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# The numbers tell a DART story

## The Didymos, Dimorphos system is about 11 million kilometres away from us

DART, a man-made spacecraft, crashed on an asteroid last week. I realize there’s a lot going on in this world—a war, a yatra, election campaigns, economies tanking, take your pick—but even with all that, to me this asteroid-crash news tops them all. For more reasons than one.

I wrote about DART (Double Asteroid Redirection Test) in my last column here. In this column, let’s talk numbers—some of the numbers behind this mission. Space travel and research are full of eye-popping numbers, true, and DART’s story is no exception. It’s always worth trying to understand just what the numbers mean. For me, that’s one way I get a sense of the remarkable feats we humans are attempting. Then I can marvel at them.

First, the distance. Somewhere out there is this asteroid pair, Didymos and Dimorphos, and DART crashed into Dimorphos, by far the smaller of the two. This binary asteroid system is about 11 million —11,000,000—km from us. How far is that?

You’d have to travel between Mumbai and Delhi about 10,000 times to cover that many kilometres. That hints at a reality of space travel: distances on Earth are of no real help in making comparisons. So try this instead: you’d have to travel between Earth and our Moon about 35 times to rack up 11 million km.

Pretty far, right? Yet it’s important to retain some perspective. As large as that distance seems, it’s puny compared to other stretches in space. Want to travel to the Sun? It’s about 150 million km from Earth, or better than 13 times as far as DART voyaged to reach Dimorphos. Or you say you want to reach the nearest star that isn’t the Sun? That would be a certain Proxima Centauri, which is 4.25 light years away, or about 40 trillion km, or nearly 4 million times as far as Dimorphos.

That’s just the nearest star. It took DART ten months to reach Dimorphos. Zooming along at that pace, it would take over three million years to get to Proxima Centauri. Yet the simple truth of our universe is that other stars and galaxies are so much further still that they, in turn, make the distance to Proxima Centauri seem puny.

But if not the numbers themselves, you probably had some idea of their eye-popping scale. Maybe you’re even weary of regular gasping over celestial distances. So, consider some different ways to grasp them, and thus the challenges they present to the intrepid scientists who set out to observe celestial objects.

Come back to Didymos and Dimorphos. How do we know they are out there at all? Because we’ve actually seen them. Not with the naked eye—they are too tiny and too distant for that—but through powerful telescopes. Imagine a process like this. Point your telescope in a particular direction in the sky and take an image of all that’s in the field of view. You’ll see stars and galaxies and possibly some other objects. Repeat this some time later—maybe a few minutes, maybe an hour, whatever—and compare the two images. Most of what’s visible in the frame will not appear to have moved. Again, stars and galaxies are so distant that even though they are actually moving rapidly, a few minutes—maybe an hour, whatever—is too short a time for us on Earth to visibly detect that movement.

But every now and then, comparing the two images will indeed show you something that has moved. Typically, that will be a much nearer object—a planet, an asteroid—that scudded across the field of view. This is how we first located Didymos and Dimorphos. This is also how astronomers created a short and dramatic video of the moment DART barrelled into the asteroid. Through a telescope, they took several images of the part of the sky that Didymos was in, then strung them together. The effect is that we see Didymos as a spot of light streaking past 10 or 12 other luminous spots, and then it suddenly explodes. It becomes a bigger, brighter spot of light and a cloud of fainter dust rises from it like some fetching gossamer veil.

But wait, DART smashed into Dimorphos. So why do we see Didymos exploding? That’s another fascinating thing about this pair. The two rocks are so far away that it’s not just that we cannot see them with the naked eye. It’s also that we cannot distinguish them as separate rocks through even our most powerful telescopes. We know there are two only because the light from them dims every now and then, regularly. The obvious inference is that this isn’t one asteroid, but two. As it orbits larger Didymos, Dimorphos passes in front of Didymos, momentarily dimming the larger asteroid’s brightness.

And what about that cloud? The Sun’s so-called “radiation pressure"— a subject for another time—quickly shaped it into a comet-like tail. Days after the impact, two astronomers released a spectacular photograph of this plume of dust, trailing out behind Didymos. How long was this plume?

Well, if you could actually have seen it without a telescope, the angle it would make on your eye is about 3 arc-minutes, or about one-twentieth of a degree. That’s positively tiny. But given that the plume is about 11 million km away, simple trigonometry tells us that it is—hold your breath—10,000 km long, the distance between Mumbai and Sydney. Truly, that plume hints at the kind of impact DART made last week.

And finally, can we get a measure of that impact? Try this. We know DART weighed about 600 kg and was travelling at about 22,000 kmph at impact. Dimorphos weighs about 5 trillion kg. If it was stationary when DART hit—which it wasn’t—that transfer of momentum would send Dimorphos hurtling along at—hold your breath again—2.5 metres per hour. Yes, metres.

Not much to write home about? And yet, that kind of crash, that kind of transfer of momentum, might just save our planet some day. Ponder that awhile.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun.

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