna Kea is already close to the theoretical Earthly maximum.

    That's with typical crust material making up the mountain - but what if it were made entirely of diamond?

    Here's the kicker: After figuring out to the nearest foot the how tall this mountain could be (a foot higher and gravity would smoosh it back to the maximum), what would happen to a six foot mountain climber approaching the summit? Would some mysterious "force" repel the climber, preventing him from getting within 6 vertical feet of the peak?

    For purposes of the puzzle the base of this theoretical mountain could if necessary cover the entire spherical surface of the planet (i.e. there'd only be a small dimple on the Earth's surface lower than every other point on the surface).

    Something to occupy the mind in a moment of boredom ---
     
    #1 airportkid, Jun 10, 2008
  2. qbee42

    qbee42 My other car is a boat

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    Remember that the earth's crust floats on a fluid center. Too much mass on one side will shift everything and your mountain won't be as high as you think. How are you measuring the height of this mountain? From the base to the top? From the center of the earth? From the "normal" surface level if the mountain did not exist? It makes a big difference.

    Tom
     
    #2 qbee42, Jun 10, 2008
  3. Wildkow

    Wildkow New Member

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    #3 Wildkow, Jun 11, 2008
  4. patsparks

    patsparks An Aussie perspective

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    There were once much taller mountains than Everest but they have eroded away now.
    I suspect Everest was once taller too but how can it be proven?

    I remember reading that the Flinders Ranges in South Australia which is several rows of smallish mountains was once taller than Everest but erosion has reduced what was once a massive single fold in the earth's crust into several smaller ranges.
     
    #4 patsparks, Jun 11, 2008
  5. tochatihu

    tochatihu Senior Member

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    I think this is a complicated question. Many of the taller mountains occur where the earth's crust gets pushed up over oceanic crust. The former is often less dense, but it may not be entirely accurate to say that this crust-sandwich is floating on the mantle. Anyway, this is the isostasy in Wildkow's first link.

    The rate of uplift is indeed counteracted by the rate of erosion. Erosion is largely water-driven, ad precipitation inputs increase with elevation, but only up to a point. Then you get up to air that carries very little water in any form.

    So, a fast-rising mountain has more erosion until it gets to some height, then it might be able to stay ahead of erosion processes as long as the uplift rate continues. How long would that be for? I don't know.

    We can tell (sort of) how much material has been weathered off a mountain (range) by the depth of sedimentary material around its toes. But this cannot really tell you how tall it was in prehistory. Only the total amount it has uplifted through time, if you see what I'm saying.
     
    #5 tochatihu, Jun 11, 2008
  6. qbee42

    qbee42 My other car is a boat

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    Recall that the OP said that this theoretical mountain could cover the entire surface of the earth, save one little dimple. This isn't any ordinary mountain, which is why I asked about the definition of height. If height is defined as the distance from the top of the mountain to the center of the earth relative to the distance from the lowest point on earth to the center, then limits of how aspherical the earth can be becomes the controlling factor, not normal geology.

    Tom
     
    #6 qbee42, Jun 11, 2008
  7. airportkid

    airportkid Will Fly For Food

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    Nice work, Kow! You got much better results than I did, proof that the answer to anything probably IS lurking in Google if you know exactly how to phrase the search terms.

    But the question - MY question - is still unanswered. To resolve the ambiguity GBee42 refers to, the question might be better phrased as "what's that maximum out of round planet Earth could get?" and if the mountain was solid diamond covering the entire surface could the out of round be greater?

    But to me the more intriguing question is what happens at the limits. If we could calculate the maximum out of round to the nearest foot (or millimeter), what would happen to a body bigger than that tolerance at the limit? Let's say we calculate that maximum out of round to be (just picking an arbitrary number here) 52.4673248 miles. Plus or minus .0001 miles - so the extreme possible maximum is actually 52.46783248 miles. Get out the bulldozers and make that mountain (being sure to file all the correct environmental impact statements first, of course). Then have a six foot tall climber try to stand atop the peak (making the mountain six feet higher than its maximum tolerance - an impossibility). What would happen to that climber?

    Mark
     
    #7 airportkid, Jun 11, 2008
  8. Wildkow

    Wildkow New Member

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    I da Google man at your service! :rockon:

    Wildkow
     
    #8 Wildkow, Jun 11, 2008
  9. kenmce

    kenmce High Voltage Member

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    I don't think diamond is a good structural material for your project. It is very hard, but it is also brittle. The hardness is irrelevant to your project. Brittleness would hamper it. What you need is material that can take a compressive load.
     
    #9 kenmce, Jun 12, 2008
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