How far from Event horizon are you safe?

[avito009]

The event horizon, or schwarzschild radius for a black hole with the mass of the Earth is 3 km. But according to http://hubblesite.org/reference_desk/faq/all.php.cat=exotic, objects would have to be as close as about 6.2 miles (10 km) to the black hole's center before they began spiraling in.

Event horizon is 3km from the centre of the Black hole the mass of the sun, so if you are say 4 km away from the radius you should be able to escape being sucked into the black hole. But the distance according to the above website is 10 km. Why?

 

[vociferous]

I would have to do the math, but I believe the Schwartzchild radius would be the theoretical limit for both massive and massless objects to escape.

You have to keep in mind however that in reality, a massive technological object is incapable of using near-infinite energy to accelerate itself, so how close you could approach an event horizon strongly depends on how much acceleration on a path away from the horizon you would be able to generate.

 

[DrStupid]

But according to http://hubblesite.org/reference_desk/faq/all.php.cat=exotic, objects would have to be as close as about 6.2 miles (10 km) to the black hole's center before they began spiraling in.

I don't know where the 10 km come from. The limit of stable orbits is outside 1.5 times the Schwarzschildradius. That would be 4.5 km in case of the Sun. Inside this so called photon sphere everything without sufficiently strong rocket engines spirals into the black hole.

 

[tadchem]

The determinant would be the tensile strength of the object.
As it nears the BH, the gravitational gradient (the difference between the strength of gravity on end of the object versus the other) will result on gravity pulling harder on the near ('downhill') end harder than on the far ('uphill') end.
This will apply a tension force on the object, trying to pull it apart.
The name given this tension is 'tidal force'.
When it gets strong enough the object will be pulled apart.
When the sundered parts of the object get close enough the BH's tidal force will pull them apart.
Eventually, even the individual molecules will be pulled apart to become separated atoms.
This will happen before it gets close enough to ionize the atoms.
Finaly, electrons and atomic nuclei will reach the event horizon and join the BH.

I believe Larry Niven discussed this in some detail in the "Ringworld" series. The protagonist of the series (Louis Wu) deduces that the homeworld of his ultra-secretive companion (Nessus) lacks a substantial moon because of his companion's demonstrated lack of understanding of tidal forces, revealed when the companion executes a 'slingshot' hyperbolic orbit around a BH and discovers an unanticipated stress on his ship and his own body.

 

[stevebd1]

For static black holes, you have the photon sphere at 3M (the radius of the black hole being 2M), the marginally bound orbit at 4M and the marginally stable orbit at 6M which is often where the inner edge of any accretion disk resides.

Regarding tidal forces, Edward Wheeler came up with the 'ouch' radius which is derived from the equation for gravity gradient- dg=(2Gm/r^3)dr which can be rewritten in respect of a change of 1g (g_E) from head to toe (i.e. dr=2m) which is considered a limit we could tolerate-

r_{ouch}=\left(\frac{4Gm}{g_E}\right)^{1/3}

this ouch radius will occur well outside the event horizon of small black holes and inside the event horizon for very large black holes such as SMBHs.

 

[kjhskj75]

The event horizon, or schwarzschild radius for a black hole with the mass of the Earth is 3 km.

Schwarzschild radius of an earth-mass black hole is around 9 millimetres, not 3km

3km is the radius of a solar-mass hole.

 

[soulmartyr]

Wouldn't the firewall incinerate you long before the tidal force would pull you apart. What about considering this new idea of an apparent horizon, that is chaotic and fluctuating like a storm, that physicist like Hawking and Susskind are favoring now, since they believe Hawking radiation would hold information.

 

[avito009]

The event horizon, or schwarzschild radius for a black hole with the mass of the Earth is 3 km.

This is by mistake I meant to say "for a black hole with the mass of the Sun is 3 Km".