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/sci/ - Science & Math

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10527165 No.10527165 [Reply] [Original]

At what speed should a 1kg object travel to destroy earth?
Remember the gravitational binding energy is about 2x10^32 Joules

>> No.10527174

>>10527165
Just because an object has more energy than the gravitational bonding energy doesn't mean it can destroy or nearly destroy earth. If a tiny object had that much energy it would just shoot through earth. There's a limit to energy transfer.

>> No.10527175

Depends on its size

>> No.10527179

>>10527174
It wouldn't just shoot through earth nigger

>> No.10527206

>>10527179
Yes, it would. At that energy level it's essentially the speed of light. There's no time for anything to happen. The object would could not be destroyed, if anything it'd get bigger as it fused with the atoms in its path. It would leave a trail of fusion explosions but by the end of it, you'd just have a hole through earth.

>> No.10527222

>>10527206
could you survive it if your, say arm, got hit by it?

>> No.10527320

>>10527222
Considering a .50cal will blow your head off if it whizzes by, no. But we're talking about planets, not arms

>> No.10527323

>>10527165
3

>> No.10527324

>>10527165
2

>> No.10527339

in the ultrarelativistic limit, [eqn]E_k \simeq m\gamma c^2 \ \ \ \text{ where } \ \ \ \gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \simeq \sqrt{\frac{c}{2(c-v)}}\\\
\implies E_k^2 \simeq m^2\frac{c}{2(c-v)} c^4 \\\
\implies (c-v)=\frac{m^2c^5}{2E_k^2} \\\
\simeq \frac{(8.988 \cdot 10^{16} \ \ \text{J})^2}{2\times(2\cdot10^{32} \ \ \text{J})^2}c = \frac{8.988^2\cdot10^{32}}{8\cdot10^{64}}c=(10.1\cdot 10^{-32})c
[/eqn]
so in other words, to have the required kinetic energy, the 1kg mass would need to be going slower than the speed of light by only one part in 10^31

>> No.10527475

>>10527339
what is the name of the phenomenon where /sci/ threads with an OP who asks an answerable but not trivial question start out with a bunch of shitposters, but then one guy posts a real answer with some equations and the shitposter all mysteriously stop shitposting? i’ve observed this here at least 5 times

>> No.10527607

>>10527475
why post in a ruined thread?

>> No.10528203

>>10527320
This is not true. a .50 BMG round won't even shatter a wine glass it misses by an inch. that's just not how shit works.

>> No.10528207

>>10527475
The first response in this thread is correct though. At that speed it's pretty unlikely that the object will deliver all of it's energy into breaking the gravitational binding energy, although it does give us a minimum bound.

>> No.10528379

>>10527174
Yeah but it would collide with other atoms and deposit a lot of energy that way

>> No.10528407

>>10527165
Kike detected

>> No.10529126

>>10527475
Its called pwnage