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comment by Devac
Devac  ·  1532 days ago  ·  link  ·    ·  parent  ·  post: Why the world is waiting for Betelgeuse to go supernova

I'm approaching shitfaced at 1g, but got around 3.5 years elapsed for the people on the ship and 17.6 years for people on Earth.





am_Unition  ·  1532 days ago  ·  link  ·  

Did you do it like:

d(t' = t/š›¾), with š›¾(t), after substituting v=9.8*t into š›¾(v), and then integrate both sides, solving for the upper limit of the t' integral?

Unprimed is Earth's frame, for posterity.

Also, "approaching shitfaced at 1 g": not sure if claiming to be drunk or ugly... :|

Edit: no but if you really hate yourself, do d(š›¾*t' = t), with š›¾(t), and then do algebra for days. It reminds me of some homework shit once with deriving a particularly simplistic expression algebraically for a Rankine-Hugoniot shock jump condition expression.

Devac  ·  1531 days ago  ·  link  ·  

Drunk. Probably still are. Definitely had too much, but flatmate finally got his M.Eng after years of bullshit, so at least it seemed like a good occasion.

    but if you really hate yourself, do d(š›¾*t' = t), with š›¾(t), and then do algebra for days.

I have a math major and loved courses like real analysis, so obviously started drinking and deriving from Lorentz transform. For kb's case I got:

  t = sqrt(xĀ²/cĀ² + 2x/g)

t' = (c/g) asinh(gt/c)

x - distance from stationary frame's perspective.

Mea maxima culpa if I fucked it up along the way, but it looks reasonable to me.

am_Unition  ·  1531 days ago  ·  link  ·  

Looks good to me. I might come back with pictures of my chickenscratch, but yeah, I can see how some geometric substitution in the integral leads to a sinh function.

Perhaps somewhat ironic is that the asinh function is sometimes pronounced "a cinch", a.k.a. American slang for something considered easy. But some would say "arc shine". As for "inverse hyperbolic tangent", it's just that no one wants to take the time to say an 8 syllable thing. The fact that pronunciation runs the gamut is proof that we've needed to standardize communication since science got off the ground. It's just dumb luck that I'm born into the English-speaking contingent of the world. But meanwhile, you know at least two languages thoroughly, and your brain is all the more ductile for it. Long term benefit! But yeah, I do genuinely feel kinda guilty for just having been born in the U.S., for what seems like an ever-increasing number of reasons, when I consider it.

For now, at the very least, enjoy that booze. Kill off the weak brain cells. You'll make more, no worries.

Devac  ·  1531 days ago  ·  link  ·  

  t' = Integral[1/sqrt(1 + (gt/c)Ā²), {t,0,t}] = (c/g) ln(g/c + sqrt(1 + (gt/c)Ā²)) = (c/g) asinh(gt/c)
am_Unition  ·  1531 days ago  ·  link  ·  

That's it, thanks :). I promise to never outsource looking up integral tables for another few posts.

user-inactivated  ·  1531 days ago  ·  link  ·  
This comment has been deleted.
am_Unition  ·  1531 days ago  ·  link  ·  

FutureNeg: bebe, U pretty on the surface (Earth's), but at the 2 g's we gotta get to Titan at, that's just U 2 shitfaced 4 me, srry~

kleinbl00  ·  1532 days ago  ·  link  ·  

...and I'll bet that took you like six minutes. I stared at it and even with the equations in hand, went "fuck this shit I never wanted to be an engineer in the first place."

This is why I trick other people into doing my work for jokes.

Devac  ·  1532 days ago  ·  link  ·  

1 round of hot-seat match at Heroes III, actually. I dare anyone to be more of a Slav.