4.7 KiB
[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
Post:
Comments:
u/DocFuture [+3] (a minute later)
Or 'when ignoring special relativity can get you into real trouble', along with a plea for a general relativist.
u/Charlie___ [+2] (an hour later)
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).
There's a straightforward power equation (can be found on wikipedia - 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.
u/DocFuture [+2] (2 hours later)
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.
u/Charlie___ [+3] (3 hours later)
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.
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, 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 ).
u/DocFuture [+2] (6 hours later)
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-)
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-)
u/Empiricist_or_not [+1] Aspiring polite Hegemonizing swarm (a day later)
Have you considered sending this as a what if to Randal Monroe of XKCD?
u/DocFuture [+3] (a day later)
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.
u/want_to_want [+2] (8 hours later)
I think the Moon's atmosphere and dust might be more serious problems. Too lazy to calculate, but I don't think anyone survives.
u/None [+1] (17 minutes later)
I don't know enough about the math to critique it, but "the moon as a victim" is hilarious.