So how high can mountains be?

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Today I’ve read online on the BBC World Service, this article about how high a mountain such as the Everest, can get.
In other planets, Mars in particular, there are mountains that are much higher than any on Earth, mostly extinct volcanoes.

A height measurement made in the 18th Century as part of the Great Trigonometrical Survey of India (*), arranged by the then British colonial government, determined the height of the Everest with the, for the time, outstanding precision: with only a nine-meters (some 27 feet) difference from very precise measurements, made to better than a quarter of an inch, using GPS in modern times.
I have been always quite keen on the use of GPS, for my own professional reasons, and I knew personally the scientific leader of the first expedition to Mount Everest to install a GPS receiver at the top and get a precise measurement, who told me that it was certainly a hard thing to do.
Several other similar expeditions have followed since then.

But, as explained in the article, mountain heights change due to the whole area where they stand rising up as a result of plate tectonic movements underneath, such as those resulting from the collision between India and Eurasia that first created and, still going on, continues to raise the Himalayas as big “carpet wrinkles” on the Earth’s surface; and the opposite effect of erosion that tends to lower mountains in the long run. Understanding the latter effect is not a simple matter, as explained in the article.

There is also the fact that heights are measured relative to sea level; this is hard to do in mountainous areas, because it is difficult there to make the necessary measurements to find the sea level. The best results are based on the mapping of the bumps in the gravity field of the Earth using satellites, something I have worked on for many years. At present, sea-level height determined in this way, in most parts of the world, is known to better than four inches.

https://www.bbc.com/future/article/20220407-how-tall-will-mount-everest-get-before-it-stops-growing

(*) Considered these days as the equivalent of a land surveyor’s “Moonshot.”, it has a truly fascinating history.

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zeddy, Mike

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What’s even more amazing, is when you consider measuring a mountain from its base, which in some cases would be seafloor level.

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Mike, If you are referring to the measurement made during the Great Trigonometric Survey of India, those were made from the tops of other mountains already measured, in that region also pretty high themselves.

That, in itself, was truly amazing.

Ex-Windows user (Win. 98, XP, 7); since mid-2017 using also macOS. Presently on Monterey 12.15 & sometimes running also Linux (Mint).

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Mike

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1. I had just read an article on BBC online about Mauna Kea.  But then there’s also this which I found interesting (as also mentioned in your article link).

https://oceanservice.noaa.gov/facts/highestpoint.html

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Mike, Thanks: good linked article.

With GPS, heights are measured above the flattened ellipsoid that best fits the shape of the Earth (and this is a whole other story) The results are called “ellipsoidal heights.” These are then corrected to get things measured at “sea level”, which technically is “the gravity field’s equipotential surface” that bests fits the ellipsoid (the “level” surface that water in repose, if it covered the whole world, will have). So, for finding results above sea level, the ellipsoidal height is corrected using a map of this surface derived from ground, airplane and satellite observations. This is done with the software used to calculate heights with GPS data (and the data from other systems like GPS, collectively known as Global Navigation Satellite Systems, or GNSS).

One more thing that is amazing about the Great Trigonometric Survey of India (and this one is definitely about “Tech“) was that processing all the data took some really big and complicated calculations that were made well  before there were electronic computers. So the “computers” were people seating around long tables, where each one would do part of the calculations by hand, with the help of some simple mechanical calculator (just +. -, *, /), as well as trig and log tables, and pass the results to the next one, and so it went, production-line style, following a “program” that told each “computer” what to do. With India’s often hot and humid climate, servant boys who moved large overhead vanes to make some refreshing air circulate, called “pukka wallahs”, had a serious and important job to do.

Ex-Windows user (Win. 98, XP, 7); since mid-2017 using also macOS. Presently on Monterey 12.15 & sometimes running also Linux (Mint).

MacBook Pro circa mid-2015, 15" display, with 16GB 1600 GHz DDR3 RAM, 1 TB SSD, a Haswell architecture Intel CPU with 4 Cores and 8 Threads model i7-4870HQ @ 2.50GHz.
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Hi Oscar
When I first saw this post about Everest, it reminded me of my favourite question..
“What was the highest mountain on Earth before Mount Everest was discovered?”***

Now, as for measuring to “better than four inches” that sounds like the back of a cigarette packet, so maybe using a twin-laser-interferometer would get you within say, 10 hydrogen-atoms. That’s much less than a cat’s whisker.

zeddy

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zeddy: “o maybe using a twin-laser-interferometer would get you within say, 10 hydrogen-atoms. That’s much less than a cat’s whisker.”

Maybe just one laser interferometer? If I understand this correctly, you are referring to the LIGO setup, with two laser interferometers at two wide apart sites used to detect gravitational waves.

But, then again, you might have meant “a dual-frequency laser interferometer.”

Still presenting similar problems I am about to describe for the LIGO type, I am afraid.

First off all, one measures the relative phase and phase changes between the two signals bouncing back from the arms to a detector, and these results are ambiguous in a whole number of the laser light wavelengths: the same reason a 12-hour clock tells the time without letting you know if “10:15” is AM or PM.

These phase wavelengths are at most at the micron level (one millionth of a meter) and the ambiguities are an unknown and a huge number of times that much, corresponding to the actual length of the arms, but that is OK in the case of those instruments, because they are meant to determine changes in the lengths of the arms that are tiny compared to this wavelength.

