How astronomers weigh the universe (and everything in it)

With a long enough lever and a place to stand, Archimedes knew he could move the Earth. Similarly, weighing massive objects like planets and stars on a balance scale as one might with a pound of salmon is conceivable only in theory, but a quick search of Wikipedia reveals a wealth of such unfathomable information: The eight planets in our solar system each weigh between 10^24 and 10^27 kilograms (that means a number from one to nine, dealer’s choice, with between 24 and 27 zeros after it). The sun hits 10^30. Our galaxy weighs in at around 10^42 kilograms and the entire visible universe reaches something like 10^53.

You can try to convert those figures to something a little more familiar, such as the weight of a blue whale, by subtracting 5 from any of those exponents. But the numbers are unwaveringly huge no matter how you try to wrap your brain around them. Changing from kilograms to pounds doesn’t make much of an appreciable distance at these scales, either. When it comes to imagining such colossal masses, the human mind is completely out of its depth.

Yet physicists and astronomers somehow continue to refine their measurements of the seemingly unmeasurable and definitely inconceivable. Earlier this month a team of researchers published a new, not-yet-peer reviewed, estimate of the mass of the Milky Way galaxy on the pre-print server arXiv, including both the disk of twinkling stars and an invisible sphere of dark matter that presumably surrounds it. They got a mass equivalent to 890 billion suns (most of which is dark matter, with just 60 billion sun masses representing all the stars and gas that we can see), give or take 100 billion suns. Such figures may seem inscrutable, but you can trace almost all of them back to one interaction—the mutual dance of objects pulling on each other gravitationally.

But first, a note about weight and mass—intimately related but technically distinct qualities. Officially, “weight” describes the gravitational force acting on an object, so anything from a blue whale to a galaxy “weighs” nothing while floating in empty space. What researchers are really after is mass—the unvarying amount of stuff in an object, or equivalently, how much oomph it takes to get the thing moving. Ultimately though, whether one relies on a bathroom scale or astronomical observations, “weighing” an object usually comes down to measuring the gravitational force between it and a massive partner.

The Earth

The first really big object inquisitive minds attempted to weigh was the thing beneath our feet. Early attempts went the route of guessing the planet’s size and density and calculating its mass from there. By the 1600s, estimates of Earth’s diameter—and therefore its volume—weren’t terrible. But no one was sure of the density piece of the puzzle—whether the planet was made of water or rock. Everyone was wrong, however, because the planet is actually made up mostly of metal, which is denser than both.

To figure out that density (and therefore the mass of the Earth), British scientist Henry Cavendish measured the overall strength of gravity in 1798. Isaac Newton had shown in the 1600s that all objects pull on all other objects, and those with more mass pull harder. Cavendish hung small metal balls from a wire, placed heavier spheres nearby, and watched the wire twist as the spheres attracted each other. In this horizontal twisting he was able to determine the intensity of the gravitational force in general. And, knowing how hard the Earth’s mass tugged downward on his spheres (that is, their weights), he could use Newton’s equations to peg the Earth’s composition at a suspiciously metal-like 5.42 times the density of water. Modern physicists have found that he was off by just seven-tenths of one percent.

The Sun, planets, and more

One definition of mass is related to how strongly two objects tug on each other gravitationally. So once Newton and Cavendish had worked out the strength of gravity in general and the mass of the Earth in particular, scientists had the tools they needed to go forth and weigh much of the rest of the universe.

The sun pulls on the Earth just hard enough to swing it around once every 365 days, implying a certain force, and therefore mass. Similarly, by considering the sun as the prime partner of various heavenly body pairings, researchers could calculate the heft of the rest of the planets based on the length of their years. Watching how moons orbited planets provided another check, as well as a way to weigh the moons. Asteroid mass estimation remains something of a dark art based on guessing plausible densities and sizes. But those space rocks that have hosted a spacecraft couldn’t help giving the probe (with known mass) a tug, revealing their own mass in the process.

Galaxies

Just as researchers can infer the mass of the Earth by watching how hard it drags down objects on or near its surface, or the mass of the sun by watching how quickly planets orbit around it, they can read the galaxy’s mass in the motion of the objects that circle it.

It was these trajectories of orbiting stars that first flagged the presence of dark matter in the 1970s. In our solar system, Mercury zips around nearly nine times faster than Neptune does because it lies much closer to the source of the vast majority of our solar system’s mass—the sun, Heather Goss explains in Air and Space Magazine. Researchers expected that a similar pattern should play out in other galaxies, far-out stars tracing slower orbits than close-in ones.

This relationship holds close to the center of most galaxies, but then stops. After a point, no matter how far out they looked, astronomers discovered that stars orbited at surprisingly similar speeds. Their confuddling motions imply that a second, invisible source of mass is also pulling on them. (A theory known as Modified Newtonian Dynamics alternatively suggests that Newton and Cavendish’s results falter over large scales, but it struggles to explain other cosmological results.)

Regardless, astronomers weigh our galaxy through similar analyses of local stars and groups of stars. The recent research, which extends another estimate from earlier this year, harnesses a database of nearly 3,000 “tracer” objects, such as stars, star clusters, and gas clouds, that orbit the center of the Milky Way. Using the motion of these tracers, researchers calculated how much mass, visible and dark, the galaxy contains.

The Universe

The cosmos, inconveniently, lacks visible orbiting partners. Here, the standard gravitational scale breaks down.

The absolute size of the universe is unknown, and is constantly expanding, so its mass is similarly undefined. Astronomers can define the volume of the observable universe, however, based on the distance light has been able to travel between the Big Bang and present day.

But the density of existence, averaged out over all of the cosmos’s planets, stars, galaxies, and voids, has proved challenging to measure. One estimate came from the Wilkinson Microwave Anisotropy Probe (WMAP), a satellite that measured warm spots and cool spots in the universe’s earliest light from 2001 to 2010. These patches are the remnants of a power struggle from when a dense soup of matter and light filled the young universe. Gravity drew particles together while light pushed them apart, creating sloshing ripples that grew with the expanding cosmos until WMAP picked them up. From the patterns in these variations today, cosmologists can calculate the age and composition of the universe, including its overall density: about six protons worth of stuff per cubic meter.

That number technically represents an energy density (since matter and energy can be converted using Einstein’s famous equation), so it includes visible matter, dark matter, and the unknown dark energy driving the expansion of the universe. WMAP and its successor, the Planck satellite, estimated that by this metric the universe is about 5 percent visible matter, 27 percent dark matter, and 68 percent dark energy.

In this way cosmologists can, much as Cavendish did in 1798, combine their estimates of their target’s volume and density to estimate the universe’s overall mass as something like 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 kilograms. That’s roughly 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 blue whales, or maybe 100 billion Milky Way galaxies, but who’s really counting.