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When a big volcano erupts like Krakatoa or Mt St Helens does it send steam, smoke, dust, rocks high enough and fast enough to escape Earth?

Could any lightweight matter from a volcano actually get enough of a push to escape into outer space?

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No way. Escape velocity from Earth is ~11km/s. Volcanic eruptions can be supersonic in the case of Volcanic Pipes, but that's only ~1000m/s, not even 1% of the kinetic energy required to escape Earth's gravity.

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    $\begingroup$ Furthermore, any such materials expelled at the earth's surface with that kind of velocity would almost certainly be slowed down far below escape velocity, if not completely ablated away, by air resistance. $\endgroup$ – Tristan Nov 30 '16 at 19:32
  • $\begingroup$ And even if we only require escaping Earth's atmosphere (which a liberal reading of "escape into outer space" could allow for), there is the pesky detail that an orbit includes the point of the last propulsive maneuver, which in this case would be on Earth (though almost certainly not at the volcano, because of Earth's rotation and movement through its orbit). $\endgroup$ – a CVn Dec 1 '16 at 8:50
  • $\begingroup$ See this answer for a python program to calculate it. $\endgroup$ – uhoh Dec 1 '16 at 9:52
  • $\begingroup$ @Tristan: Air resistance would be fairly limited. You're looking at a rather large plume. Yes, the edges of this plume will be slowed down due to heavy turbulence. But inside the plume, speed differences are going to be much slower. $\endgroup$ – MSalters Dec 1 '16 at 12:15
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    $\begingroup$ The other issue at hand is that there is a practical upper limit on the velocity of projectiles propelled by expanding gas, dependent on the molecular weight of the gas doing the propelling. Spitballing it, I'd say you're looking at an absolute maximum volcanic projectile velocity (limited by thermodynamics) of around 3 km/s. $\endgroup$ – Tristan Dec 1 '16 at 23:10
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It's not possible. Escape velocity is too high (11.186 km/s), an eruption cannot impart such speed.

Even if such velocity could be achieved, the possible object thrown out (e.g. a rock or a shard) would just disintegrate because of the heat generated by the friction of the air.

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  • $\begingroup$ I might be wrong, but isn't that how atmospheric gases escape the Earth: a small portion of them are traveling fast enough to reach escape velocity? Presumably, some molecules of volcanic gases could reach escape speed, although it make the volcano a red herring. $\endgroup$ – barrycarter Dec 2 '16 at 16:37
  • $\begingroup$ Actually, the OP is talking about lightweight matter so I supposed that he was referring to solid matter. $\endgroup$ – A.Danzi Dec 5 '16 at 8:13

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