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I'm no expert, but I once studied basic from advanced physics and understand

  • gravity
  • action/reaction
  • escape velocity of 11.2 km/s from the earth surface
  • escape velocity changing as the object go far away
  • Karman line for space (100 km)

What I want to know, can a natural object, from a natural process, reach the escape velocity 11.2 km/s and get free of earth gravitation?

I have in mind some volcano explosions. Tornados seem weak. Or also a Comet impact. Question is not limited in time, maybe it was possible millions of years before, when activities and gravity might have been different.

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    $\begingroup$ By omitting the constraint on the escape velocity, hydrogen and helium are two likely candidates for "natural" objects escaping the Earth's gravity. $\endgroup$
    – polfosol ఠ_ఠ
    Aug 9, 2021 at 12:54
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    $\begingroup$ Well [putting my tongue in my cheek], since oxidation and catalytic hydrazine decomposition are both natural processes, Voyager2 qualifies... $\endgroup$
    – Peter - Reinstate Monica
    Aug 9, 2021 at 13:54
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    $\begingroup$ There are many rocks from Mars on Earth. If they could escape Mars gravitation, why couldn't comparable processes on Earth go the other way? $\endgroup$
    – Barmar
    Aug 9, 2021 at 15:14
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    $\begingroup$ "I once studied basic from advanced physics". That sentence puzzles me. (It does not make grammatical sense, and don't want to change the meaning via an incorrect edit.) $\endgroup$
    – RonJohn
    Aug 9, 2021 at 19:30
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    $\begingroup$ @Barmar it's easier to escape small, barren Mars than big, atmosphere-encircled Earth. Being closer to the Sun might also make it harder. $\endgroup$
    – RonJohn
    Aug 9, 2021 at 19:41

3 Answers 3

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Yes, it is not only possible, but has almost certainly happened on Earth. The asteroid that killed the dinosaurs is thought to have produced these high velocity fragments on the order of one-thousandth of the mass of the impactor according to Poveda and Cordero [2008]. In fact, they estimate the volume of escape velocity ejecta from the Chicxulub event as quite substantial in that:

the number of fragments with sizes larger than 10 cm and 2 cm is about 4x10^10 and 2x10^12, respectively

The authors of the above paper call these "Chicxulubites" and speculate on the possibility of finding them on the Moon and Mars.

The larger the impactor radius and velocity, the higher a percentage of its overall mass will reach escape velocity. In an asteroid impact, the fastest moving ejecta comes from near the center of the crater. The ejecta closer to the edge of the crater has much lower velocity:

enter image description here

The equation governing the velocity of the ejecta $V_{ej}$ is therefore partly a function of $r$, the distance from the center of the crater.

$$V_{ej} = \frac{2\sqrt{Rg}}{1+\epsilon }\left(\frac{r}{R}\right)^{-\epsilon}$$

Where $\epsilon$ is a material coefficient of 1.8 for hardpack soil, $g$ is the surface gravitational acceleration, $R$ is the total radius of the equator, and $r$ is the radius at which the ejecta was ejected.

Notes:

  1. I go into more detail in this answer: What percentage of a lunar meteor strike is blown back into space?.
  2. Practically, an object near sea level must achieve higher than escape velocity in order to overcome atmospheric drag as it escapes.
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    $\begingroup$ related: Could rocks from Earth have reached the Kuiper belt, or Neptune at least? If so, how? $\endgroup$
    – uhoh
    Aug 9, 2021 at 1:02
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    $\begingroup$ @uhoh I suspect that so much small material in such a wide variety of escape velocity trajectories is similar to a monte carlo simulation, in that various pieces end up all over the solar system. $\endgroup$
    – Connor Garcia ♦
    Aug 9, 2021 at 2:56
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    $\begingroup$ @uhoh very useful answer, thanks $\endgroup$
    – KeitelDOG
    Aug 9, 2021 at 17:03
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    $\begingroup$ Good answer. It's tough to find a natural store of energy that can hold enough energy to make a reasonably sized object move at escape velocity - a much larger object that's already moving at escape velocity is a great solution! $\endgroup$
    – Nuclear Hoagie
    Aug 10, 2021 at 14:38
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    $\begingroup$ @KeitelDOG Ejecta is indeed composed of both Earth and asteroid material. The high concentration of iridium in the KT-Boundary sediment layer on Earth is what led Louis and Walter Alvarez to hypothesize the Chicxulub event. $\endgroup$
    – Connor Garcia ♦
    Aug 10, 2021 at 15:59
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If the object can be as small as an atom, then it's happening constantly. Atoms in a hot gas mixture will have an average velocity related to the average kinetic energy which is in turn related to temperature.

tl;dr: The Earth loses 95,000 tonnes of hydrogen and 1,600 tonnes a year of helium in the form of atoms or molecules.