Regardless of the ambiguities, and of the type of interferometer, one could only measure with an interferometer height relative to some other, possibly inconvenient place, not directly with respect to the Earth’s center, as when using GPS, then with this GPS measurement corrected, with a simple calculation, to a height about the reference ellipsoid, or this further corrected to sea-level height, as already explained. Besides that there is this: Everything moves on the Earth’s surface, because of different, often simultaneous causes: there are always tiny tremors going on we never notice, or anything else that might shake a place, such as people or animals walking around; not so much on the top of those mountains, perhaps, but there is always the gusty wind. The more sensitive a measurement, the more sensitive it is to this noisy background.

For an example of what makes the use of interferometry problematic, let’s consider one regular two-arms, single-frequency laser interferometer of the LIGO kind (or perhaps of the ESA-projected space mission LISA’s triangular arrangement kind), one would have to set up the mirror at the end of one long arm at the top of Mt. Everest, the splitting mirror on top of another mountain and the one at the end of the second long arm at the top of yet a third mountain. Then one would need to have clean shots between all the mirrors, the one on Everest and the other two on top of the two other mountains. Weather allowing.

But that would also mean having the mechanically seismic-disturbances super-isolating suspension of each mirror in place, to hold each of the two mirrors at the ends of the arms and the splitting mirror in between, steady enough that not any disturbance around them (such as howling winds, or pelting snow) can shake them in the slightest. And it will be necessary to house each top-of-a-mountain mirror in a specially constructed building. Along with the people that should visit those buildings for regular maintenance, mirror realignments, etc.

I suspect that taking a GPS receiver to the top of Mt. Everest, if not using as precise a technique, might be somewhat cheaper in terms of the cost of labor and materials, and also not as deplorable as the loss of all those Sherpas.

Ex-Windows user (Win. 98, XP, 7); since mid-2017 using also macOS. Presently on Monterey 12.15 & sometimes running also Linux (Mint).

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What ever the measurement technique the important data is the delta that matters for what is changing.

🍻

Just because you don't know where you are going doesn't mean any road will get you there.

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OscarCP

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wavy: “What ever the measurement technique the important data is the delta that matters for what is changing. ”

It depends on whom you ask: a cartographer will need the height for making a map of the region, specially one to be used to define a country’s border that, by international treaty, is to run along the tops of a mountain chain (what is usually called “the waters divide”), or for charts to be used by trekkers and climbers.
The geophysicist will be interested in the height, as well as the other dimensions, for calculating various things, such as the mountain’s mass, the gravitational effect of this mass, how deep are the underground roots of the mountain compared to its height, and also would like to know the change in height over a given period of time, to understand better the processes that are building up the mountain.

Putting a GPS receiver on top of such mountains as Everest, that are not only very high, but also very hard to climb, is not easy and can only be done, given the weather conditions up there, for a few hours, that limits the amount of data collected and, in consequence, the precision of the results. To find change over time, repeated tricky surveys like this have to be repeated time and again.

Other methods less strenuous and risky exist, for example using laser altimetry (lidar) surveys from airplanes flying repeated parallel traverses to make topographic relief maps of large regions, or of repeated surveys of surfaces to find their changes in height. For example to find how glaciers are losing ice by observing their surfaces getting lower and lower. I have been involved in both types of survey, chiefly processing the GPS data from the airplane receiver, using specialized software I have developed for doing things like that with high enough precision.
To determine the height of the surface, one needs to know from where was the height measured with the laser (height of surface = height of airplane – its laser measured height above this surface).

Ex-Windows user (Win. 98, XP, 7); since mid-2017 using also macOS. Presently on Monterey 12.15 & sometimes running also Linux (Mint).

MacBook Pro circa mid-2015, 15" display, with 16GB 1600 GHz DDR3 RAM, 1 TB SSD, a Haswell architecture Intel CPU with 4 Cores and 8 Threads model i7-4870HQ @ 2.50GHz.
Intel Iris Pro GPU with Built-in Bus, VRAM 1.5 GB, Display 2880 x 1800 Retina, 24-Bit color.
macOS Monterey; browsers: Waterfox "Current", Vivaldi and (now and then) Chrome; security apps. Intego AV

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zeddy

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Hi Oscar

I wanted to thank you again for this interesting topic. It’s amazing how fast things have changed and how useful and accessible modern technology is, especially with GPS.

OscarCP: “If I understand this correctly, you are referring to the LIGO setup”

I don’t have the LIGO budget. My budget is more like a LEGO setup. The twin-laser setup is to destructively cancel ‘local-effects’, they are also counter-rotating and circular-polarized, one is RHCP and the other is LHCP. This is to deal with signal-chirality issues (the target-image-reflection cannot be superimposed by any geometric combinations of rotations, lateral translations etc etc).

But never mind all that, within 4-inches is definitely accurate enough for me for measuring mountain heights. Not so for my thoracic surgeon – that’s the size of a spleen (I wish I still had mine).

As for sea-level height, is that with or without all the sea sponges taken out? (I tried to calculate that some years ago, please refer to previous Lounge postings).

It’s a busy travel travel time ahead for me. The faster I travel, it seems the less energy I have. I must’ve had tachyons for breakfast again.

zeddy

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OscarCP

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