What-If 0057: "Dropping a Mountain"

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Mike Rore
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Re: What-If 0057: "Dropping a Mountain"

Postby Mike Rore » Wed Aug 07, 2013 1:41 pm UTC

I really liked this post.

On the last part I thought "wow, is it really that easy to miss a planet?" but then missing a planet and hitting Mars (sorry, "New Netherlands") has to be extremely difficult.

Very funny

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Re: What-If 0057: "Dropping a Mountain"

Postby PM 2Ring » Wed Aug 07, 2013 2:23 pm UTC

gene123 wrote:
Dropping it from higher up won't do anything; there won't be enough force pulling it toward the—


I thought gravity, while getting weaker and weaker at a rate square to the distance, still had an unlimited range, and never becomes exactly zero?

So is there really a fixed limit to Earth's gravity well, or does it just get asymptotically weaker? If the mountain is at rest relative to Earth (e.g. following the same Solar orbital rotation to be at relative rest to Earth) be gravitationally attracted to Earth at any distance (assuming it isn't caught in another planet or other object's own gravity well)? And thus, wouldn't it be only matter of time before it falls back to Earth?


Yes, the range of gravity is unlimited, but there is a limit on the falling speed. If the Earth had no atmosphere, the maximum speed that a falling body (initially at rest with respect to the centre of the Earth) could hit the Earth's surface with would be exactly equal (but opposite) to the escape velocity from the surface.

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Re: What-If 0057: "Dropping a Mountain"

Postby davidstarlingm » Wed Aug 07, 2013 2:33 pm UTC

PM 2Ring wrote:Yes, the range of gravity is unlimited, but there is a limit on the falling speed. If the Earth had no atmosphere, the maximum speed that a falling body (initially at rest with respect to the centre of the Earth) could hit the Earth's surface with would be exactly equal (but opposite) to the escape velocity from the surface.

True, but that's not really the point of the whole "gravity well" business. ~1.5 million km is the farthest extent of space in which the Earth's gravitational field dominates. Further out than that, and the sun's gravity will be stronger than the Earth's. Earth's escape velocity is 11 km/s; dropping the mountain from the edge of the gravity well would result in a slightly lower velocity of 10 km/s.

Unless you put your falling body opposite the sun, so the sun's gravity pulls it into Earth's gravitational well. But you'd have to line it up exactly or you'd end up ejecting your body in a hyperbolic orbit toward New Netherlands or something.

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Re: What-If 0057: "Dropping a Mountain"

Postby Pfhorrest » Wed Aug 07, 2013 5:52 pm UTC

davidstarlingm wrote:
Pfhorrest wrote:I think it's something like the place where Earth's gravity becomes insignificant compared to other attractors. So, an object set sufficiently far away from Earth, at rest relative to Earth (at the moment it's magically set there), won't tend to fall to Earth, but will instead fall another direction, say more toward the sun. But set it close enough to the Earth and there comes a point where it will always fall to Earth (again, assuming an initial state of relative rest).

He didn't say "the outer limits of Earth's gravitational field" -- he said "the outer limits of Earth's gravitational well." Two very different things.

Earth's gravitational field extends to the edge of the observable universe, where it continues to propagate at the speed of light. Its gravitational well, on the other hand, is the spherical region of space in which the overall gravitational vector points toward Earth, also known as the Hill sphere. This region has a radius of is around 1.5 million km. It is the farthest extent within which you can place an object at rest and still have it fall directly onto the Earth.

That's about what I said already, but thanks for the wikilink to the technical term.
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Re: What-If 0057: "Dropping a Mountain"

Postby gparker » Wed Aug 07, 2013 7:49 pm UTC

References for the Chicxulub global firestorms:

Survival in the first hours of the Cenozoic (Robertson et al, 2004)
"For several hours following the Chicxulub impact, the entire Earth was bathed with intense infrared radiation from ballistically reentering ejecta. The global heat pulse would have killed unsheltered organisms directly and ignited fires at places where adequate fuel was available. Sheltering underground, within natural cavities, or in water would have been a necessary but not always sufficient condition for survival."

