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Everything posted by sevenperforce

  1. It’s based on an image stack which I believe was already linked upthread.
  2. 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. 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. 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. 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. 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. 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. 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. And images from Shanghai: And a video from an observatory in the Indian Ocean:
  10. 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. 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. Another video of the collision, this one picked up from a telescope in South Africa:
  13. I've made a few slight modifications to my pixel counting approach from Friday, now with added tank volumes (I assumed that the spherical caps were geometrically perfect and that the volumetric split on the upper stage was equal to the measurable volumetric split on the booster): Based on these numbers (and using standard density for LOX and LCH4) we would be looking at an O:F ratio of 2.99 which seems shockingly fuel-rich. Of course, it is possible that the engineering in this image is inexact with respect to the positioning of the common bulkhead and the O:F ratio is closer to 3.4-3.6 or even higher. If the noted O:F ratio holds, however, then we are looking at 363 tonnes of propellant on the booster and 84 tonnes of propellant on the upper stage. The design proposed in December of last year (which is still what shows up on their site) had a launch mass of 480 tonnes, which would mean a ~6.9% total vehicle dry mass percentage, which is pretty impressive but not out of the realm of possibility for carbon-fiber construction. But GLOW could have changed since December; the vehicle height went from 40 m to 42.8 m. Total liftoff thrust then, with 7 G/G methalox engines, was 5.96 MN; it is now 6.61 MN (165 klbf x nine engines). I'm not sure if they said exactly why they went from 7 engines to 9; if it was GLOW increase and they were adding engines to maintain the same 1.27:1 TWR at liftoff, then we'd be looking at 532 tonnes GLOW, which (with this prop load) corresponds to 16% dry mass percentage which is honestly pretty bad. More likely that the increased engine count will merely increase TWR. The engines themselves lost 14% of their sea level thrust but of course 9 is 29% more than 7. That sounds problematic you have to take the second stage with you? Benefit of the falcon 9 system is that the abort system fuel can be used for the rcs system. Yeah, I don't think my idea was particularly well thought through. That upper stage is far too heavy. Both Dragon 2 and Starliner allow the abort system fuel to be used for the RCS/OMS system. The difference is that Starliner keeps the abort engines, abort propellant, and RCS/OMS engines separate from the capsule, which has only monopropellant RCS for pointing during re-entry. Dragon 2 keeps everything onboard. Advantage for Dragon 2 is being able to reuse the abort engines and prop tanks and OMS/RCS; disadvantage is that all of those systems are inside the capsule with the crew which is fundamentally more risky than having them in a separate service module. And of course Starliner has no space for unpressed cargo. I wonder if RocketLab would use Rutherford engines for abort. Electric turbopumps are good for quick starts, after all. But you'd probably need more than four, since all together they'd only push 100 kN which would give a notional 10-tonne crew capsule only about a gee of acceleration. And using kerolox for OMS would be...interesting. They've already got experience with appropriate RCS via Curie and HyperCurie. For Electron, yes. Neutron will be using staged combustion with a single oxygen-rich preburner and a single turbine to drive both the LOX turbopump and the CH4 turbopump. Varying the combustion ratio would require variable gearing between the shaft and the CH4 turbopump which would add an incredible amount of complexity and additional failure points.
  14. 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. 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. 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?
  17. 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.
  18. 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:
  19. Well.... technically it was already timelapse. But I'll post something if I see something.
  20. 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.
  21. Probably a combination of RCS and small perturbations. We have a meaningful view of the Dimorphos disc:
  22. 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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