What-If 0057: "Dropping a Mountain"

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Vroomfundel
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What-If 0057: "Dropping a Mountain"

Postby Vroomfundel » Tue Aug 06, 2013 9:52 am UTC

What-If 0057: Dropping a Mountain

What if a huge mountain—Denali, say—had the bottom inch of its base disappear? What would happen from the impact of the mountain falling 1 inch? What about 1 foot? What if the mountain's base were raised to the present height of the summit, and then the whole thing were allowed to drop to the earth?


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

Postby dalcde » Tue Aug 06, 2013 9:59 am UTC


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

Postby Sjö » Tue Aug 06, 2013 10:04 am UTC

What about air resistance? In the one-inch and one-foot scenarios you have a cushion of air that has to get out of the way when the mountain drops. Surely that would slow the fall and decrease the impact forces?
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Re: What-If 0057: "Dropping a Mountain"

Postby bachaddict » Tue Aug 06, 2013 10:06 am UTC

Heehee :D so many classic xkcd themes!
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Re: What-If 0057: "Dropping a Mountain"

Postby Demki » Tue Aug 06, 2013 11:22 am UTC

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 could've gone higher, tho it would have diminishing effects. Earth can pull stuff everywhere, although the sun would probably win this tug of war... another thing Randall forgot.

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

Postby Klear » Tue Aug 06, 2013 11:38 am UTC

For those of you smart enough not to google the industrial accident photos, here's a link to tempt you:
Industrial accident photos.

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

Postby Barstro » Tue Aug 06, 2013 12:02 pm UTC

If you put a lump of coal under the meteor, the impact

Should be "mountain".

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

Postby Barstro » Tue Aug 06, 2013 12:08 pm UTC

"A total collapse of modern civilization would be a serious blow to the already sluggish economy"

Great line. I hope that some people in D.C. read this comic and actually use the above argument in discussions on the environment or nuclear (nukular) war.

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

Postby flamewise » Tue Aug 06, 2013 12:24 pm UTC

As long as "height" is defined as "above mean [Earth] sea level" there is no "higher" I guess.

But, you know, you could add some serious levels of enough power by adding gravitational pull from the sun...

I laughed a lot about this one, and the last image was a great resolution.

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

Postby Sandor » Tue Aug 06, 2013 12:46 pm UTC

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).

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

Postby cellocgw » Tue Aug 06, 2013 12:47 pm UTC

First mistake: not dope-slapping John Clark (clearly a Red Lectroid ) for using English units.
Second mistake: the 1815 volcanic eruption is only the largest in recorded history.

Followup question: if you drop the mountain from a few km or higher, what are the chances it'll land pointy-end-down? It's not a cat, or even a redundakitty, after all. :mrgreen:
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Re: What-If 0057: "Dropping a Mountain"

Postby CharlieP » Tue Aug 06, 2013 2:19 pm UTC

cellocgw wrote:First mistake: not dope-slapping John Clark (clearly a Red Lectroid ) for using English units.


We English don't use them as much as you do[1]. Maybe you should call them "American units". :wink:



[1] We've been stuck in a halfway house for a while now where food and drink is packaged in metric yet draught beer and milk delivered to the doorstep is still sold in pints. Road signs are still in miles, but Ordnance Survey map grids have been in kilometres for decades now, and new roads and railways are specified in metric. And, most annoyingly, newspaper headlines are in Celsius in the winter and Fahrenheit in the summer!
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Re: What-If 0057: "Dropping a Mountain"

Postby peewee_RotA » Tue Aug 06, 2013 2:22 pm UTC

That impact calculator is fun. Epsecially when it doesn't work

You can create impact craters that are wider and deeper than the diameter of the earth.

I hit the earth with a meteor 1000 times bigger than the sun. It only slightly shifted the earth's axis.
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Re: What-If 0057: "Dropping a Mountain"

Postby richP » Tue Aug 06, 2013 3:15 pm UTC

Nice, a hint at fanservice for the cuegan shippers in picture 2?

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

Postby Klear » Tue Aug 06, 2013 3:22 pm UTC

richP wrote:Nice, a hint at fanservice for the cuegan shippers in picture 2?


Based on the alt-text of the first picture, the girl isn't Megan but John-Clark.

