sevenperforce

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.

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.

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?

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.

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.

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:

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

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.

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.

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.

Reminded of this XKCD from 2016. . . .

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.

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:

Well.... technically it was already timelapse. But I'll post something if I see something.

Me too! It's a really strange shape.

Closest image

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.

Probably a combination of RCS and small perturbations. We have a meaningful view of the Dimorphos disc:

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.

The image at the left is the digitally-centered view of the target. The DRACO camera on DART has an overall field of view (FOV) which is shown in total at right.

About 25 minutes to impact.

I'm not aware of any live feed from LICIACube.

Finally visible. I think they're livestreaming DART's camera They need a camera for targeting, so they're using the targeting camera to provide the live feed back in real-time. That's what we're watching.