Tag: DART mission

Hiding Among The Hill Spheres

On By rolcottIn Astronomy, Physics: Black Holes and Relativity, Space Travel, UncategorizedLeave a comment

Bright Spring sunlight wakes me earlier than I’d like. I get to the office before I need to, but there’s Jeremy waiting at the door. “Morning, Jeremy. What gets you here so soon after dawn?”

“Good morning, Mr Moire. I didn’t sleep well last night, still thinking about that micro black hole. Okay, I know now that terrorists or military or corporate types couldn’t bring it near Earth, but maybe it comes by itself. What if it’s one of those asteroids with a weird orbit that intersects Earth’s orbit? Could we even see it coming? Aren’t we still in danger of all those tides and quakes and maybe it’d hollow out the Earth? How would the planetary defense people handle it?”

“For so early in the day you’re in fine form, Jeremy. Let’s take your barrage one topic at a time, starting with the bad news. We know this particular object would radiate very weakly and in the far infrared, which is already a challenge to detect. It’s only two micrometers wide. If it were to cross the Moon’s orbit, its image then would be about a nanoarcsecond across. Our astrometers are proud to resolve two white‑light images a few milliarcseconds apart using a 30‑meter telescope. Resolution in the far‑IR would be about 200 times worse. So, we couldn’t see it at a useful distance. But the bad news gets worse.”

“How could it get worse?”

“Suppose we could detect the beast. What would we do about it? Planetary defense people have proposed lots of strategies against a marauding asteroid — catch it in a big net, pilot it away with rocket engines mounted on the surface, even blast it with A‑bombs or H‑bombs. Black holes aren’t solid so none of those would work. The DART mission tried using kinetic energy, whacking an asteroid’s moonlet to divert the moonlet‑asteroid system. It worked better than anyone expected it to, but only because the moonlet was a rubble pile that broke up easily. The material it threw away acted as reaction mass for a poorly controlled rubble rocket. Black holes don’t break up.”

“You’re not making getting to sleep any easier for me.”

“Understood. Here’s the good news — the odds of us encountering anything like that are gazillions‑to‑one against. Consider the probabilities. If your beast exists I don’t think it would be an asteroid or even from the Kuiper Belt. Something as exotic as a primordial black hole or a mostly‑evaporated stellar black hole couldn’t have been part of the Solar System’s initial dust cloud, therefore it wouldn’t have been gathered into the Solar System’s ecliptic plane. It could have been part of the Oort cloud debris or maybe even flown in on a hyperbolic orbit from far, far away like ‘Oumuamua did. Its orbit could be along any of an infinite number of orientations away from Earth’s orbit. But it gets better.”

“I’ll take all the improvement you can give me.”

“Its orbital period is probably thousands of years long or never.”

“What difference does that make?”

“You’ve got to be in the right place at the right time to collide. Earth is 4.5 billion years old. Something with a 100‑year orbit would have had millions of chances to pass through a spot we happen to occupy. An outsider like ‘Oumuamua would have only one. We can even figure odds on that. It’s like a horseshoe game where close enough is good enough. The object doesn’t have to hit Earth right off, it only has to pierce our Hill Sphere.”

“Hill Sphere?”

“A Hill Sphere is a mathematical abstract like an Event Horizon. Inside a planet’s Sphere any nearby object feels a greater attraction to the planet than to its star. Velocities permitting, a collision may ensue. The Sphere’s radius depends only on the average planet–star distance and the planet and star masses. Earth’s Hill Sphere radius is 1.5 million kilometers. Visualize Hill Spheres crowded all along Earth’s orbit. If the interloper traverses any Sphere other than the one we’re in, we survive. It has 1 chance out of 471 . Multiply 471 by 100 spheres sunward and an infinity outward. We’ve got a guaranteed win.”

“I’ll sleep better tonight.”

~~ Rich Olcott

DARTing to A Conclusion

On By rolcottIn Astronomy, Space Travel, Uncategorized2 Comments

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.”

“Not a bad bet.”

“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.