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

Postby davidstarlingm » Tue Aug 06, 2013 3:27 pm UTC

Sjö wrote:What about air resistance? In the one-inch and one-foot scenarios you have a cushion of air that has to get out of the way when the mountain drops. Surely that would slow the fall and decrease the impact forces?

Nah. Air is pretty darn compressible. Air resistance depends on velocity, anyway.

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

Postby Himself » Tue Aug 06, 2013 3:50 pm UTC

Assuming the one foot gap is filled with air at a desnity typical of the altitude of the mountain's base, how fast of an air blast would you get?
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Re: What-If 0057: "Dropping a Mountain"

Postby moody7277 » Tue Aug 06, 2013 4:19 pm UTC

peewee_RotA wrote:That impact calculator is fun. Epsecially when it doesn't work

You can create impact craters that are wider and deeper than the diameter of the earth.

I hit the earth with a meteor 1000 times bigger than the sun. It only slightly shifted the earth's axis.


I'm just sad you can't do relativistic impacts with it. I mean if it allows you to use an impactor the size of a Gallilean satellite, you should be able to set the velocity to 0.7c.
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Re: What-If 0057: "Dropping a Mountain"

Postby davidstarlingm » Tue Aug 06, 2013 4:28 pm UTC

Himself wrote:Assuming the one foot gap is filled with air at a desnity typical of the altitude of the mountain's base, how fast of an air blast would you get?

Click on Citation 8 in the post:

Randall wrote:If your magical mountain-cutter put air in the space where the rock used to be, you should avoid standing near the crack when it falls. The air will come jetting out from the closing crack, spraying rocks and dust at speeds approaching, or even--thanks to some fun heat-related effects--exceeding, Mach 1.

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

Postby keithl » Tue Aug 06, 2013 4:35 pm UTC

Himself wrote:Assuming the one foot gap is filled with air at a desnity typical of the altitude of the mountain's base, how fast of an air blast would you get?

Approximately the speed of sound, a thin jet of hot air for a very short time. Maybe - it depends on what the various layers of mountain do when closing the gap, trapping air, etc. It seems likely that 99.99% of the air will stay trapped in the rock, only the outer few meters will blow out over a fraction of a second.

My guess is that there are a lot of horizontal shear forces across all that rock, and cutting the gap will cause them to release a heck of a lot more energy than the drop itself.

EDIT: Denali is caused by the Pacific plate slamming eastwards into the North American plate, squeezing Denali up like toothpaste out of a tube. The part of the mountain above the gap would be released from those horizontal compression forces, and slide outwards, perhaps by tens of meters. Cueball and John-Clark decapitated.

The pressure at the core of the mountain is enormous. When the magic gap force disappears, the "average" of the whole mountain will descend at 9.8 m/s2, but in fact the rock just above and below the gap will be accelerated into it at enormous accelerations by all that pressure, fastest near the center of the mountain. Vertical pressure gradients will be huge, horizontal pressure gradients relatively small. So the air in the gap will be compressed to about double the pressure of the rock, adiabatically heated to a plasma, and do some interesting chemistry to a few millimeters of rock above and below, but probably not get forced sideways very far. Only the air underneath the new overhang will move outwards fast, because the pressure gradient to outside atmosphere is high, blowing the torched, decapitated bodies of Cueball and John-Clark away from the gap.

CSI:Denali will find themselves with a very interesting investigation. This will be a real boost for the science of Forensic Geology

EDIT EDIT: Thinking more, the air will come out much faster than the speed of sound. For the one foot gap, and the mountain squeezing into the gap very rapidly, this will be more like a high velocity gun or cannon blast from a barrel the height of the gap and as wide as the mountain, with lots of spalled and shock-wave entrained rock from the edges of the gap. Cueball and John-Clark bodies and levitator shredded into tiny fragments. Just as well, there are some things Man Was Not Meant To Know.
Last edited by keithl on Tue Aug 06, 2013 5:52 pm UTC, edited 4 times in total.

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

Postby rhomboidal » Tue Aug 06, 2013 4:37 pm UTC

hehe, I like this version of "Space Mountain" so much more than the Disneyland one.

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

Postby MrT2 » Tue Aug 06, 2013 5:31 pm UTC

CharlieP wrote:We English don't use them as much as you do[1]. Maybe you should call them "American units". :wink:

[1] We've been stuck in a halfway house for a while now where food and drink is packaged in metric yet draught beer and milk delivered to the doorstep is still sold in pints. Road signs are still in miles, but Ordnance Survey map grids have been in kilometres for decades now, and new roads and railways are specified in metric. And, most annoyingly, newspaper headlines are in Celsius in the winter and Fahrenheit in the summer!

