What is the highest point on Earth as measured from Earth's center? | Hacker News Reader

What is the highest point on Earth as measured from Earth's center?

oceanservice.noaa.gov

197 pointsDoreenMichele59 comments

>You may be surprised to learn that Everest is not the tallest mountain on Earth, either. That honor belongs to Mauna Kea, a volcano on the Big Island of Hawaii. Mauna Kea originates deep beneath the Pacific Ocean, and rises more than 33,500 feet from base to peak.

Can someone explain this? How do you differentiate "the mountain" from "the rest of the earth that it comes out of"?

(Side note: the issue of "tallest mountain", as discussed here, is a great example of dealing with an ambiguous concept and clarifying it by asking what you're trying to do with the answer.)

When comparing the actual height of a mountain, they're measured from their base (which is whatever elevation the ground they sit on is) to their peak, rather than just looking at their peak altitude. This is how you compare mountains on other planets, and why Mons Olympus on Mars is the tallest mountain in the solar system. For Mauna Kea, the mountain is taller than it looks because its base sits at the bottom of the ocean, whereas Everest sits on an already-lofty piece of continental plate.

Right, I got that much. I'm asking, how do you rigorously distinguish "the base" from the rest of the earth (or that earth from the mountain itself)?

Edit: IOW, if Kea's base were on some raised ocean floor, when do you count that as part of Kea too?

Why is "height from the solid matter base" more correct than "height from the non-gaseous matter base" though. From the perspective of humans, who generally live at the border of gaseous matter not the border of solid matter, I think the latter might make more sense.

I get the impression that the asker knows that but that their question is more like, is there any official way to define where the mountain starts? Could we keep tracking the side of Everest right down into a far-off ocean trench and say it's now the tallest again, it's just also really wide?

I guess you're looking for obvious local minima. If the land slopes back up a lot or stays mostly flat for a long time it's probably not part of the mountain anymore. Would a smaller mountain in the middle of Uluru be measured starting from ground level at the top of Uluru?

Edit: Asker has now confirmed in a separate comment that this is what they meant.

I like your clarification better though!

My definition would involve some definition of geological homogeny such that you could classify the terrain as mountain and not-mountain. Probably based on whether it was involved in the process that formed the mountain.

Yeah, that was what I was hoping/expecting the definition would use, that mountains come from some plate interaction involving lava which would provide a natural boundary between "mountain" and "rest of earth".

I think a lot of mountains don't involve lava at all, they're just the product of continental plates running into each other. I'm pretty sure Everest is an example of this. Hawaii is the opposite; those mountains don't involve plates at all, they're solely the product of lava.

I had to look this up, but apparently "sea level" on Mars (called "topographic datum") is decided using the average elevation near the equator.

http://passporttoknowledge.com/lfm/ask/terrain-geo/Determini...

Right, basically, in a different context accrding to this principle volcanoes at higher altitudes (say close to andes but not in the andes proper) are not as tall as more coastal/lower altitude volcanoes, if the cone’s rise isn't as high.

It's wet :) (under water surface)

The claim of the article that mount Everest is the tallest point from the earth's center happens because earth's surface, relative to its size, is as smooth as a billiard ball. Even the tallest mountains are nothing. So high mountains located at the equator can easily "outperform" higher mountains elsewhere.

Apparently it's not quite as smooth as a billiard ball. More like very fine sandpaper.

https://skeptics.stackexchange.com/questions/10763/is-earth-...

The article is likely referring to the estimated dry prominence of Mauna Kea. Topographic prominence [1] measures the height of a peak relative to its lowest surrounding contour line (that doesn't also contain another, taller peak). Usually the ocean's surface is considered "flat ground" when computing this measure (called a "wet prominence"), but one can alternatively imagine the Earth to have no water, and compute a "dry prominence" that permits the lowest surrounding contour line to be below sea level.

[1]: https://en.wikipedia.org/wiki/Topographic_prominence

The above Wikipedia article specifically mentions the dry prominence of Mauna Kea, estimating it to be 9330m which is taller than Everest's conventional height of 8848m. However, an apples-to-apples comparison would use the dry prominence of Everest too, which is the distance from the bottom of the Challenger Deep (-10,911m) to the summit. This would make Mauna Kea the second tallest mountain by topographic prominence if the Earth had no oceans.

