Rick Robinson

Aug 28th 2020

How Much Does the Universe Weigh?


In 1763, a pair of surveyors named Mason and Dixon were hired to settle a boundary dispute between two territories that were then British colonies, Maryland and Pennsylvania. The geographical line they drew, the Mason-Dixon line, would go on to become the dividing line between the North and South of the United States.

But, as the American Physical Society (APS) reports, the survey effort by Mason and Dixon had another intriguing result. It inspired a search for the answer to the question, “How much does the universe weigh?”

Newton’s Apple

Long before Mason and Dixon set to work, Sir Isaac Newton had demonstrated that gravity is a universal force, acting in the same way on both everyday objects and celestial bodies. Gravity not only caused an apple to fall from a tree (instead of just floating away), but also caused the moon to orbit the Earth instead of flying off through space.

Until Newton, early scientists weren’t sure that the question, “How much does the universe weigh?” had any answer at all. Newton showed that it could be answered, at least in principle. But actually working out the answer was another matter.

Enter Henry Cavendish, a British physicist and chemist. Famously eccentric and notoriously shy, Cavendish was in his early 30s when Mason and Dixon did their survey work, and he saw a subtle complication. The region they were surveying included the Allegheny Mountains. According to Newton’s law of universal gravitation, the enormous weight of the mountains should affect their survey instruments, perhaps throwing off their measurements.

This complication had no effect on the Mason-Dixon survey, which came out “good enough for government work.” But the problem continued to irk Henry Cavendish. The issue, he realized, wasn’t just how much mountains weighed, but how much the Earth itself weighed.

Weight or Mass?

Pause here for an important distinction. In everyday life here on Earth we think of weight and mass as the same thing. But as Wired points out, in physics they’re quite different things. Mass is an inherent property of all material stuff, while weight is the effect that a gravitational field has on mass. If you take a ride to the International Space Station, once in orbit you’ll be effectively weightless, able to float around, but your mass will be the same as it was on the ground.

When we ask how much the universe weighs, we are really asking what its mass is. But for convenience, we talk about “weighing” the universe, without worrying about how you would put it on a scale, even if you had one big enough.

Weighing the Earth

The challenge of weighing the Earth continued to nag at Cavendish for decades. In principle, Newton’s laws provided a solution. If he could determine the gravitational pull of, say, a 100-pound weight, he could compare it to the gravitational pull of the Earth, and some complicated but straightforward math would give him the weight (or, strictly speaking, the mass) of the Earth.

The problem is that gravity is a remarkably weak force. A toy store magnet can lift an iron nail, overcoming Earth’s gravity. The gravitational pull of any easily weighed object is so slight as to be exceedingly difficult to measure even with a precision apparatus. Certainly no apparatus available in the 18th century was up to the job.

So, in 1797, Cavendish set out to build his own ultra-precise measuring apparatus, called a torsion balance. In essence, this consisted of two small weights, set at each end of a horizontal bar suspended from a string at the midpoint, with two larger weights nearby. Left to rotate freely, the bar would rotate under the gravitational influence of the larger weights.

How Much Does the Universe Weigh?

After months of measurements, Cavendish was able to determine the gravitational forces acting within his torsion balance — and, by comparison to Earth’s gravity, he was then able to calculate how much the Earth must weigh, and, from Earth’s known size, the average density that must correspond to that weight. The Earth, he announced, was 5.48 times denser (and heavier) than an equal volume of water.

Modern scientists have refined that figure to 5.52 times denser than water, meaning that Cavendish was off by less than 1%.

From weighing the Earth to weighing the universe is a pretty big step, but Cavendish did the heaviest lifting. Once the weight (or mass) of the Earth is known, measurements of orbital distances and velocities provide a framework for calculating the mass of other celestial bodies. Or even estimating the combined mass of all celestial objects, thus answering how much the universe weighs.

Pretty nifty, huh? But in recent decades this has led to one result that might have startled even Henry Cavendish. When cosmologists use the gravitational method to determine how much the universe weighs, the answer comes out much higher than the estimated combined mass of everything we can see in the universe — all its galaxies, large and small, with their stars, gas and dust, and various bits and pieces.

Most of the mass — and therefore weight! — in the universe turns out to be in a form that we cannot see or detect at all, except by its gravitation. This is the mysterious dark matter you’ve probably heard about. What it is, no one yet knows.

Between them, Sir Isaac Newton and Henry Cavendish showed that the dark matter must be out there. But we’re still waiting for a new experimental apparatus — and a new scientist — to show us exactly what it is.