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NASA plans to launch a mission called DART to kinetically impact an asteroid, primarily for the defense of Earth. One thing that I've been thinking about is the same mission could be used potentially to very accurately measure the fundamental constant G.

For reference, G is the constant that says how much gravity an object will have for a given amount of mass. It is currently only known to about 4 significant digits, making it one of, if not the biggest unknown among fundamental constants. The reason why it is so hard to accurately know is it is very difficult to accurately measure the mass of an object. We know to a very high value what the gravitational force is of Earth, which directly corresponds to G times the mass of Earth. But we don't accurately know the mass of Earth, and thus can't accurately know G.

DART will take an impactor with a fixed mass, and transfer its momentum to an asteroid. If we can take in to account any mass lost, it seems like it might be a reasonably good way to measure G. In addition, DART's target of Didymos’ moonlet can have its Gravitational field accurately determined, as it is orbiting Didymos.

Has any study been done to see if this is even possible, and if not, is it?

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    $\begingroup$ Re DART's target of Didymos’ moonlet can have its Gravitational field accurately determined, as it is orbiting Didymos. I suspect this is incorrect. That Didymos’s moonlet is orbiting Didymos will aid in determining Didymos's and its moonlet's combined gravitational parameter -- but not so much that of the moonlet. It won't help that Didymos itself is so small that Didymos (and hence its gravitational field) is far from spherical. $\endgroup$ Commented Jan 29, 2019 at 0:55
  • $\begingroup$ @DavidHammen this is somewhat related, any thoughts there? Which point in an orbiting body most closely follows its Keplerian trajectory? or perhaps this is the central question: Constraints on the mass distribution within each body such that their mutual orbits are Keplerian? $\endgroup$
    – uhoh
    Commented Jan 30, 2019 at 9:31
  • $\begingroup$ @PearsonArtPhoto this is an interesting question, can't stop thinking about it... $\endgroup$
    – uhoh
    Commented Jan 30, 2019 at 9:33

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Assuming the asteroid stays in one piece you end up knowing its mass pretty accurately (depending on how big it is compared to the impactor and how accurately you can measure its position). But then you need to measure the acceleration due to its gravity, which is going to be very small, and hard to untangle from a lot of other sources of acceleration on whatever you ate using, I would imagine.

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  • $\begingroup$ It should be easier with it being a moonlet that will be struck, but.. $\endgroup$
    – PearsonArtPhoto
    Commented Jan 28, 2019 at 21:19

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