Thank you, that's the kind of concept I was looking for.

>However, an apples-to-apples comparison would use the dry prominence of Everest too, which is the distance from the bottom of the Challenger Deep (-10,911m) to the summit. This would make Mauna Kea the second tallest mountain by topographic prominence if the Earth had no oceans

What? This does not make sense, if I am not mistaken? Topographic prominence would place Mauna Kea as the tallest (highest peak from base contour line), but it would certainly not be the second highest above the Challenger Deep... And the Challenger Deep is not the base contour line of any mountain..?

Think about it this way: imagine standing at the bottom of the Challenger Deep. Draw a small circle around yourself on the ocean floor. Now step outside the circle. Because you're standing on a spherical object (Earth), the area outside your circle isn't infinite like it would be on a plane. It's another finite region, which covers almost the entire Earth, and contains both yourself (standing just beside the lowest point of the Challenger Deep) and also the peak of Mount Everest. Therefore the circle is a base contour line for Everest, and Everest's wet prominence can be measured from the circle.

However, this same contour line cannot be used for the wet prominence measure of Mauna Kea, since it contains every mountain on Earth, many of which are taller. Mauna Kea's lowest contour line that doesn't contain another taller mountain would probably enclose a sizeable portion of the floor of the Pacific Ocean, but wouldn't include the Andes, Japan, or the Sierra Nevada, since those peaks are taller. The contour line would therefore be deep below the ocean surface, but not as deep as the Challenger Deep.

>Draw a small circle around yourself on the ocean floor.

That circle encloses two areas. One roughly a square metre, and the other one roughly 5e8 km². In geology only the smaller area is used, and the smaller area does not contain the peak of the Everest and thus is not considered a valid base contour line of the Everest.

Why not? You are looking for the lowest contour that can surround everest, at what would would you stop going lower because the countour is getting too big? 50% of the planet's surface? This seems like an arbitrary bound.

Is this measurement conceptually useful, or is it completely arbitrary? I thought it was an attempt to rigorously define "surrounding terrain" for purposes of measuring a mountain's height above the surrounding terrain, but if it defines the Challenger Deep as "surrounding" Everest, that's topologically interesting but doesn't seem like a useful way of thinking about geology.

Yes, that is correct. At almost 20,000 km, the dry prominence of Everest is by definition the maximum possible on Earth. You only get to claim Kea more prominent if you use a different standard to measure it!

I'm not seeing why that is true. If one were to imagine a deep moat around Kea, wouldn't that increase its prominence w/out impacting that of Everest? Or are you suggesting that Everest's dry prominence would be measured from whatever the deepest point on Earth is? Or something else?

Everest dominates Mauna Kea in prominence. In fact, Everest dominates any peak on Earth in prominence, since it's the tallest peak. By the mathematical definition of prominence, the dry prominence of Everest is always measured from the deepest point on Earth, the Challenger Deep.

If you dug a moat around Mauna Kea, it would indeed increase its prominence, but would not affect the prominence of Everest. Until you dug the moat deeper than the Challenger Deep (about -11,000 m), at which point the dry prominence of Everest would start to be measured from the bottom of your moat and not Challenger Deep. At this point, digging the moat any deeper would increase the prominence of both Everest and Kea by equal amount, but Everest as the higher mountain would nevertheless always dominate Kea.

From your link, the lower elevation of a dry prominence of Everest would be the lowest contour that encircles Everest. That won't be nearly as deep as Challenger Deep but a quick google search does not find the correct dry prominence for me.

The lowest bottom of the Challenger Deep encircles the Everest. Think of the "outside" of the circle being the deepest point, and the "inside" of the circle being all rest of the Earth.

Got me on that one.

Seems to me "topographic prominence" is useful for people talking about peaks in a mountain range. Not so much when the spherical shape of the Earth starts to be significant.

Reminds me of the joke where the mathematician is told to use a fixed length of fencing to enclose the biggest area possible and builds a tiny corral and stands inside and says "I define myself as outside the corral".

