How Far Away are You Safe from Spaghettification?

[Arthur d. S. Jr.]

I was wondering, If you're near to a blackhole... how far away minimum you have to be from it to be pulled towards it at a considerable strength, but not strongly enough to be stretched or ripped apart, in other words, alive and in one piece yet. How can I calculate that? Is there a formula, or a way to know it?

 

Thanks;

Arthur

[Raider5678]

 

F = Magnitude of the force of gravity

R = Distance between the two objects.

m₁ = Object ones mass

m2 = Object twos mass

G = Gravitation Constant.

 

I'm not sure how high F has to be for spagettification to occur, but there's the formula.

Edited February 7, 2017 by Raider5678

[Janus]

It depends on the mass of the black hole. Tidal force decreases by the cube of the distance while acceleration due to gravity decreases by the square.

 

So lets say you have a black hole of mass M and you are a distance of R from it. You will feel a certain value of gravitational acceleration towards it and a certain value of tidal force stretching you.

 

Quadruple M and and double R. You will feel exact the same acceleration towards M (4 x 1/2^2 =1) but only 1/4 the tidal force (4 x 1/2^3 = 1/4)

[MigL]

Not to take anything away from Janus' excellent explanation...

But if the BH is small enough so that you can get close enough to it, once the gravitational differential between your head and feet exceeds the 'tensile' strength of your body, it will get stretched or 'spaghettified'.

In effect, once the difference provided by 1/r^2 over approx. 6 ft is strong enough to tear you apart.

This can be well outside the event horizon for a small BH, and well inside the event horizon for a large BH.

Edited February 7, 2017 by MigL