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Let's say that some aliens fling a hyper-super-duper-lightspeed impactor at the Earth.

They barely hit it.

Instead of a direct hit through the center of mass, the impactor "clips" the Earth , Basically, it's a secant trajectory where the entry point and exit point are about 450 kilometers (EDIT: NOT 450 KILOMETERS, ABOUT 597 KILOMETERS; MY INITIAL MATH WAS WRONG) from one another in a straight line. It enters and exits cleanly; basically, Earth didn't take much energy off of it. As Alexander pointed out, it's probably made of something like degenerate matter. What it's made of is irrelevant; what matters is the valley/trench/scrape in the Earth left behind.

Ignore the effects of this thing on life on Earth, of course. It's probably all dead, given the amount of energy put into the atmosphere.

If my math is right, it results in a valley ~600 kilometers long, perfectly straight, and ~7 kilometers deep at its widest point. Let's call it hemispherical for the sake of ease of math, meaning that it's 7 kilometers wide as well.

Let's also say that it hits in the American Midwest.

Would the trench that this thing carves into the Earth remain geologically stable/recognizable as a trench over, say, 2 million years?

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  • $\begingroup$ Likely yes, but not necessarily. Think of it as a meteorite impact craters. And also, impactor won't be able to "exit cleanly" unless it is made of something very dense like degenerate matter. $\endgroup$
    – Alexander
    Commented Aug 18, 2021 at 20:45
  • $\begingroup$ @Alexander Then that's what it's made of. The point is not the impactor, it's the trench that it carves into the Earth. $\endgroup$
    – KEY_ABRADE
    Commented Aug 18, 2021 at 20:49
  • $\begingroup$ How big is your impactor? That's worth considering here, because it determines the characteristics of your valley; a wider valley won't necessarily behave the same way as a narrow one under geological forces. Over the distance you describe, it's quite possible that you made a tunnel and not a valley at all! $\endgroup$
    – Palarran
    Commented Aug 18, 2021 at 20:58
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    $\begingroup$ SOrry, but "Earth didn't take much energy off of it" is nonsense. a near-lightspeed object impacting solid matter will cause nuclear degeneration of the impacted matter. Followed by fusion of everything fusable, and creating the equivalent of a continuous multi-gigatonne nuclear explosion along the whole length of the traverse. It will not leave a crater or canyon, it will blast off a large percentage of the whole planet. $\endgroup$
    – PcMan
    Commented Aug 19, 2021 at 8:06
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    $\begingroup$ editing the question in a way that invalidates answers is discouraged, it is better to ask a new better question. Also degenerate matter can't exist outside a massive gravity well, degenerate matter will have exploded long before it reached earth. $\endgroup$
    – John
    Commented Aug 19, 2021 at 14:23

2 Answers 2

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Sorry, physics says otherwise. (at least in the original question)

Light-Speed impactor, lets dial it down to a mere 0.9C just to keep an element of reality

You don't specify size, but do assert it will dump lots of energy into the atmosphere as well as survive a secant hole 497 km long.

The great and powerful XKCD has already shown the way by considering a baseball at 0.9C - some key observations

  1. At about 0.3C you are fast enough to overcome the coulomb barrier and engage in fusion the entire passage of your journey because the target atoms can't get out of the way of the baseball fast enough to avoid nuclear fusion

  2. To survive a the 597 km secant journey your impactor will have to have a great deal more mass than a baseball (correcting an error I made of 450 miles when originally 450 km).

  3. A colossal amount of energy will be released into the Earth during the secant journey. Many, many nuclear bombs worth.

That's gonna leave a big scar, assuming there is enough planet left.


OP altered the question after I answered, in the original question somehow the impactor barely affected the planet during transit - that is what I objected to as not going to happen.

Second, the original question did not specify degenerate matter, but that is not important in determining the size of the object - it must of necessity be a much larger diameter than a baseball to have the effect of destroying on life on the planet from the energy released during transit through the atmosphere. Even at 0.9C, a large diameter object will be required to do so (again, the question omitted size and mass of impactor)

This large diameter object will pass through billions (trillions?) of metric tons of matter during its secant transit and convert millions (billions) of tons of matter to energy during its passage - far greater than the energy released by the Chicxulub event.

Assuming the impactor had a 1 sq km cross-sectional energy, the energy released by converting a full 1% of the atmosphere in its transit path to energy would be about 1.4E25 J - about the same as the total Chicxulub event - to destroy all (or event nearly all) life from the atmospheric transit, the impactor have to be even larger.

Anyone confusing this with a baseball sized object, I'm sorry if you were mislead by my reference to XKCD illustrating the devastation unleashed by 0.9C object.


Re: objection to degenerate matter.

I agree that the physics that we understand suggests that degenerate matter cannot exist outside of something like a neutron star or a black hole where gravity allows such matter to exist (a possible exception of the theoretical stranglet).