(Legit point on your part, though.)

In Douglas Adams''So Long And Thanks For All The Fish', Wonko the Sane resided either outside or inside, depending on your point of view, an inside-out house that he had built as an asylum for the world, after reading the instructions on a packet of toothpicks.

The correct dry prominence of everest is the same as the regular prominence of everest, because there are no bodies of water between it and the nearest peaks.

Incorrect. There are no higher peaks than everest, so it's prominence is the same as its summit. Dry prominence would be measured from sea level, wet prominence would be based on the lowest point in the ocean floor.

> The article is likely referring to the estimated dry prominence of Mauna Kea.

It's talking around a mountain's "surrounding base" which is a related concept but doesn't take you in the absurd direction of 'drawing a circle around yourself in the challenger deep and claiming everything else is part of Everest'.

There is no precise definition of surrounding base, but Denali, Mount Kilimanjaro and Nanga Parbat are possible candidates for the tallest mountain on land by this measure. The bases of mountain islands are below sea level, and given this consideration Mauna Kea (4,207 m (13,802 ft) above sea level) is the world's tallest mountain and volcano, rising about 10,203 m (33,474 ft) from the Pacific Ocean floor. Ojos del Salado has the greatest rise on Earth—13,420 m (44,029 ft) from the summit[citation needed] to the bottom of the Atacama Trench about 560 km (350 mi) away, though most of this rise is not part of the mountain.

https://en.wikipedia.org/wiki/List_of_highest_mountains_on_E...

Yeah that has always seemed a bit jumbled to me. It's not clear to me why that point, 33,500 feet below the peak of Mauna Kea, is appropriate to use as a basis of measurement for the mountain. And why not a lower point? And why can that point not be used to measure the height of Mount Everest as well?

Anyway, I think what you're asking can usually be described by the concept of Topographic Prominence[1], one definition of which is "the height of the peak’s summit above the lowest contour line encircling it but containing no higher summit"

[1] https://en.wikipedia.org/wiki/Topographic_prominence

Which center? The centroid of the spheroid that is the earth (i.e. the point that's as close to equidistant from all points as possible)? The center of mass? The gravitational center (I think this would be the same as the center of mass, but i'm not positive)?

I'd be curious how the different centers change the results.

I would assume all of these (add center of volume) to be quite close to each other for all practical intents and purposes, given how smooth Earth's surface is in the big picture:

https://what-if.xkcd.com/46/

You would be wrong.

Make the problem simpler by thinking in 2 dimensions. Where's the center of the United States? There are an infinite number of different answers. Think about how many different map projections there are.

Now where is the center of the Earth? The point furthest from sea level? The point furthest from the surface? Do you include mountains, ocean basins, ocean trenches, etc.? What % of a substance has to be water before it doesn't count as part of the earth? The point furthest from the edge of the atmosphere? How do you determine where that is? Or is the center of mass? These are all going to give you wildly different answers.

Humanities questions cannot be easily solved scientifically.

The variation cause by mountain or sea trench is absolutely tiny compared to the earth diameter, as explained by his xkcd's link.

"That makes Chimborazo the closest point on Earth to the stars."

That statement sold me. If I want to be on the top of any mountain now, it's that one.

It's not an easy mountain but it's of a substantially lower degree of difficulty than the high Himalayan peaks. It's harder than the lower Ecuador volcanoes for reasons of elevation and other factors and has glaciers, etc. like they do but the weather tends to be better than mountains much further north or south. (I've climbed other volcanoes there but only made it part way up Chimborazo.)

ADDED: i.e. so it's not unthinkable for a person in good physical shape who gets some winter hiking experience, has a fair bit of experience hiking up mountains overall, gets some glacier skills, and goes on a guided climb. Of course, people react to altitude a lot differently.

Looks like a few hours walk and $250 for a guide:

https://www.mountainproject.com/route/110735330/standard-rou...

From the description I see on net this is indeed true, with big IF - you already have prior acclimatization to 5000m+. Without it, its almost impossible to make it to the top and back at that altitude, unless you have some super genes. And descriptions mention still 10 hours of hiking and altitude difference of some 1300m.

