# sevenperforce

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2. ## totm oct 2022 DART: Double Asteroid Redirection Test

Someone on Twitter overlaid all the images to get the maximum possible resolution, and so I used that to put together an animation of the last five seconds prior to impact in real-time at the blazing speed of ten frames per second (which is at least enough to get a sense of motion). I think I'll do an animation of the full impact but double the speed every five seconds, so it's 1x speed from T-5 to T-0, 2x speed from T-15 to T-5, 4x speed from T-35 to T-15, 8x speed from T-75 to T-35, and so forth. That should be nice for viewing.
3. ## totm oct 2022 DART: Double Asteroid Redirection Test

It's accurate in the sense of a head-on collision. However, it is flipped relative to ecliptic north. This should be readily apparent because Dimorphos orbits Didymos retrograde to the solar orbit. I'm not qualified to duel numbers with you - but this strikes me as wrong. I googled a bit and I wonder if your number is classic newtonian? "If the impactor has pushed a mass equal to its own mass at this speed, its whole momentum has been transferred to the mass in front of it and the impactor will be stopped. For a cylindrical impactor, by the time it stops, it will have penetrated to a depth that is equal to its own length times its relative density with respect to the target material. This approach is only valid for a narrow range of velocities less than the speed of sound within the target or impactor material. If the impact velocity is greater than the speed of sound within the target or impactor material, impact shock causes the material fracture, and a higher velocities to behave like a gas, causing rapid ejection of target and impactor material and the formation of a crater. The depth of the crater depends on the material properties of impactor and target, as well as the velocity of impact. Typically, greater impact velocity means greater crater depth. You're absolutely correct, but that's why I characterized it as a point impactor. For a hypervelocity impact like this one, the crater depth is not a function of penetration depth, but a function of the energy delivered to the substrate via the impact shock. Basically you can ignore the size and physical characteristics of the impactor and just treat it as an energy source emanating from a single point. To your ballistic examples from earlier...imagine firing a plastic BB at ballistic gel at such terrific speeds that the BB completely disintegrates on impact. Ordinarily, temporary cavity formation is approximately cylindrical because it is formed by the conical shockwave coming off the bullet as it penetrates the gel. Here, however, there is no penetration, and so the cavity formation is hemispheric from the point of impact. It makes sense, though. Sure, there's a massive amount of energy compared to the gravitational binding energy of the moon, but there's no way to transfer that energy uniformly throughout the moon. You could almost liken it to the Liedenfrost effect.
4. ## totm oct 2022 DART: Double Asteroid Redirection Test

But the system is near periapsis of a more elliptical orbit, so it could still be going faster than Earth. I took exception to this earlier, but having reviewed it in more detail, I was completely wrong. The velocity of Didymos at periapsis is 34.8 km/s, significantly faster than Earth, and DART was not "catching up" to it; rather, it was catching up to DART. In other words, DART's solar-orbital velocity at impact was lower than Didymos's, not higher. This also explains why the view on approach looked the way it did. Per NASA, the images shown are mirrored on the x-axis (due to the design of DRACO's camera) and show the ecliptic north toward the bottom. The actual approach image, if corrected for how we would intuit it should be viewed, would look like this: Dimorphos has a retrograde orbit, so since DART was coming in "against" the orbital direction, it needed to impact Dimorphos while it was on the sunward side of its orbit. This also explains why the right-hand side is illuminated.
5. ## totm oct 2022 DART: Double Asteroid Redirection Test

I don't think over-penetration is even remotely feasible. The density of rock/rubble is several times greater than the density of the spacecraft so DART wouldn't have been able to punch more than a meter or so deep. But it seems that the energy clearly wasn't transferred. Perhaps the answer is that >99.99% of the kinetic energy was converted into thermal energy at impact due to the high collision speed. DART is about 1.3 meters wide and would have penetrated less than a meter, so we can take it as a point impactor. You can approximate the energy required to completely crush a volume of rock to powder if you know the compressive strength of the rock, since compressive strength is given in units of pressure (pressure units, force per unit area, are equivalent to energy per unit volume). Brittle material silicate rock usually has a compressive strength on the order of 140 MPa. Do a bit of math and you find that the entire kinetic energy of DART would be sufficient to obliterate about 89 cubic meters of rock . . . a crater about 3.5 meters deep. Of course, it's a rubble pile, not a solid homogenous silicate rock, so that approximation will only get you so far. But it's potentially a good indicator of how quickly kinetic energy can be dissipated.
6. ## totm oct 2022 DART: Double Asteroid Redirection Test

But with three orders of magnitude at play, even if only 0.11% of the kinetic energy actually ended up pointed into the rubble pile, you've still got full delivery of the gravitational binding energy. My guess is that it would penetrate roughly nine times its length, since it's about 9 times as dense as a rubble pile asteroid.
7. ## totm oct 2022 DART: Double Asteroid Redirection Test