Reentry of fast ejecta: the global effects of large impacts (Melosh, 1990)
"These power levels are comparable to those obtained in a domestic oven set at 'broil.'"

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Re: What-If 0057: "Dropping a Mountain"

Postby tibfulv » Thu Aug 08, 2013 4:39 pm UTC

On an unrelated topic: anyone else having trouble with the rss feed for What If? Mine has been stuck on "Random Sneeze Call" since probably last week, so I forgot about it until today. Updating the live bookmark (Firefox) does not help at all.

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Re: What-If 0057: "Dropping a Mountain"

Postby gmalivuk » Thu Aug 08, 2013 10:54 pm UTC

Sandor wrote:
Demki wrote:BlackHatGuy was right, you didn't drop it from high enough, earth's escape velocity is 11.186 km/s, and at the best height you dropped it you only reached 10 km/s.

You can do better than Earth's escape velocity. Solar escape velocity from Earth orbit is about 42 km/s, and galactic escape velocity from the solar system is about 525 km/s (according to wikipedia).

I'm pretty sure these should be combined for something hitting the Earth. After all, if an object from outside the solar system hits the Earth it will have fallen down both the Sun's gravity well as far as Earth orbit and the Earth's gravity well as far as the planet's surface. However, I suspect just adding the velocities together won't work (you probably have to add the kinetic energies together).

They don't combine linearly, because if it's already travelling at e.g. 525km/s as it gets near the solar system, it has rather less time than normal to be accelerated by the sun, and won't speed up by a full 42km/s.
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Re: What-If 0057: "Dropping a Mountain"

Postby irino » Fri Aug 09, 2013 3:31 am UTC

What-if wrote:The pressure from the impact would be high enough to produce some unusual geologic strutures.


Is this a typo, or are "strutures" an actual thing?

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Re: What-If 0057: "Dropping a Mountain"

Postby Jave D » Fri Aug 09, 2013 4:02 am UTC

Yay, a Minecraft reference!

Or was that just a reference to pickaxes and diamond ore, neither of which Minecraft created, and I'm only thinking Minecraft because Minecraft Minecraft?

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Re: What-If 0057: "Dropping a Mountain"

Postby Copper Bezel » Fri Aug 09, 2013 5:16 am UTC

I had to work through the same check myself, but yeah, "diamond ore" has no meaning outside of Minecraft, so it is a reference. = )
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Re: What-If 0057: "Dropping a Mountain"

Postby ConMan » Fri Aug 09, 2013 5:39 am UTC

Jave D wrote:Yay, a Minecraft reference!

Or was that just a reference to pickaxes and diamond ore, neither of which Minecraft created, and I'm only thinking Minecraft because Minecraft Minecraft?

Looking closely at the pickaxe itself, it is most definitely a Minecraft-style one, so I'd say the reference is valid.
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Re: What-If 0057: "Dropping a Mountain"

Postby Nylonathatep » Fri Aug 09, 2013 4:48 pm UTC

I'm just curious, but just like a meteoroid falling from outer space, wouldn't some of the mountain's mass disintegrate as it enters the earth's atmosphere, and thus reduces the impact of the mountain falling back onto earth?

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Re: What-If 0057: "Dropping a Mountain"

Postby davidstarlingm » Fri Aug 09, 2013 5:15 pm UTC

Nylonathatep wrote:I'm just curious, but just like a meteoroid falling from outer space, wouldn't some of the mountain's mass disintegrate as it enters the earth's atmosphere, and thus reduces the impact of the mountain falling back onto earth?

Not much of it. Icy meteors break up quickly; rocky ones not so much. We're talking hundredths or thousandths of a percent for an object of this magnitude.