For example, in a standard atmosphere near the surface, the average speed of a molecule is also roughly the speed of sound, or about 330 m/s for an average molecular mass of 28. For helium atoms in air with a mass of 4 the speed will be $\sqrt{7}$ larger, or about 870 m/s.

That still sound very far from escape velocity, but that's the average. There's always a distribution in velocities and for a given velocity component the Maxwell-Boltzman velocity distribution is

$$f_v(v_i) = \sqrt{\frac{m}{2 \pi k_B T}} \exp\left( \frac{-mv_i^2}{2 k_B T} \right)$$

But at the tippy-top of Earth's atmosphere a few things are different. Atoms can be much hotter than 300 Kelvin and the distributions of kinetic energy can be non-thermal in nature, and the densities are so low that once an atom achieves escape velocity there's a good chance it will escape without hitting anything further.

At lower altitude the atmosphere's mixture has relatively constant ratios, but (as the plot shows) once you get above 90 to 100 km the density is so low that the gases are no longer automatically mixed. At this point each gas can have its own scale height such that the exponential rate of drop off is faster for the heavier gases.

This produces a sequence of primary gas component as a function of altitude.

See concepts of scale height and turbulent mixing in answers to Why does Earth's atmospheric density have a big “knee” around 100 km? Is there a good analytical approximation?

As shown in the plot below, above about 190 km monatomic oxygen (O, not O2) is the primary component of Earth's atmosphere. At 450 km helium is the primary component and above roughly 1250 km hydrogen becomes the primary component.

At about 190 km monatomic oxygen is the primary component of Earth's atmosphere. Above 450 helium is the primary component and above about 1250 km hydrogen becomes the primary component.

Source

This answer to Is Earth getting heavier or lighter? says:

It seems a similar question was asked in Astronomy Stack Exchange, and this short answer links to the BBC News article Who, What, Why: Is the Earth getting lighter? which answers this question.

[...]

"Physicists have shown that the Earth is losing about three kilograms of hydrogen gas every second. It's about 95,000 tonnes of hydrogen that the planet is losing every year.

"The other very light gas this is happening to is helium and there is much less of that around, so it's about 1,600 tonnes a year of helium that we lose."

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    $\begingroup$ I thought that most light gas atoms (or maybe molecules) are blown away by the solar wind, so they don't (initially) need escape velocity. That's why the magnetic field is essential for retaining an atmosphere. What happens if it's missing can be seen on Mars. $\endgroup$
    – Peter - Reinstate Monica
    Aug 9, 2021 at 14:03
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    $\begingroup$ @Peter-ReinstateMonica now that's an interesting point, but the situation for helium is special; even though it is constantly being released into the atmosphere and there is no sink for it (nothing else removes it, it's not chemically active) it never builds up, unlike N2, O2, CO2, H2O. There's much less release of Ar than He from Earth and yet Ar is 1% and He is only 0.0005 %. It's the mass that's different; He escapes, Ar stays put. $\endgroup$
    – uhoh
    Aug 9, 2021 at 16:37
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    $\begingroup$ Thanks for those details at the top atmosphere, it makes sense for the gaz up there to occasionally leave when there is few gaz resistance. $\endgroup$
    – KeitelDOG
    Aug 9, 2021 at 17:23
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    $\begingroup$ @uhoh The mass will also influence the impact of the solar wind. $\endgroup$
    – Peter - Reinstate Monica
    Aug 9, 2021 at 17:59
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    $\begingroup$ @Peter-ReinstateMonica that can be, but as you can see from the edit I've made one above about 200 km mixing stops and each gas has a very different height profile. $\endgroup$
    – uhoh
    Aug 9, 2021 at 23:14
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I'd be surprised if the event that created the Moon didn't scatter some debris beyond the Earth's Hill sphere (in order to choose one meaning of "escape Earth gravitation").

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