I feel like that's more likely when you are using a projectile which is many times more dense than the target, like lead. Per Newton's approximately for kinetic impactor penetration depth, the penetration of an impactor is independent of velocity and is a function of the impactor length and the relative densities of the impactor and the target. DART's physical dimensions (box only, not including solar panels or other protrusions) are 1.2m * 1.3m * 1.3 m, giving it a total volume of 1.87 cubic meters and thus a density of approximately 300 kg/m3. Using the numbers from NASA's tweet above, Dimorphos has an approximate/average density of 4.8 billion kg / 2.14e6 cubic meters or 2,243 kg/m3. That's about what we would expect for the density of a gravel pile. But this means we would not expect DART to penetrate significantly more than its own body length. Is it under-penetration, rather than over-penetration, that would prevent Dimorphos from simply exploding? Does all of the impact energy get concentrated into a tiny region, blowing all that to atoms and flinging it out at terrific velocity but failing to deliver the energy to the object itself?
8. ## totm oct 2022 DART: Double Asteroid Redirection Test

Ah mite nawt be a maths guy, but one of those thangs looks bigger than t'other. There's some variation in the impact mass of DART (I've seen a range from 500 kg to 570 kg) and the stated impact speed (I've seen 5.95 km/s to 6.6 km/s) but still, we are dealing with three orders of magnitude here. Either my numbers are wrong, or Dimorphos got obliterated. Here's a NASA tweet which seems to confirm these numbers. To a first-order approximation, GBE = (3*G*M2)/(5*R). 3 * 6.67e-11 N*m2/kg2 * (4.8 billion kg)2 / (5 * 80 m) = 1.15e7 Joules. Surely I'm missing something here.
9. ## totm oct 2022 DART: Double Asteroid Redirection Test

And images from Shanghai: And a video from an observatory in the Indian Ocean:

The grid fins are much closer to the center of mass on the way up so their moment effect on the ascent is negligible. There's a little drag of course but probably less than if they were folded. Drag on a big vehicle like this is pretty low regardless. You're already out of most of the atmosphere by the time you hit supersonic speeds, at least on ascent. Descent is another issue altogether.
11. ## totm oct 2022 DART: Double Asteroid Redirection Test

To a first-order approximation, the gravitational binding energy of Dimorphos is 1.18e7 J. At impact, DART had a mass of 570 kg and a relative impact speed of 6.6 km/s, giving it a total kinetic energy of 1.24e10 J. Wait, what? Here's another view from an Earth-based telescope:
12. ## totm oct 2022 DART: Double Asteroid Redirection Test

Another video of the collision, this one picked up from a telescope in South Africa:

14. ## totm oct 2022 DART: Double Asteroid Redirection Test

But the system is near periapsis of a more elliptical orbit, so it could still be going faster than Earth. Then we would see the the ejecta cloud moving from left to right in the video.
15. ## totm oct 2022 DART: Double Asteroid Redirection Test

I think this video should be rotated 180 degrees to show the proper path. The Didymos/Dimorphos system is orbiting the sun in the same direction as Earth, of course, but it is orbiting at a greater distance and thus its apparent motion relative to the fixed stars is from left to right, as viewed from the northern hemisphere. And the ejecta cloud, also, would have been moving from left to right since the impact was from right to left.
16. ## totm oct 2022 DART: Double Asteroid Redirection Test

Reminded of this XKCD from 2016. . . .
17. ## What If Starship's Hull Was.... Tungsten or a Tungsten Alloy?

No, you just optimize your staging. What? No. Nothing at any point in this thread would suggest such a thing. But we don't have arbitrarily powerful energy sources, so the propellant type is not irrelevant. WHAT no no nothing whatsoever like this. Are you proposing we poach the crew?

My best guess is that the 7-engine static fire toasted a few sensors a little more than expected and so they realized they needed to add extra shielding. What was it Elon said about BPINP? "If you don't find yourself needing to add parts back into the design, you're not removing enough." Or something like that.
19. ## totm oct 2022 DART: Double Asteroid Redirection Test

Well it was in real-time. But here, I sped it up to 300%. https://www.tiktok.com/t/ZTRmNTftj/ And in case TikTok isn’t embedding properly:
20. ## totm oct 2022 DART: Double Asteroid Redirection Test

Well.... technically it was already timelapse. But I'll post something if I see something.
21. ## totm oct 2022 DART: Double Asteroid Redirection Test

Me too! It's a really strange shape.
22. ## totm oct 2022 DART: Double Asteroid Redirection Test

Closest image
23. ## totm oct 2022 DART: Double Asteroid Redirection Test

Impact in 5 minutes. 60 seconds until the start of the final correction burn. Clear detail visible on Didymos and some on Dimorphos. DART is about as far from Dimorphos as New York City is from Cape Canaveral.
24. ## totm oct 2022 DART: Double Asteroid Redirection Test

Probably a combination of RCS and small perturbations. We have a meaningful view of the Dimorphos disc:
25. ## totm oct 2022 DART: Double Asteroid Redirection Test

Obligatory: Sadly I'm in class RN so I can only follow along with non-audio sources. DART is now approximately one Earth radius away from impact and closing at 20 times the speed of sound.
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