#### Re: Spaghettification - not always

Here are some numbers using the mass of Earth (M) as a guideline...

c= 299792458 m/s

G= 6.6740831e-11

M= 5.97237e+24 kg

Key: Schwarzschild Radius = rs, Escape velocity at rs = evrs, Escape velocity at rs + 2m = evrs+2m

I give the evrs+2m i.e. two metres out from rs to give an idea of the relative escape velocity, and thus the gravitational gradient that a tall person would experience.

Mass= 5.97e+024 kg, rs= 0.0088700671 m, evrs= 299792458 m/s, evrs+2m= 19920866.79 m/s.

So the Schwarzchild radius for an Earth sized mass is a smidge under 9 mm and the difference in escape velocity 2m from its event horizon is about 279871591 m/s - that's a pretty steep and unhealthy gradient.

At ten times the Earth's mass...

Mass= 5.97e+25 kg, rs= 0.088700671 m, evrs= 299792458 m/s, evrs+2m= 61779736.59 m/s

The Schwarzchild radius is now a little under 90 mm and the +2m escape velocity difference is now about 238012721 m/s - still far too steep.

At one hundred times the Earth's mass...

Mass= 5.97e+26 kg, rs= 0.88700671 m, evrs= 299792458 m/s, evrs+2m= 166172922.8 m/s

...the ev difference has come down to 133619535.2 m/s - still too steep... In fact, it's not until we get to around a mass of 5.97e+35 that the ev difference is less than 1 m/s...

Mass= 5.97e+35 kg, rs= 887006709 m, evrs= 299792458 m/s, evrs+2m= 299792457.6 m/s

...the Schwarzchild radius is now 887,006.09 km and whilst you might survive the difference in ev it would still be uncomfortable. To get to less than 1 mm/s difference in escape velocity we need to increase the mass by another factor of 1000, to 5.97e+38 kg, at which point the Schwarzchild radius becomes 887006709435 m, or 887,006,709.4 km - that's pretty big. In fact, that radius is about 44 times greater than the current distance of Voyager 1 from Sol.

However, the estimated mass of our galaxy is between 1.15e+42 kg and 1.69e+42 kg, so it would seem that a sufficiently large BH would be between about 1/1930th and 1/2829th of our galaxy.

Proviso: I think I've got the numbers right but wouldn't mind someone checking them.

As DNA said "Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space..."