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This is assuming that the direction of the gravitational gradient remains the same ("down") - it's just the magnitude that's varying.

I don't need an accurate figure, just a ballpark one, which is good considering that I don't believe that an accurate figure exists.

I'm working out how large a flat disk of neutronium or similar would need to be in order to live comfortably on it. The answer seems to be surprisingly small (even 100m radius gives only about 20cm/s^2 difference between head to toe at the center), but without this figure I can't really figure out how small.

Note that this should include things like pressure variation due to the difference in gravity.

TLW
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  • Are you after how large the variation needs to be before it becomes noticeable or whether the current variation on Earth is noticeable? – Separatrix Sep 01 '16 at 16:51
  • I think the coriolis effects are normally blamed for being bothersome, long before the simple variation. When you bend over you’ll feel torques from the rotating habitat. – JDługosz Sep 01 '16 at 16:56
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    I don't think this question is particularly off-topic (though you might edit and include what sort of world will be creating this sort of wacky gravity), but it's possible you might receive a good answer in Physics or Biology. Like you said, this is not a topic I would expect to have received much attention, so it might help to cast your net a little wider. – MozerShmozer Sep 01 '16 at 17:10
  • @JDługosz - I'm assuming "living near a absurdly-dense mass", not on a rotating habitat. No spinning required. – TLW Sep 01 '16 at 17:24
  • @MozerShmozer - Isn't cross-posting normally frowned upon here? – TLW Sep 01 '16 at 17:28
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    @TLW I honestly couldn't say. I basically only chill on Worldbuilding and haven't asked any questions herein. – MozerShmozer Sep 01 '16 at 17:34
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    Cross-posting is, like the rest of the sites in the SE network, discouraged. The question appears to be on-topic for us, and we have plenty of members who are members of the other exchanges who should have the wherewithal to answer this. – Frostfyre Sep 01 '16 at 17:55
  • I think what is being asked for is the tidal forces acting on the head and feet of a person standing on a neutronium sphere. If I am understanding the question, the issue will not arise unless the person is orbiting the neutronium sphere, in which case the tidal forces will probably be immense; a 4 million ton neutronium sphere only 32cm in diameter will provide 1g at the surface. – Thucydides Sep 01 '16 at 18:23
  • @Thucydides - A (very) thin disk, actually. And I have the expression for the variations in gravity, I'm just wondering as to what the maximum acceptable deviation is. – TLW Sep 01 '16 at 18:34

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My initial thought:

Vertical acceleration deviations noticeable by a human are ballpark 6.5 cm/s2.

But I don't know how much this would change when people are allowed to move around.

TLW
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  • Of course, that study concerned different whole-body perceptions. Your question is about how relatively "comfortable" or "uncomfortable" a human would be if different parts of their body were subject to differing degrees of gravitation, correct? – Lord Dust Sep 01 '16 at 17:55
  • @LordDust - pretty much, or rather where the threshold between "noticeable if you look for it" and "makes itself known to the point of being uncomfortable" is. A rather vague question, I know. – TLW Sep 01 '16 at 18:03
  • And I guess we'll leave out noticeable environmental factors like atmospheric alterations. – Lord Dust Sep 01 '16 at 19:49
  • @LordDust - Actually, I hadn't thought of that. Atmospheric pressure variations should also be included - I'll edit the question. – TLW Sep 01 '16 at 21:48