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this post was submitted on 28 Aug 2023
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No Stupid Questions
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I'd argue against that. For one thing it is impossible to imagine a situation where there is no change in the gravitational gradient across your body over time. Your orbiting a black hole situation is a perfect example of a situation where the gradient alone would tear you apart. The conditions you've specified are tautological. There's no way to maintain a zero gravitational gradient while also simultaneously having extremely high gravitational field. The two are mutually exclusive in any conceivable scenario.
It's like saying a human being in a hypersonic wind stream won't necessarily hurt you, burn you alive and rip you to pieces (not necessarily in that order) as long as there is no turbulence and you have a sufficient boundary layer -- but you're a non-aerodynamic human body in a hypersonic wind stream, so of course there will be turbulence and the boundary layer will not protect you at all, you're going to die, basically instantly.
Does the change in gravity gradient across your body kill you right now? No? You are currently orbiting the supermassive black hole in the center of the milky way. You and everything else in the milky way aside from a few intergalactic objects just traveling through.
I am not an astrophysicist, but I do understand basic physics.
It was implied by "accretion disc" and by the fact that we're talking about gravitational gradients at all that we're talking about a close orbit. Gravitational strength gets smaller with distance according to the inverse square law, so by the time you're a few light years out from the galactic core the gravitational gradient is already extremely insignificant.
Accretion discs can be large enough that I am pretty sure a human body wouldn't be torn apart at that distance (at least the outer bits) by the difference in gravity across it's length. In the linked article about the supermassive black hole at the center of the Milky Way, we're talking 1000 astronomic units, so 1.5 * 10^14 meters.
The current value of this black hole's mass is estimated at ca. 4.154±0.014 million solar masses.
So let's calculate the equivalent distance from the sun in terms of gravitational force on an object at the outer edge of the accretion disk:
F_sun = C * (R_equivalent)^-2 * m_object
F_black_hole = C * 4.15*10^6 * (R_accretion_disk)^-2 * m_object
where C equals the gravity constant times the mass of our sun.
==> C * (R_equivalent)^-2 * m_object = C * 4.15*10^6 * (R_accretion_disk)^-2 * m_object
divide by C and m_object:
<=> (R_equivalent)^-2 = 4.15*10^6 * (R_accretion_disk)^-2
invert:
<=> R_equivalent^2 = (1/4.15) * 10^-6 * (R_accretion_disk)^2
==> R_equivalent^2 ~= 0.241 * 10^-6 * (R_accretion_disk)^2
square root (only the positive solution makes sense here):
==> R_equivalent ~= 0.491 * 10^-3 * R_accretion_disk
with R_accretion_disk = 1000 astronomic units = 10^3 AU
<=> R_equivalent ~= 0.491 * 10^-3 * 10^3 AU
<=> R_equivalent ~= 0.491 AU
Unless I have a mistake in my math, I sincerely hope you will agree that the gravitational field (tidal forces) of the sun is very much survivable at a distance of 0.491 astronomical units - especially since the planet Mercury approaches the sun to about 0.307 AUs in its perihelion.
If the gravity were strong enough and the source close enough then the tidal force would absolutely be strong enough to simultaneously crush you and rip you apart. The same effect gives rise to tides on this planet, hence the name.
I just proved this claim of yours wrong, and then you move the goalposts. I said from the very beginning that a gravity gradient is a problem.
I studied Relativity at university as part of combined Physics/Maths degree, but please feel free to continue entertaining us with your popular magazine-based learnings.