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In particular, I'm thinking of spaghettification that occurs as an object falls into a black hole (as an extreme example). But what about tidal forces like the tidal heating taking place on Jovian Moons like Io and Titan?

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Relativity is not really that essential for solving this problem, Newtons gravity is good enough. If you are asking how to calculate the tidal forces, all you have to do is calculate how the gravitational acceleration changes in given axis. For this, you can use derivation of accelaration with respect to position. Jerk has no effect, especially on circular orbit (otherwise you could use it to describe change of the tidal force in time). The formula for tidal force is following:

$F=-\frac{\text{d}F_g}{\text{d}r}R=\frac{2G M m}{r^3}R$

$R$ is the radius of the affected body.

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