The mountain that weighed the Earth | Hacker News Reader

The mountain that weighed the Earth

signoregalilei.com

107 pointssurprisetalk15 comments

Interesting...

A few years later, the gravitational deflection of the Himalayas on a plumb line by Airy proved less than expected, which suggested that mountains have 'roots' that extend below them, displacing more dense rock--like icebergs more or less.

I used the gravitational force of the Longmenshan range to calculate the perturbations in the elastic stress field of the Earth's crust in Sichuan province, China, to estimate the tectonic forces in the region, which caused the 2008 Wenchuan earthquake: https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/201...

> The Schiehallion experiment wasn’t the state of the art for long. A more precise result was achieved in 1798 by Henry Cavendish, who was on the committee for the Schiehallion experiment. Cavendish’s experiment measured the gravity of large lead spheres using an extremely precise torsion pendulum, and cut the error from 20% down to 1.2%.

Cavendish was a peculiar fellow.

> At his death, Cavendish was the largest depositor in the Bank of England. He was a shy man who was uncomfortable in society and avoided it when he could. He could speak to only one person at a time, and only if the person were known to him and male. He conversed little, always dressed in an old-fashioned suit, and developed no known deep personal attachments outside his family. Cavendish was taciturn and solitary and regarded by many as eccentric. He communicated with his female servants only by notes. By one account, Cavendish had a back staircase added to his house to avoid encountering his housekeeper, because he was especially shy of women.

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

Who was saying that autism rates are increasing because more people have it now and not because we are better are recognizing it??

> Primary sources:

> Maskelyne’s notes: https://doi.org/10.1098/rstl.1775.0050

> Hutton’s notes: https://doi.org/10.1098/rstl.1778.0034

> Cavendish’s notes on his own experiment: https://doi.org/10.1098/rstl.1798.0022

I got to reproduce Cavendish’s experiment when I was a student. Love that we can easily read the primary source today, archived and indexed by DOI.

> Using the stars as a reference, Maskelyne’s team found that the plumb lines on either side of the mountain pointed just 0.0152 degrees apart.

I'm really interested in knowing how they could get such a precise measurement (even accounting for errors), especially in the field (outdoor). There's no figure depicting the apparatus they used, I wonder how it looked like.

Sometimes, I just ponder at how ignorant I am. If I was tasked with the same assignment, I'd definitely fail and this was performed 250 ago!

Maybe something similar to a vernier caliper.

From Wikipedia:

> The first caliper with a secondary scale, which contributed extra precision, was invented in 1631 by the French mathematician Pierre Vernier (1580–1637).[1] Its use was described in detail in English in Navigatio Britannica (1750) by mathematician and historian John Barrow.[2] While calipers are the most typical use of vernier scales today, they were originally developed for angle-measuring instruments such as astronomical quadrants.

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

So it would have been a contemporaneous technique with that initial angle measurement, and the use of a Vernier scale for angular measurements would have itself been common.

They had a vertical 'Zenith Telescope' that looked at the same star from two locations. They measured how far from vertical it shifted in the magnified field of view. https://en.wikipedia.org/wiki/Ramsden_surveying_instruments#... Similar instrumends measured the wobble of the Earth's axis. https://en.wikipedia.org/wiki/International_Latitude_Service

I'd love to know what a sufficiently high precision plumb bob is like. Is it very tall? How on Earth does one calibrate it?

Broadly speaking, you want it as tall as possible, usually we're talking a few stories high, so 20m or so.

Without the attracting masses on either side you can set it swinging and measure the period, which lets you compute the restoring force in the wire.

I remember reading about this in Mason & Dixon. Mason, who worked at the Royal Observatory, was the one who identified this mountain as the best place for the experiment (and was asked to help with it but declined).

IIRC, it was partly the Mason Dixon line that inspired this experiment. They noticed syatematic errors in the line because their plumb bobs were deflected by gravitational pull from local terrain. At the time they speculated it was because of the Alleghenies, though it was probably more localized variations in gravity.

The precision they achieved with 18th century tools is remarkable. Measuring 0.0032 degrees of deflection without modern instruments, then getting within 20% of the correct answer.

I love stories where the constraint forces creative problem-solving. They couldn't measure gravity directly, so they found a mountain-sized workaround.

It's interesting that a device based on specifically constructed weights, at a scale to fit in a lab bench experiment (or at least a room) were capable of providing this much accuracy compared to a field experiment which used significantly larger masses, but was probably subject to many many more distorting qualities and estimation/rounding errors.

I can imagine that given enough motivation to chase down accuracy, they could have re-scaled the lead weight experiment to fit larger spaces, larger pendulums, assuming they could control for drafts, pigeons living in St Pauls Cathedral...

can GPS sats figure out the mass of the earth by being able to detect its gravitational distortion on their orbit?

or maybe that upcoming space laser interferometer (LISA) since it has to figure precisely how all mass is affecting its position?

I love the history of figuring the circumference of the earth, imagine getting it right within 2% in 240 BC

(then Columbus effing it up by 25%)

https://en.wikipedia.org/wiki/Earth%27s_circumference#Histor...

Scientists use pairs of satellites to map the small variations in Earth's gravitational field. It is possible to see groundwater depletion and changes in distribution of glacial ice, among many things.

https://en.wikipedia.org/wiki/GRACE_and_GRACE-FO

The primary challenge in determining the mass of Earth is actually measuring the gravitational constant, G, itself. Everything else involved is known at much higher precision. The product of G and Earth's mass is known to two parts in a billion, but the uncertainty in G is ~22 parts per million.

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

LISA is primarily sensitive to time-varying gravitational gradients on timescales of a fraction of a minute to a few hours and won't be terribly useful for determining the orbits of objects in our solar system. (but it is very, very cool).

How far does it deflect the Sun?

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