# DARTing to A Conclusion

The park’s trees are in brilliant Fall colors, the geese in the lake dabble about as I walk past but then, “Hey Moire, I gotta question!”

“Good morning, Mr Feder. What can I do for you?”

“NASA’s DART mission to crash into Diddy’s mos’ asteroid—”

“The asteroid’s name is Didymos, Mr Feder, and DART was programmed to crash into its moon Dimorphos, not into the asteroid itself.”

“Whatever. How’d they know it was gonna hit the sunny side so we could see it? If it hits in the dark, nobody knows what happened. They sent that rocket up nearly a year ago, right? How’d they time that launch just right? Besides, I thought we had Newton’s Laws of Motion and Gravity to figure orbits and forces. Why this big‑dollar experiment to see if a rocket shot would move the thing? Will it hit us?”

“You’re in good form today, Mr Feder.” <unholstering Old Reliable> “Let me pull some facts for you. Ah, Didymos’ distance from the Sun ranges between 1.01 and 2.27 astronomical units. Earth’s at 1.00 AU or 93 million miles, which means that the asteroid’s orbit is 930 000 miles farther out than ours, four times our distance to the Moon. That’s just orbits; Earth is practically always somewhere else than directly under Didymos’ point of closest approach. Mm… also, DART flew outward from Earth’s orbit so if the impact has any effect on the Didymos‑Dimorphos system it’ll be to push things even farther away from the Sun and us. No, I’m not scared, are you?”

“Who me? I’m from Jersey; scare is normal so we just shrug it off. So why the experiment? Newton’s not good enough?”

“Newton’s just fine, but collisions are more complicated than people think. Well, people who’ve never played pool.”

“That’s our national sport in Jersey.”

“Oh, right, so you already know about one variable we can’t be sure of. When the incoming vector doesn’t go through the target’s center of mass it exerts torque on the target.”

“We call that ‘puttin’ English on it.'”

“Same thing. If the collision is off‑center some of the incoming projectile’s linear momentum becomes angular momentum in the target object. On a pool table a simple Newtonian model can’t account for frictional torque between spinning balls and the table. The balls don’t go where the model predicts. There’s negligible friction in space, you know, but spin from an off‑center impact would still waste linear momentum and reduce the effect of DART’s impact. But there’s another, bigger variable that we didn’t think much about before we actually touched down on a couple of asteroids.”

“And that is…?”

“Texture. We’re used to thinking of an asteroid as just a solid lump of rock. It was a surprise when Ryugu and Bennu turned out to be loose collections of rocks, pebbles and dust all held together by stickiness and not much gravity. You hit that and surface things just scatter. There’s little effect on the rest of the mass. Until we do the experiment on a particular object we just don’t know whether we’d be able to steer it away from an Earth‑bound orbit.”

“Okay, but what about the sunny‑side thing?”

“Time for more facts.” <tapping on Old Reliable> “Basically, you’re asking what are the odds the moonlet is in eclipse when DART arrives on the scene. Suppose its orbit is in the plane of the ecliptic. Says here Dimorphos’ orbital radius is 1190 meters, which means its orbit is basically a circle 3740 meters long. The thing is approximately a cylinder 200 meters long and 150 meters in diameter. Say the cylinder is pointed along the direction of travel. It occupies (200m/3740m)=5% of its orbit, so there’s a 5% chance it’s dark, 95% chance it’s sunlit.”

“The real odds are even better. The asteroid casts a shadow about 800 meters across. Says here the orbital plane is inclined 169° to the ecliptic so the moonlet cycles up and down. At that tilt and 1190 meters from Didymos, 200‑meter Dimorphos dodges the shadow almost completely. No eclipses. DART’s mission ends in sunlight.”

~~ Rich Olcott

• Thanks to my brother Ken, who asked the question but more nicely.

## 2 thoughts on “DARTing to A Conclusion”

1. Ken Olcott

Watching the impact, I was awed by the the high-contrast detail, imagining a much flatter view from a straight-on sun, and also wondered what the chances were of the impact happening in Didymos’ umbra. So I wondered if NASA had timed the launch to impact at an optimum position in both Didymos’ and Dimorphos’ orbits to capture such detail with the best sun angle. Then again, with so much rubble, perhaps the light and shadow details were inevitable. ( And I like the NASA folded airplane too)

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2. So DART’s impact didn’t result in a cone of ejecta, which you’d expect from hitting a solid rock, or an expanding sphere, which you’d expect from a uniform rubble pile. Instead we got rays of stuff coming out (see Hubble and Webb images at https://www.nasa.gov/feature/goddard/2022/webb-hubble-capture-detailed-views-of-dart-impact). Prediction — yes, it’s a rubble pile, but some of the component rocks are really big. They channeled the outbound momentum to push smaller particles into preferred directions. You read it here first.

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