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Re: What-If 0057: "Dropping a Mountain"

Postby gmalivuk » Fri Aug 09, 2013 6:20 pm UTC

Bits might break off from the edge, which just means when it finally hits it'll be surrounded by a layer of highly compressed and superheated air, which I wouldn't call much of a mitigation of the effects.
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Re: What-If 0057: "Dropping a Mountain"

Postby Plasma Man » Sat Aug 10, 2013 12:18 pm UTC

It might make it prettier. Instead of one giant solid glowing mountain, we'd get a giant glowing mountain surrounded by shooting stars.
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Re: What-If 0057: "Dropping a Mountain"

Postby ijuin » Sun Aug 11, 2013 3:19 am UTC

Copper Bezel wrote:I had to work through the same check myself, but yeah, "diamond ore" has no meaning outside of Minecraft, so it is a reference. = )


Generally speaking, "ore" applies to metals or other materials where the material in question is mingled with other stuff at a microscopic (or molecular) level such that you need to melt it or use chemical means to separate them. Gemstones and other macroscopic crystals, however, can be separated out by mechanical means (just chip the softer rock away from around the diamonds--or put the whole thing in a rock breaker and then sort out the diamonds--diamonds are the hardest naturally-occurring substance under human-survivable conditions, after all, so you don't have to worry about the diamonds getting crushed).

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Re: What-If 0057: "Dropping a Mountain"

Postby najodleglejszy » Tue Aug 13, 2013 10:44 am UTC

Copper Bezel wrote:I had to work through the same check myself, but yeah, "diamond ore" has no meaning outside of Minecraft, so it is a reference. = )

you could just check the alt-text:
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Re: What-If 0057: "Dropping a Mountain"

Postby Fire Brns » Tue Aug 13, 2013 2:36 pm UTC

gparker wrote:Reentry of fast ejecta: the global effects of large impacts (Melosh, 1990)
"These power levels are comparable to those obtained in a domestic oven set at 'broil.'"

Reading this is really giving me a craving for velociraptor steak or perhaps a nice triceratops cut.
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Re: What-If 0057: "Dropping a Mountain"

Postby Red Hal » Tue Aug 13, 2013 3:17 pm UTC

Fire Brns wrote:
gparker wrote:Reentry of fast ejecta: the global effects of large impacts (Melosh, 1990)
"These power levels are comparable to those obtained in a domestic oven set at 'broil.'"

Reading this is really giving me a craving for velociraptor steak or perhaps a nice triceratops cut.

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Re: What-If 0057: "Dropping a Mountain"

Postby TheLochNessCheeseBurger » Wed Aug 14, 2013 5:38 pm UTC

I feel like the effects of the Denali-from-space impact should be animated and put to the music of "When I'm Bored"

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Re: What-If 0057: "Dropping a Mountain"

Postby bmonk » Fri Aug 16, 2013 9:09 pm UTC

If we really want more power (than gotten by falling an infinite distance), we could use rocket motors attached to the upper side of the mountain. Toy rocket motors.

But how many would be required to add significant velocity?
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Re: What-If 0057: "Dropping a Mountain"

Postby gimmespamnow » Wed Sep 04, 2013 8:35 pm UTC

I'm having trouble imagining that sticking your hand in that 1 inch crack would actually hurt, let alone damage your hand... Obviously I'm ignoring the implications of the wind coming out the hole, (in which case you don't want to be anywhere near it in the first place.)

The thing is that Denali isn't a solid unbreakable object, specifically near the surface near the base it is some loose soil. If you lifted all of the mountain up at once and dropped it it would fall as one object (more or less,) but if it encountered an obstacle, (like your hand,) the mountain or the obstacle would proceed to break up, and that loose soil near the top is pretty weak... The shear strength of a couple inches of loose soil depends on a lot of things, (what type of dirt it is and the moisture content,) but regardless it would break way before your skin/bones/etc did, and the weight of a couple inches of loose soil wouldn't hurt you either, (given that it is Alaska your largest sensation would probably be that your hand felt cold.) You can do this experiment in your back yard with a shovel: drop a shovel of dirt on your hand from an inch up. The dirt goes everywhere and isn't shovel shaped anymore but your hand is still very much there, (and your hand is now dirty.) Now from a foot up, with your entire arm in the hole, you might do some minor damage to your hand, (if there are rocks in the dirt and they are sharp, for instance.) I know from talking to construction workers that have been in trenches when they collapsed that the impact does hurt, but as long as it doesn't press against the lungs, (so quite a bit more than a foot of soil,) they generally (but not always) walk away from it with no damage, but they were wearing boots and pants; exposed skin would fare worse.


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