How much the Earth weighs and how a humble Scottish mountain helped discover it

In the summer of 1774, the British astronomer, Nevil Maskelyne, stood on the side of a Scottish mountain gazing at something deeper than sight. He was trying to find out how much the Earth weighed.

Schiehallion Mountain in Perthshire is what is often referred to as a ‘hump’. It goes from east to west, (its north and south slopes are very steep), with a complicated and steep west slope that marks the head of the mountain. And a much longer east slope that marks the tail, the path where most of the climbs are attempted.

When I had the first glimpse of the headland of Schiehallion, from the north shore of Loch Rannoch, I realized that it could pass like a volcano, because it was steep on the sides and tapered to a sharper point.

The necessary mountain

This was exactly the type of mountain that Maskelyne asked his fellow astronomer, Charles Mason, to look for in 1772, because it was just the right size to study.

Mason also needed to measure the volume of the mountain and predict its average density according to the type of rock that made it up.

With these figures, Maskelyne could then calculate the mass of the mountain. In turn, use these findings to determine the mass of the Earth more precisely, using the radius of the Earth to calculate its volume and have the best possible prediction of the density of our planet at that time. Knowing the mass of the earth would allow scientists to predict the relative masses of every known object in the universe, such as that of the Sun.

Mason traveled extensively until you find Schiehallion, the 1,083 meter mountain with the help of local experts. Although he was a distinguished surveyor, having returned to Britain after a land dispute in the United States by establishing the Mason-Dixon line (later to be known as a division line in the Civil War), the The idea of ​​spending more months in the Scottish highlands was not to his liking.

So Maskelyne chose to personally supervise Schiehallion Mountain which would later become in a famous attraction in the hiking world, with more than 20,000 hikers a year.

Climbing

At the beginning of the hike, in the Braes of Foss parking lot, visitors pass a memorial stone cluster, commemorating the work of Maskelyne and her team.

Shortly after my own ascent from Schiehallion, I saw my first hiking partner walking through a busy part, looking somewhat disheveled. The onset of autumn had turned the fern-strewn slopes into brown soil.

Above me, there were only clouds and presumably the rest of the mountain. However, with no large mountains nearby, the view from the lower slopes revealed central Scotland.

As a hiker approached, I realized I was exhausted. “I did,” he said. “My first Munro”, referring to the 282 mountains throughout Scotland whose heights were above 3,000 feet.

Looking at the parking lot, he was eager to get down the mountain. “I’m glad it’s over,” said the hiker.

Your shocked dog springer spaniel He came down next to him, and stopped to smell my boot.

Gravity never looks as challenging as when you are climbing uphill. In just a few minutes, I felt like a part of the mountain was drawing me.

Before long, the ground in front of me was all I could see. Plus a quagmire of stones and boil, which guided me until we fell weary like heavyweight boxers every time we stopped for water.

Weak gravity

Isaac Newton was the first to determine that everything has its own gravitational force. He also believed that gravity was too weak to measure below the planetary level. But without having a gauge of the Earth’s gravity, it was impossible to calculate its weight, because gravity is variable.

For example, if I measured my weight on Earth it would weigh more using the same scales on Mercury, a smaller planet with a lower gravitational force, even though my mass would be the same.

Maskelyne and other scientists realized that if you can get closer to the center of its mass, the gravity of a mountain could be strong enough to measure it. Which would mean they had to look for mountains with steep slopes. The funny thing was that if one mountain had a gravitational pull, so would the others, potentially distorting the measurements.

For that reason, Schiehallion, which was far from other similar mountains, was a perfect fit.

Maskelyne requested that observation stations be built on the steep north and south slopes of Schiehallion, from the points closest to the center of the mountain.

From there, a pendulum was hung, dragged towards the center of the Earth by our own planet, greater than gravitational force.

Crucially, Maskelyne needed to prove that the mountain’s gravity was pulling the pendulum’s tilt from its vertical position.

Maskelyne did this by tracking the transit of 43 different stars from each of the observatories to triangulate what is known as “true vertical” (the pendulum angle), suspended in a plain and affected only by the gravitational pull of the earth and nothing. plus.

With this experiment, he found that from each observatory in different parts of Schiehallion, there was a clear deflection of the pendulum from the true vertical towards the mountain.

The gravitational pull of the mountain was proven, but the work had only begun. The next thing was to study it to calculate what its volume was, a task that was in charge of the team of mathematician Charles Hutton.

Inclement weather is no stranger to Schiehallion. It took Hutton’s team two years to come up with a complete map of the mountain.

Lost in the Schiehallion

When I reached the ridge, the clouds descended, clouding everything around me. Soon the path disappeared to become a difficult rock field. Only the dark pile of stones showed the way.

A couple appeared out of the gloom to tell me that the top was not that far. Ten minutes later, the path he was going seemed to be going downhill. Worse still, the way down had disappeared and the new route it was showing me was up a slope in the steep north.

It was hard to tell if the rock he was on hung in the abyss or there were more stones. In this situation, I stopped to see my map and my compass.

When Hutton finished studying the mountain, he had a map with thousands of notations about the lengths and elevations.

In school we learned to compute the volume of the cube by multiplying its length, width, and weight. But in real life they don’t give us the precise lines. They give us curves, anomalies, hills and fissures. These were the results that Hutton’s measurements showed.

They were trying a bit of trickery in computing, and calculating the volume of the entire mountain seemed virtually impossible. But Hutton had the ingenious idea of ​​dividing the mountain grouping values ​​at similar altitudes.

Taking a pencil, he connected all the points of the altitudes, forming a series of imperfect rings. Without realizing it, he had just invented contour lines, which are among the most valuable elements on a map.

As I had suspected, I was lost. After the correct path descended one of the false tops of the mountain, I took the wrong one.

My map was showing contour lines right where I thought I was standing, which would mean it was going to be steep very soon. Luckily I found my way by thanking Hutton and the contour lines for saving me from not falling off the cliff.

Estimates of the weight of the Earth

In 1775, Maskelyne presented the final results to the Royal Society. We knew that their estimates were within 20% of the mass that the Earth is believed to have (5.97 x 10^24kg, in case you were wondering), correct compared to previous data.

In 2007, the Maskelyne and Hutton measurements they were used to obtain a close estimate of the mass of the Earth.

This scientific discovery is no different than climbing a cold, wet and cloudy mountainside. However, the feat of the 18th century cleared a lot of doubts to future astronomers and physicists, and to the thousands of hikers trying to reach the top of Schiehallion in tribute to the contribution of this geological wonder.

Thanks to those experiments, those ingenious contour lines will always give us an idea of ​​the shape of a mountain, even when our eyes cannot.