Cars are almost the perfect example of how much our (UK) measurement system has been stuck in a blender and left on too long:
- Fuel economy is in miles per imperial gallon, petrol/diesel is priced per litre.
- Road signs are all in miles and yards, vehicle tax is based on either (for cars new since 2001) CO2 emissions in grams/km, or (pre-2001 cars) engine size in cc.
- The size of the car is quoted in mm, the bleep of parking sensors changes depending on whether an obstruction is 8/5/3/1 feet away from your car.
- Tyre diameters are in inches, the minimum legal tread depth is in mm.
- Beer is in pints, the legal breath/blood alcohol levels for driving are in mg or µg per 100 ml.
- About 10-15 years ago, all the gradient road signs were changed from ratios to percentages, which caused quite a bit of confusion (going from small numbers = steep hill to big numbers = steep hill).

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

Postby mathmannix » Tue Aug 06, 2013 5:34 pm UTC

rhomboidal wrote:hehe, I like this version of "Space Mountain" so much more than the Disneyland one.


Yeah, the Disneyland version has only killed one person so far. (Two for the Disney World one.)
I hear velociraptor tastes like chicken.

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

Postby Klear » Tue Aug 06, 2013 5:58 pm UTC

MrT2 wrote:
CharlieP wrote:We English don't use them as much as you do[1]. Maybe you should call them "American units". :wink:

[1] We've been stuck in a halfway house for a while now where food and drink is packaged in metric yet draught beer and milk delivered to the doorstep is still sold in pints. Road signs are still in miles, but Ordnance Survey map grids have been in kilometres for decades now, and new roads and railways are specified in metric. And, most annoyingly, newspaper headlines are in Celsius in the winter and Fahrenheit in the summer!

Cars are almost the perfect example of how much our (UK) measurement system has been stuck in a blender and left on too long:
- Fuel economy is in miles per imperial gallon, petrol/diesel is priced per litre.
- Road signs are all in miles and yards, vehicle tax is based on either (for cars new since 2001) CO2 emissions in grams/km, or (pre-2001 cars) engine size in cc.
- The size of the car is quoted in mm, the bleep of parking sensors changes depending on whether an obstruction is 8/5/3/1 feet away from your car.
- Tyre diameters are in inches, the minimum legal tread depth is in mm.
- Beer is in pints, the legal breath/blood alcohol levels for driving are in mg or µg per 100 ml.
- About 10-15 years ago, all the gradient road signs were changed from ratios to percentages, which caused quite a bit of confusion (going from small numbers = steep hill to big numbers = steep hill).


This is off topic, but it reminds me of this scene:
https://www.youtube.com/watch?feature=player_detailpage&v=ay0TDQuq7XI&t=189

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

Postby Euphonium » Tue Aug 06, 2013 6:04 pm UTC

One thing Randall seems to ignore, though (unless I didn't read carefully enough) is, if you drop Mt. Denali from space, how much of it would actually be left to impact once it reached the surface? I have no clue on what order of magnitude the loss due to ablation would be, so I don't know if it would make an impact--would it?

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

Postby TimeLurker » Tue Aug 06, 2013 6:48 pm UTC

Euphonium wrote:One thing Randall seems to ignore, though (unless I didn't read carefully enough) is, if you drop Mt. Denali from space, how much of it would actually be left to impact once it reached the surface? I have no clue on what order of magnitude the loss due to ablation would be, so I don't know if it would make an impact--would it?

I'm sure there would be enough left to make an impact. :wink:
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Re: What-If 0057: "Dropping a Mountain"

Postby The Synologist » Tue Aug 06, 2013 6:51 pm UTC

I just have to point out citation #6 for the sound a dropping mountain would make:

"Citation: A dream I had once."

Freakin' hilarious :lol:

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

Postby J-Hammy » Tue Aug 06, 2013 7:01 pm UTC

Anybody else using the Dictionary of Numbers GLR recommended in a recent blag post? Some of the approximations are redundant in this what-if. :)
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buffygirl wrote:
StratPlayer wrote:
Dracomax wrote:
bighaben wrote:I think she's going to slide down the dune, hopefully taking Cueball with her. :twisted:

Possibly on purpose. sliding down a hill is fun.


