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NASA's DART impactor made a head-on collision with the asteroid Dimorphos on September 26, 2022. A real-time video feed gave immediate confirmation of the direct hit. But according to this press release, NASA had to observe Dimorphos for two more weeks before being able to confirm that Dimorphos's trajectory was indeed noticeably altered (as planned).

Why? It seems to me that determining the collision's effect on Dimorphos's orbit would be a very simple exercise in Newtonian mechanics. I assume that Dimorphos's total mass was well-known from its orbital dynamics with Didymos. I know that its internal composition wasn't well understood, but is that really so important for understanding its post-collision dynamics? Conservation of momentum means that the subsequent overall motion of Dimorphos's center of mass should not be affected by the details of its internal composition.

I know that the collision ejected some material off of Dimorphos's surface, so there's a bit of a semantic question as to whether after the collision, the term "Dimorphos" should refer to "all of that material that made up Dimorphos before the collision" or "what's left on the largest connected component of that material after the collision". But it doesn't seem to me that this would make a big difference regarding Dimorphos's overall dynamics. It seems to me that approximating the collision as a perfectly inelastic collision between two point particles would probably give a pretty good model. Even if the impactor did knock off a significant fraction of Dimorphos's mass (which seems unlikely), then it seems to me that this outcome would count as "significantly changing its trajectory" almost by definition.

Was there ever really any genuine uncertainty whether DART would redirect Dimorphos given that DART directly impacted Dimorphos? What kind of plausible internal composition of Dimorphos could have led to a failure to be redirected?

Edit to clarify question scope: As is often the case, many people are interpreting the title of my question too literally. (My understanding is that Stack Exchange's convention is that the "official" version of an SE question is found in the question body, and the purpose of the question's title is to draw attention rather to precisely state the question.) I'm not trying to have a general philosophical debate about how much you should trust theory vs. experiment. Nor am I trying to understand why NASA actually did observationally confirm the redirection, as a lot of complicated non-physics factors enter into that decision. (So any speculation about NASA's political incentives, etc. are out of scope for this question.) I'm just asking, very concretely, what were the main sources of scientific uncertainty in the extent to which Dimorphos would be redirected given a successful collision, and how those uncertainties would affect the extent of redirection. "The composition of Dimorphos" would not be a concrete enough uncertainty; I'd like to know how the composition of Dimorphos would change the redirection. Of the many comments and answer to this question so far, only John Doty's answer addresses my question within the scope that I intended it.

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    $\begingroup$ Seems like a better fit for Space Exploration but offhand what's wrong with good old fashioned needing to scientifically verify an experimental result as many ways as possible ? $\endgroup$ Commented Dec 5, 2022 at 23:58
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    $\begingroup$ In a more fundamental sense, the scientific method requires that all hypotheses should be verified by observation and/or experimental results. In other words, if the observation or experimental results don't match up with predictions, the predictions either need to be modified or rejected. $\endgroup$ Commented Dec 6, 2022 at 2:51
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    $\begingroup$ @tparker, you may well be making the hidden assumption that all the important variables are known to a high degree of certainty. While that may be true, there is no way to know that without performing the experiment and accurately measuring the results. $\endgroup$ Commented Dec 6, 2022 at 2:56
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    $\begingroup$ Or let's look at it this way: you spend over 300 million $ to launch a probe which will impact an asteroid, and then you don't bother to spend a bit more money to check if the impact actually changed the asteroid's trajectory by the amount you expected? I mean, if all the variables were already known beforehand, you could have simulated the whole thing for a lot less money? $\endgroup$
    – rob74
    Commented Dec 6, 2022 at 10:29
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    $\begingroup$ @tparker: NASA set the success criterium for DART at a change in orbital period of 73 seconds or more. The fact that they set a success criterium at all seems to indicate that there was, in fact, uncertainty. The fact that they were off by a factor of 25, more than an order of magnitude seems to indicate the uncertainty was not insignificant. $\endgroup$ Commented Dec 6, 2022 at 20:25

4 Answers 4

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The spacecraft had a large amount of energy, but not a lot of momentum. Most of the impulse delivered to the target was due to the momentum of the ejecta. Energy scales as $mv^2$, but momentum scales as $mv$. For a given energy, cut the ejecta velocity in half, eject four times as much, and deliver twice the impulse. But whether the energy produces a small quantity of fast ejecta or a large quantity of slow ejecta depends the the material properties of the target. These were poorly known.

