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Given the shortcomings of applying the gravitational equation to distant astral objects, I am wondering if it has ever been attempted to replicate the Cavendish Experiment in a zero gravity scenario (such as the ISS). If $G$ is different in a zero gravity setting than it is on earth's surface, this could help explain discrepancies in the current equation.

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  • $\begingroup$ Zero gravity, or free fall? $\endgroup$
    – Jon Custer
    Commented Oct 7, 2021 at 18:39
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    $\begingroup$ the ISS is not a place where g=0. $\endgroup$ Commented Oct 7, 2021 at 19:49

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In a typical Cavendish experiment, the timescale for the masses and the torsion fiber to equilibrate after an adjustment to the setup is hours. In low-Earth orbit, your laboratory orbits the Earth every 90 minutes. That’s a lot of background rotation to cancel out. I’m pretty confident it’s never been done.

The closest thing to a Cavendish-type experiment in space, to my knowledge, was the never-launched Project SEE, which I've described previously here on Physics. As I wrote on that other answer: I think what doomed Project SEE was the discovery that its analysis was sensitive to changes in Earth's mass distribution at the scale of a cattle drive. I see a straight line from the failure of Project SEE to the astonishing success of GRACE, in which the gravitational interaction between the two satellites (separated by 200 km) really was negligible, and whose gravimetry made important discoveries about the movement of groundwater aquifers, ocean currents, ice sheets, and underground magma flows — all of which are much more massive than a cattle drive.

Listening to talks about precision gravimetry is basically a litany of the audience saying "but surely that effect doesn't matter" and the experimenter saying tiredly, "yes, it actually does." Cavendish himself had to set up his experiment in a shack in a cow pasture — but he watched the experiment from outside the shack, and I'm pretty sure he had to keep the cattle out of that pasture. I have a vague recollection of a university gravimetry experiment that could only make progress in the springtime, because the seismic activity associated with weekday campus activity disturbed the setup too much, and in the autumn the university had big football crowds on the weekend.

For a hint at the challenges of space-based gravitation experiments that are actually about gravity, consider that Gravity Probe B was first proposed in 1959, finally launched forty-five years later in 2004, and published their results in 2015.

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I do not know if the Cavendish experiment has been duplicated in free-fall, but since the rotational plane of the weights originally used by Cavendish was horizontal, and the weights themselves were vanishingly small compared to the earth, you'd get the correct result even in the presence of gravity.

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