And it's only fair. If he goes down first, she should go down, too.

THAT'S WHAT SHE SAID!!!

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

Postby PolakoVoador » Tue Aug 06, 2013 7:33 pm UTC

A what-if with massive destruction, that's more like it!

Since when there are jokes in the citations? I think I never bothered to click the sources before.

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

Postby LosDovakins » Tue Aug 06, 2013 7:36 pm UTC

By far one of the funniest things I've read on this site. And informative. Another masterpiece Randall

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

Postby peterz » Tue Aug 06, 2013 7:55 pm UTC

But, but, given the diagram of dropping it from way far out in space and giving it a little extra shove, Denali is unlikely in the extreme to hit Earth. It will likely be in a hyperbolic orbit and then exit the system.

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

Postby runetrantor » Tue Aug 06, 2013 8:15 pm UTC

The ending was so unexpected it cracked me up. I love it when I do not scroll too far down. XD

What would What Ifs be without Black Hat Guy and that Black Cat that loves the 0 key?

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

Postby Amarantamin » Tue Aug 06, 2013 10:57 pm UTC

The citations here are super cute. I started noticing at Citation 4, which is self-aware of the fact that there are a lot of citations. =D

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

Postby gene123 » Tue Aug 06, 2013 11:53 pm UTC

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?

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

Postby The Synologist » Wed Aug 07, 2013 2:55 am 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?

I was just about to come back here and post this! Yes, what's the significance of the "outer limits of the Earth's gravity well"? Is that just where it gets so weak that for all intents and purposes it's nonexistent?

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

Postby Pfhorrest » Wed Aug 07, 2013 3:21 am UTC

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

Postby willpellmn » Wed Aug 07, 2013 5:35 am UTC

So the What-Ifs officially have continuity now....

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

Postby CharlieP » Wed Aug 07, 2013 9:16 am UTC

MrT2 wrote:
CharlieP wrote:We English don't use them as much as you do[1]. Maybe you should call them "American units". :wink:

[1] We've been stuck in a halfway house for a while now where food and drink is packaged in metric yet draught beer and milk delivered to the doorstep is still sold in pints. Road signs are still in miles, but Ordnance Survey map grids have been in kilometres for decades now, and new roads and railways are specified in metric. And, most annoyingly, newspaper headlines are in Celsius in the winter and Fahrenheit in the summer!

Cars are almost the perfect example of how much our (UK) measurement system has been stuck in a blender and left on too long:
- Fuel economy is in miles per imperial gallon, petrol/diesel is priced per litre.
- Road signs are all in miles and yards, vehicle tax is based on either (for cars new since 2001) CO2 emissions in grams/km, or (pre-2001 cars) engine size in cc.
- The size of the car is quoted in mm, the bleep of parking sensors changes depending on whether an obstruction is 8/5/3/1 feet away from your car.
- Tyre diameters are in inches, the minimum legal tread depth is in mm.
- Beer is in pints, the legal breath/blood alcohol levels for driving are in mg or µg per 100 ml.
- About 10-15 years ago, all the gradient road signs were changed from ratios to percentages, which caused quite a bit of confusion (going from small numbers = steep hill to big numbers = steep hill).


Indeed. Though while miles per gallon are used colloquially (and on in-car displays), official figures are published in litres per 100 km. Furthermore, while distance signs and speed limits use miles/yards and mph, marker posts and the newer Driver Location Signs on motorways show distance from the datum point in kilometres.

Outside the car world, I recently started running socially - most people use phones or GPS watches to track their speed and distance, and there's often confusion at the end as some people have paced themselves in Imperial and others in metric.

Ireland recently switched all their road signs with little fuss (though for a while they had distances in miles and speed limits in km/h!), however I fear that any similar attempts here would be met with outrage and indignation that something terribly un-British was being foisted on us "by Brussels"... :?
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Re: What-If 0057: "Dropping a Mountain"

Postby Plasma_Wolf » Wed Aug 07, 2013 11:09 am UTC

Ahh! My beautiful house on New Netherlands is going to be washed away! Just when you think you can make your country larger by draining the oceans, people start throwing with mountains. :mrgreen:

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

Postby davidstarlingm » Wed Aug 07, 2013 1:33 pm UTC

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.


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