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Earth’s mass was first determined by Henry Cavendish in 1798. Using a torsion balance to measure the tiny gravitational pull between lead spheres, he found Earth’s density, which yields its mass. The accepted figure today, about 5.972 × 1024 kg (roughly 6 sextillion metric tons), is within about 1% of his result.
That sounds like a pretty big question, so let’s start back at the beginning. It all began with Newton and his Principia. Well, perhaps a bit earlier, as many ancient scholars had tried their hand at measuring the mass of the Earth (I’m looking at you, Eratosthenes), but no one could get it right, because no one understood the density of the entire planet. When you think about it, we’re tiny creatures living on a huge island in a sea of nothingness, so how can we expect to understand anything about the universe, let alone the mass of our entire home planet?
Newton’s Plight
The route to that answer began with the neat little relationship Newton laid out in the Principia, which we now write as:
F = GmM/r2
where F is the gravitational force,
G is the gravitational constant,
M is the mass of the Earth,
r is the radius of the Earth, and
m is the mass of another object
The only problem, Newton realized, was that he didn’t know the mass of the Earth, nor the gravitational constant. (In fact, Newton himself only ever described gravity as a proportionality; the constant G that fills in the gap was pinned down long after his death.) Essentially, he had the most elegant relationship of his age, but couldn’t fill in its blanks. He did make one shrewd guess, though: he reckoned the Earth was around five or six times as dense as water, which turned out to be remarkably close to the truth.
Maskelyne And Hutton: Mountain-Weighers, Pvt. Ltd
This scientific frustration led to his conclusion that the key to calculating those two variables would be measuring the gravitational deflection of an object being exposed to a large enough mass, such as a mountain, along with the mass of the Earth. Of course, that would mean that a scientist would have to know the mass of a mountain. Fortunately, the Astronomer Royal Nevil Maskelyne was up to that task. With the help of mathematician Charles Hutton, Maskelyne set out in 1774 to weigh Schiehallion, a conveniently symmetrical mountain in the Scottish Highlands. By measuring how much the mountain’s mass tugged a hanging plumb line away from true vertical, then estimating the mountain’s own mass, they could work out how dense the Earth must be.
Extrapolating from all those tedious measurements, Hutton reported in 1778 that the Earth was about 4.5 times as dense as water, which fixes its mass at roughly 5 sextillion tons. They even invented contour lines along the way! It was a genuine first: nobody had ever put a number on the planet’s heft before. The catch was the accuracy. That density estimate runs about 20% low compared to the modern value of 5.51 times water, mostly because they had to guess at the rock buried inside the mountain. A solid first attempt, then, with contour lines thrown in as a bonus for geologists.
Maskelyne and Hutton could not convince 18th century scientists of their data, particularly one scientist named John Michell, who was highly skeptical of the data. He began making his own device to measure the mass of the Earth. Unfortunately, he died before he could use any of his equipment. Nevertheless, Michell ensured that his ingenious contraption was passed on to a brilliant, but highly eccentric, scientist named Henry Cavendish.
The Adventures Of Henry Cavendish
Cavendish was a very busy man. He had discovered or anticipated a huge range of concepts, including the conservation of energy, Ohm’s Law, Dalton’s Law of Partial Pressures, Richter’s Law of Reciprocal Proportions, and Charles’s Law of Gases, just to name a few. Sadly, Cavendish was too ‘shy’ to ever tell the world of his achievements. Born into a rich family, the man was deathly afraid of human contact. In fact, he used to run away screaming from unannounced fans at his doorstep, mumble a few words only to those who consistently avoided eye contact, and corresponded with his butler through letters. Cavendish actually turned his huge estate into a controlled laboratory where he could carry out his experiments in peace. These peaceful experiments included subjecting himself to increasingly strong jolts of electric current while diligently noting down the levels of agony he experienced.
He did publish the results of one experiment, though.
One fine day, an apparatus gathering dust in the corner of his laboratory caught Cavendish’s eye. Remembering it as being Michell’s, he pulled it out of obscurity and began devoting a great deal of attention to it. Beneath all the weights and counter-weights, pendulums and torsion wires, the apparatus suspended two small lead balls (about 0.73 kg, or 1.6 lb, each) from a rod hung on a thin wire, with a 158 kg (348 lb) lead sphere positioned near each one. The idea was to measure the faint gravitational tug of the big spheres on the small ones. From that tiny twist you can work out the average density of the Earth, and the gravitational constant that had eluded brilliant men for generations. With this device, it was thought, we could finally weigh the planet.
Positioning himself in the adjoining room and using a telescope to peep inside, he carefully observed seventeen delicate measurements over the course of a year. The end result? A profound leap in our understanding of the world. He found the Earth to be about 5.45 times as dense as water, which puts its mass at roughly 6 sextillion (6 billion trillion) tons.
Today we have far more sophisticated ways to measure the same quantity, and the accepted figure is 5.972 × 1024 kg (about 5.97 sextillion metric tons, or 6.6 sextillion US tons). Yet that modern number sits within roughly 1% of Cavendish’s groundbreaking result. Two centuries on, we have barely improved on his measurement. Cavendish was truly a legend, even if he was a bit of an oddball!