The question does not really make sense though without collapsed matter because normal matter would behave so differently. I.e., when impacting the surface, it would basically explode into a huge ball of plasma not follow a secant path through the earth.

This is just like the fact that we ignore the faster-than-light tag combined with physics - nope, that's not how physics works. Just like I ignored the light-speed description and restated as 0.9C

I suppose I could have just voted to close in the first place

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  • $\begingroup$ 450 kilometers, not miles. Let's say that the impactor has the same mass as a baseball, and simply is somehow going fast enough to carve a 7-kilometer hemispherical trench into the Earth $\endgroup$
    – KEY_ABRADE
    Commented Aug 18, 2021 at 21:02
  • $\begingroup$ *rest mass of a baseball. $\endgroup$
    – Allan
    Commented Aug 18, 2021 at 21:04
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    $\begingroup$ 0.145 kg (1 baseball) x 0.9 c = 16,865,393,849 megajoules = 4.03 megatons of TNT, which is not all that big. Likely behavior, even if the baseball is made of "exotic matter" is a somewhat angled crater with the baseball embedded somewhere in it. The querent is going to need to tweak the numbers a bit. $\endgroup$ Commented Aug 18, 2021 at 21:14
  • $\begingroup$ @GrumpyYoungMan It would burst apart in the upper atmosphere . At ground level you would hear a "whoomp" and a few windows might break. There would be no crater. See impact.ese.ic.ac.uk/ImpactEarth/ImpactEffects , but it doesn't account for relativistic speeds, so scale the size up a bit (keeping it small) while maintaining the same energy. See impact.ese.ic.ac.uk/ImpactEarth/cgi-bin/… for a projectile with the same energy as an 0.9c baseball (1m sphere iron at 9000 km/s). $\endgroup$
    – causative
    Commented Aug 18, 2021 at 22:35
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    $\begingroup$ @causative degenerate matter can't exist outside a massive gravity well, there is no such thing as a small mass of degenerate matter such an object would instantly explode no impact needed. $\endgroup$
    – John
    Commented Aug 19, 2021 at 14:26
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Would the trench that this thing carves into the Earth remain geologically stable/recognizable as a trench over, say, 2 million years?

Yes.

It is only my opinion, but I believe the impact of this object would utterly destroy the existing atmosphere, burning it or striping it away. I believe what would be left is a barren planet open to vacuum, so there would be no rain, no wind, no weather at all to cause erosion. A thin atmosphere may eventually come to pass as the water in aquifers slowly boils away... but I doubt it would be enough.

Let's assume through whatever means that the atmosphere was left intact...

The Cretaceous–Paleogene extinction event is thought to be an asteroid impact that resulted in the loss of 75% of the plant and animal species on the Earth. It was not a light speed event. Far from it. This is why my previous belief holds.

But, let's assume that we adjust mass and speed to get the trench you're looking for without killing everything on Earth and destroying the atmosphere. Would the trench last 2,000,000 years?

The Grand Canyon is thought to be between 5 and 70 million years old. So we have proof that your canyon can last as you expected.

Kinda...

The problem is that you're ripping through some huge aquifers. The nature of aquifers is to fill with water. So, while the Grand Canyon has existed a very long time, it has done so without significant rain and only as a river.

Your trench would fill with water and become the single largest inland sea the Earth had ever seen.

Worse, the size of the trench suggests that you'd either pierce the mantle at its center or come awfully close. That, combined with the heat of the impactor's passage, would mean the center of the trench would experience some serious volcanism. Would it be enough to change the shape of the trench?

No one knows. No one can know. Once the magma starts flowing it's plausible that the majority of the trench would fill with rock. The aquifers could stem that, or not. Rain could stem that, or not. It might not even happen.

This is important: There is no way to actually know whether or not your trench would still look like a trench after 2 million years. So, in the end, you can use the example of the Grand Canyon to justify your desires, or you can use the aquifers and magma to justify the opposite.

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  • $\begingroup$ "pierce the mantle at its center or come awfully close" - according to OP's calculations, impactor would go only about 7 km deep. At the target location (American Midwest), Earth crust is about 40-45 km thick. $\endgroup$
    – Alexander
    Commented Aug 18, 2021 at 21:53
  • $\begingroup$ @Alexander I'm not too sure I trust Key's calculations on this one. But I could be wrong. $\endgroup$
    – JBH
    Commented Aug 18, 2021 at 23:36
  • $\begingroup$ @JoinJBHonCodidact Yeah, I was inaccurate. I used a chord calculator; specifically, the third one on this page ("Area of circle segment by radius and height"): planetcalc.com/1421. I plugged in 6371 for radius and 7 kilometers for chord height and got a chord length of ~597 kilometers, not 450. I'll update OP to point this out. $\endgroup$
    – KEY_ABRADE
    Commented Aug 19, 2021 at 0:02

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