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59 lines
4.7 KiB
Markdown
59 lines
4.7 KiB
Markdown
## [RT][HF] Fear, Flying, and Physics
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* Author: u/DocFuture *
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* URL: http://docfuture.tumblr.com/post/144223073531/fear-flying-and-physics
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* Score: 5
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* Created: 2016-05-12T00:49:41
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### Post:
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[Link to content](http://docfuture.tumblr.com/post/144223073531/fear-flying-and-physics)
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### Comments:
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> **u/DocFuture** [+3] (a minute later)
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>
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> Or 'when ignoring special relativity can get you into real trouble', along with a plea for a general relativist.
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> **u/Charlie___** [+2] (an hour later)
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>
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> I was at a talk on gravitational waves last week, and from what I can tell it's all pretty straightfoward except for measuring them :P (This is a joke, please do not hunt me down, gravitational-wave astronomers).
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>
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> There's a straightforward power equation (can be found [on wikipedia](https://en.wikipedia.org/wiki/Gravitational_wave#Wave_amplitudes_from_the_Earth.E2.80.93Sun_system) - well, sort of, you have to substitute angular frequency back in), and I'm pretty sure it doesn't matter that Flicker accelerates herself - it's all about the rate of change of the quadrupole moment of the moon-Flicker system. But there's a bit of trouble, which is that the power is still proportional to the inverse square of the moon's radius, and the constants out front are still G^3 / c^5 (i.e. so tiny that things need to be heavy, fast, and close before they give off measurable gravitational waves). So, as far as I can guess, Flicker is spending a measly 10^-31 or so watts on gravitational waves.
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>> **u/DocFuture** [+2] (2 hours later)
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>>
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>> Unfortunately, that is how strong the gravitational waves would be if she were in orbit, moving under the influence of gravity--and gravity has almost nothing to do with how Flicker moves. In fact 4.32 x 10^16 g's is way above the surface gravity of a neutron star, which is about 7 x 10^11 and started me thinking about GR and gravity waves in the first place.
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>>> **u/Charlie___** [+3] (3 hours later)
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>>>
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>>> The number I quoted you is about a factor of 10^11 larger than the number would be if she was in orbit - which is about equal to the multiplicative increase in speed, squared. Flicker may experience high acceleration, but that itself doesn't have much impact on gravitational radiation.
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>>>
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>>> Now that I think about it, there are probably some interesting (special-) relativistic corrections - there's probably at least a relativistic mass correction, and maybe something like synchotron radiation, where you get higher-energy radiation along the direction of motion (though gravitational waves normally radiate only weakly along the direction of motion). But the literature looks like [this](https://arxiv.org/pdf/1310.1528.pdf), which seems like too much work to understand (note that gamma in that paper refers to a mixture of constants proportional to mass divided by radius (equation 225), and is not the Lorentz factor), and I'm pretty sure that the corrections are not big enough to overcome a starting point of 10^-31 (or 10^-28 ).
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>>>> **u/DocFuture** [+2] (6 hours later)
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>>>>
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>>>> Yeah, the 'now that I think about it, some interesting things are probably happening' part is what got me 8-) I don't know enough about how they derived that gravity wave equation to even know the right exponents for velocity and the Lorentz factor - there is that r^5 in the denominator that I have no idea how they derived. So I'm sure they wouldn't be as strong - but the Moon is a *lot* closer to her, too. And Earth isn't all that far away. I can get 10^30 easy if the exponents are right--which is why I'm hoping a GR expert will find it interesting enough to comment. 8-)
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>>>>
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>>>> Edit: Took a quick look at the work you linked (not all 185 pages yet 8-)) and the biggest problem is that the best approximation is the Post-Newtonian one, which assumes v small compared to c--which Flicker completely blows away 8-)
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>>>>> **u/Empiricist_or_not** [+1] *Aspiring polite Hegemonizing swarm* (a day later)
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>>>>>
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>>>>> Have you considered sending this as a what if to Randal Monroe of XKCD?
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>>>>>> **u/DocFuture** [+3] (a day later)
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>>>>>>
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>>>>>> That's a pretty good idea. Randall isn't a general relativist, but I'll bet he knows some. And I don't think he's done one about gravitational waves yet. I'll see about writing it up.
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> **u/want_to_want** [+2] (8 hours later)
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>
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> I think the [Moon's atmosphere](https://en.wikipedia.org/wiki/Atmosphere_of_the_Moon) and [dust](https://en.wikipedia.org/wiki/Lunar_soil#Moon_dust_fountains_and_electrostatic_levitation) might be more serious problems. Too lazy to calculate, but I don't think anyone survives.
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> **u/None** [+1] (17 minutes later)
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>
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> I don't know enough about the math to critique it, but "the moon as a victim" is hilarious.
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---
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