In my last column, I mentioned something we all did as kids: tie a stone to the end of a piece of string and whirl it around our heads. In that column, I used that memory as an analogy to a spacecraft orbiting the Earth. Our planet’s gravity is like the string, and the spacecraft is like the stone. So even without an actual string, in both cases it is really the same phenomenon.
That reminder, because of a new astronomical result—something revealing about our starry surroundings—and the same reasoning lead us there: scientists have weighed our galaxy, the Milky Way. Now clearly I don’t mean they put the thing on some gigantic weighing scale and read some numbers off the display. What they did do was actually far more interesting, using data from telescopes and some clever inferences. We’ve had estimates of the galaxy’s mass before, but this one is much more accurate.
So how would you do such an exercise? After all, apart from being unimaginably vast, it’s not even as if the Milky Way is one great solid object that you have to weigh. Instead, it is made up of billions of individual stars, of which our own Sun is a typical example. At least some of those stars have planets orbiting them, like our own Sun does. At least some of those planets have moons orbiting them, like our own Earth does. Then there are asteroids and comets, and sundry other objects of varying size. And even after accounting for all those, astronomers believe they are still missing 90% or more of the galaxy’s mass, something I’ll return to later. How in the world, how in the Milky Way, do you find the weight of something like this?
To start answering that, let me remind you again of your stone-whirling days. Let’s say the string you’re doing the whirling with is short, perhaps a foot long. I’m sure you’re even imagining whirling it right now, the stone making tight circles around your head with ease. Go faster, go slower, you can do it without a thought.
Without the string, this is a good model for how one object in space orbits another. And while there is indeed no string connecting them, something else connects them just as effectively as a string would—gravity. The way you pull on the string is a good analogy for the way gravitational force acts between the two objects in space. Because the force you exert acts on the stone, it keeps whirling instead of falling to the ground. In the same way, because the gravitational force of the Earth acts on the Moon, the Moon orbits the Earth.
Still with me? Well, now imagine lengthening the string to two feet, say. The stone immediately slows down, so much that you have to whirl harder to keep it going at the same speed. In fact, the longer the string, the more effort you have to put into your whirling—that is, the greater the force that you exert on the stone. If you keep lengthening the string, there will eventually come a point where you won’t be able to keep up the whirling, no matter how hard you try. That is, you are simply not strong enough to get the stone to rotate around your head. Again analogously, if the Moon reaches a point where the Earth’s gravity is not strong enough to hold it, it will drift off aimlessly into space.
But at the point when you can no longer whirl the stone, someone stronger than you would be able to keep it going. Similarly, at the point where the Moon starts drifting away because Earth’s gravity is too weak, a more massive planet than our Earth, with its stronger gravity, would be able to keep the Moon orbiting. This suggests that the length of the string, the weight of the stone and the speed at which it rotates are together a measure of how strong you are; that the distance of an orbiting object, its mass and its speed are together, similarly, a measure of the strength of the gravitational force that’s acting on it.
And the strength of gravity tells us how massive the object exerting that gravity is. The more massive an object is, the farther the reach of its gravity and the faster other, smaller objects will orbit it.
Forgive the involved explanation and analogy. But if you’ve followed it so far, we have all we need, at least in theory, to weigh the Milky Way.
We know our galaxy is made up of some 100 billion stars, all rotating around its centre. If we pick one star near the edge of the galaxy, we can treat its orbit as if it was governed by the gravity of an object at the centre that weighs as much as the entire galaxy. So if we know the star’s speed through space and its distance from the centre of the Milky Way, we can measure the mass of the Milky Way.
That’s essentially what Laura Watkins of the European Southern Observatory in Germany and her colleagues did recently, publishing their findings in early February. Only, instead of a single star, they tracked several globular clusters. These are symmetrical collections of stars—sometimes hundreds of thousands in a near-spherical shape—that are generally found in the outer reaches (the “halo") of galaxies. Their location far from the centre is the reason globular clusters “are considered the best tracers astronomers use to measure the mass of our galaxy", according to Tony Sohn, one of Watkins’ colleagues.
The Milky Way is known to have about 150 globular clusters; other galaxies have even more. Combining observations from the Gaia space observatory and the Hubble Space Telescope, these astronomers were able to use data from 46 of them in our galaxy; tracking this many clusters instead of just one star makes for more accurate and credible findings. Now of course, it’s not as if this is the first time we’ve examined globular clusters. But previous observations showed their motion towards or away from us—that is, following our line of sight to them. But using Gaia and Hubble data, Watkins and her team measured the speed of their sideways motion, across our line of sight. Put both kinds of motion together in 3D—not an easy task, but that was what Watkins and her colleagues attempted—and we get a reasonable simulation of the motion of each cluster. In particular, we get its velocity as it sails through space, orbiting the Milky Way.
So for example, the team looked at a cluster about 65,000 light years from the centre of the Milky Way. Most of the galaxy lies within a radius of about 50,000 light years—our solar system is about 25,000 light years out— so this cluster is certainly in that “halo" I mentioned. Its velocity turned out to be about 200km per second. Combining this kind of data from all 46 clusters, the team arrived at a figure for the mass of the Milky Way: about 1.5 trillion times the mass of the Sun.
There’s plenty to think over here. First, this is a much more accurate figure than earlier estimates, which ranged from 500 billion to three trillion times the mass of the Sun. Second, this suggests that the Milky Way is larger than we thought, and in fact is one of the universe’s larger galaxies. Third, this has some bearing on a catastrophe that’s coming up: the collision between the Milky Way and our nearest galactic neighbour, Andromeda. We always thought Andromeda was the larger of the two, but now it looks like the Milky Way is larger and weightier. The collision will happen about four billion years from now, so set those alarm clocks and alert the kids.
But this new measurement also underlines something astronomers have known for a long time. Remember the Milky Way has about 100 billion stars. If we assume they are all about the size of the Sun, the Milky Way should weigh about 100 billion times the mass of the Sun. But it turns out to be about 15 times heavier than that. What accounts for that difference?
Two words: dark matter. Calculations like this and plenty more data speak of something startling. About 90% of the mass of the Milky Way, and indeed of the entire universe, is actually invisible to us.
Especially on an inky night when you’re far from your city, when you look up and the night is awash in stars, when you see the Milky Way float above you like a shroud of gossamer, when you maybe even catch some meteors shooting across the sky—yes, especially on a magical night like that, remember that what you can’t see is far more than what you can.
Let that thought whirl its way through your head. And to complete the picture, pick up the nearest stone, tie it to a string and whirl it around your head.
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His latest book is Jukebox Mathemagic: Always One More Dance. His Twitter handle is @DeathEndsFun