Even though the air around equator is thicker, you would most probably already feel very bad at the carpark at 4800m, if you would come up straight from the capital. I'd say some 5-7day acclimatization prior to this should be enough for most fit people.

Right. It's not "hard" in the grand scheme of things of climbing 8000m peaks in the Himalayas, highly technical climbs, or even a peak like Denali. However, it's also a far way from pull up to a parking lot and get a little exercise for the vast majority of people. Altitude makes a big difference for most. As you say, there's acclimatization. And also there's a world of difference climbing at 5000m+ relative to climbing relatively near sea level for almost everyone.

I can confirm it is difficult. Not in terms of climbing, but in terms of breathing. The higher, the smaller your steps. Above 6.000m do you 3 steps and 10 seconds of gasping for air or more. But the view on the summit, that was the most beautiful one I have every seen. You could see the shadow of the mountain, see below. In my case there where some clouds, which made it even more beautiful. https://80d2853cc4def76b377d-54344bc01a8b066c84096a8e7a3499a...

That is beautiful! And thanks for the feedback.

I'm in shape, and there's a 4,000+ meter mountain less than 30 miles away (as the crows flies) to acclimatize with, so I'd feel pretty good about it. I'm faster than most when hiking mountains. Doable :)

The statement implies that by "Earth's center" the authors mean the center of mass, that being the point about which the body as a whole rotates.

The oceans however are part of Earth's mass, and kept in motion relative to the crust by tidal forces from the moon. This too, the piece neglects.

Calculation of the magnitude of tidal effect might be a fun exercise for someone whose calculus skills are less atrophied than my own ...

Given the depth of the crust relative to the radius of the earth, I'm going to guess that to a first or even a second approximation, the center of the earth is pretty much the center of the earth whatever type of center you care to choose.

I climbed (hiked) Cotopaxi in Ecuador, and you can see Chimborazo from the summit.

Cotopaxi is 5,897m, so it's still further from the center of the earth than Everest.

Full story of my climb and photos here http://theroadchoseme.com/cotopaxi-summit

Chimborazo in Ecuador has an altitude of 6,310 meters (20,703 feet). Mount Everest has a higher altitude, and Mauna Kea is "taller." However, Chimborazo has the distinction of being the "highest mountain above Earth's center."

This is because Earth is not a sphere - it is an oblate spheroid. As an oblate spheroid, Earth is widest at its equator. Chimborazo is just one degree south of the equator. At that location, it is 6,384 kilometers (3,967 miles) above Earth's center, or about 2 kilometers (about 1.2 miles) farther from Earth's center than Mount Everest.

So is the peak of Chimborazo the point on Earth with the lowest delta-v to orbit?

Compared to a sea level equatorial launch, https://space.stackexchange.com/questions/8486/where-is-the-... claims a 0.2% gravitational advantage due to height, and a 0.1% advantage due to rotational velociy.

Small, but not nothing.

Maybe, but how are you going to carry a rocket up there? Even building a rocket sled up a mountain seems infeasible.

Llamas. And lots of 'em.

You don't carry it!

You dig a tunnel (Boring Company), you vacuum it (hyperloop), and you propulse a rocket (Space X) in it with electromagnets, and lots of batteries (Tesla).

Theorically, you can also come back from space the same way, but 1- you still need to slow down from orbit, 2- you need to be very precise to enter the tunnel. This would allow to reload the battery using electromagnetic braking. Unfortunately, you would need to reverse the orbital speed to come back the way you came from! This is the costly part. This is why Space X lands on sea platforms, not where they took off from.

I think that's what I meant by "rocket sled", is it really feasible to dig a tunnel all the way up a mountain?

If you measure height from the bottom, the tallest building on earth is probably a shack on top of a mine, and the tallest structure of any sort is an oil well.

Or maybe a road system.

We could pitch a tent on top of Chimborazo, I'm guessing.

Isn‘t the summit of Chimborazo the farthest point from earths center?

https://en.wikipedia.org/wiki/Chimborazo

That's what the article says.

I see you didn't read the article :)

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