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    $\begingroup$ @tparker Detectably? Sure. But NASA wanted a bigger effect. $\endgroup$
    – John Doty
    Commented Dec 6, 2022 at 1:14
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    $\begingroup$ Or (I believe) equivalently, you’re saying that the orbit of the center of mass of all the material that originally comprised Dimorphos before the collision (but not including DART) did not noticeably deviate from Dimorphos’s original orbit (at least neglecting gravitational interaction effects with Didymos)? $\endgroup$
    – tparker
    Commented Dec 6, 2022 at 1:16
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    $\begingroup$ @tparker The momentum of DART+Dimorphos immediately before the collision was essentially the same as the momentum of DART+Dimorphos+ejecta immediately after. But DART wasn't in orbit about Didymos, and probably most of the ejecta wasn't either, so you can't talk about the orbit of all the stuff. $\endgroup$
    – John Doty
    Commented Dec 6, 2022 at 1:25
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    $\begingroup$ @tparker - (note: not previous commenter) "most" is an exaggeration, but just working things out as though they were elastic gives ~15m change in orbital period (physics.stackexchange.com/questions/731677/…) but the actual crash changed orbital period by ~32 minutes (nasa.gov/press-release/…) $\endgroup$
    – TLW
    Commented Dec 7, 2022 at 0:35
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    $\begingroup$ @tparker Just look at the numbers again. NASA expected 18min orbit shortening, they got 32min. That's almost twice as much speed change as anticipated. I'm pretty sure that the expected 18min included the entire spacecraft momentum plus some expected ejecta effect. As such, 14/32 = 43% of the effect must have been due to unexpected ejecta effects. Add in the expected ejecta effects, and you can be pretty certain that the ejecta effects dominated. $\endgroup$ Commented Dec 7, 2022 at 13:14
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Because sometimes things don't quite turn out as the theory expects, and the only way to know is to experiment.

Aa an example, take the main result of this experiment: the orbital period was changed by ~32min (https://www.nasa.gov/press-release/nasa-confirms-dart-mission-impact-changed-asteroid-s-motion-in-space).

If we take for correct the calculations in DART crash on Dimorphos: computation of orbital period change and we add to that an estimate of the effect due to reshaping outlined in https://iopscience.iop.org/article/10.3847/PSJ/ac7566, taking the larger estimates, we arrive at a change of 18 minutes, well short of the real world 32.

I'm no physicist and I haven't read all the details of either calculation, so there may well be some assumption made both times that could be integrated (there probably is), but I think it well shows how much value there is in actually preforming the experiment and not trusting theory blindly.

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Biliards or snooker are games where you can perfectly calculate the mechanics, nonetheless there is still a great amount of variability.

In the case of DART the impact point might have been solid rock or rubble slipping sideways and dispersing part of the momentum or something in between. Another factor of uncertainty is the angle, it is very difficult to hit with great precision a rotating body.

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    $\begingroup$ Neither of your suggestions (v1) can carry linear momentum out of the asteroid+spacecraft system. $\endgroup$
    – rob
    Commented Dec 6, 2022 at 16:58
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    $\begingroup$ Even for billiards or snooker, you cannot do the calculations without doing some measurements first: 1) How inelastic are collisions actually? 2) How high is the friction between the velt and a sliding ball? 3) How high is the drag of a rolling ball? 4) How high is the friction between colliding balls (angular momentum transfer!)? 5) How high is the friction between the queue and the ball with varying amounts of chalk in between? And that's even before you start trying to pin down the precise starting position, queue velocity/momentum and point of contact between queue and ball... $\endgroup$ Commented Dec 7, 2022 at 13:02
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This article confirms John Doty's answer that the biggest unknown was indeed how much ejecta the DART impact would throw out from Dimorphos:

Researchers estimate that this spray of rubble meant Dimorphos’ added momentum was almost four times that imparted by DART.

My take is that strictly speaking - putting aside epistemological questions about the nature of proof - it wasn't really necessary for NASA to observe the aftermath of the collision in order to determine whether DART significantly modified Dimorphos's trajectory; that would have happened even for a completely inelastic (head-on) collision with no ejecta at all. But NASA did need to observe the aftermath in order to determine by how much the impact changed Dimorphos's trajectory.

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