sheeny
17-01-2008, 11:13 AM
I did a few calculations last night just to amuse myself and to keep the grey matter working. I was a bit intrigued as to whether spaghettification occurs inside or outside the event horizon of a black hole.
I tried googling first but really didn't find the answers I was after so sat down with mathcad to work it out. A PDF copy of the calculations for the minimum size of a black hole that would allow a really unlucky and unhappy astronaut to cross the event horizon before being spaghettified.
These calcs do not take relativistic effects into account, so they could be an order of magnitude or so out either way:P.
The popular media often present spaghettification as being the result of a strong gravitation field. This doesn't make sense to me - a strong uniform gravitational field will not cause spaghettification. What causes spaghettification is the rate of change of the gravitational field strength with radius from the main mass (or black hole in this case).
So this worksheet calculates the gravitation field strength at the event horizon of a black hole, and then calculates the derivative of gravitational field strength with respect to radius (i.e. the rate of change of the field strength). By changing the Schwarzschild Radius of the black hole (and of course the mass) we can see what happens at the event horizons of different size black holes.
It turns out by my calcs that for a black hole of radius >100,000km, spaghettification won't happen to a person till they cross the event horizon - so us on the outside would not see it. If the black hole is smaller, the rate of change of the field strength outside the event horizon is higher, so spaghettification would start before the event horizon is crossed.
An interesting thing about these calcs... for some reason I intuitively expected the gravitational field strength at the event horizon to be a constant regardless of the size of the black hole, probably because the escape velocity, c, is a constant... but it isn't. The gravitational field strength at the event horizon of a small black hole is much stronger than that of a large one, and of course the differential of gravitational field strength is much higher too.
Note that spaghettification is a function of three things: the rate of change of gravitational field strength, how well a body is held together, and the size of the body. So gaseous planets, stars, etc are probably easier to spaghettify than your average hapless astronaut...:whistle:.
...That's probably a enough nerdicises for now... I need some clear sky!:rolleyes::whistle:
Al.
I tried googling first but really didn't find the answers I was after so sat down with mathcad to work it out. A PDF copy of the calculations for the minimum size of a black hole that would allow a really unlucky and unhappy astronaut to cross the event horizon before being spaghettified.
These calcs do not take relativistic effects into account, so they could be an order of magnitude or so out either way:P.
The popular media often present spaghettification as being the result of a strong gravitation field. This doesn't make sense to me - a strong uniform gravitational field will not cause spaghettification. What causes spaghettification is the rate of change of the gravitational field strength with radius from the main mass (or black hole in this case).
So this worksheet calculates the gravitation field strength at the event horizon of a black hole, and then calculates the derivative of gravitational field strength with respect to radius (i.e. the rate of change of the field strength). By changing the Schwarzschild Radius of the black hole (and of course the mass) we can see what happens at the event horizons of different size black holes.
It turns out by my calcs that for a black hole of radius >100,000km, spaghettification won't happen to a person till they cross the event horizon - so us on the outside would not see it. If the black hole is smaller, the rate of change of the field strength outside the event horizon is higher, so spaghettification would start before the event horizon is crossed.
An interesting thing about these calcs... for some reason I intuitively expected the gravitational field strength at the event horizon to be a constant regardless of the size of the black hole, probably because the escape velocity, c, is a constant... but it isn't. The gravitational field strength at the event horizon of a small black hole is much stronger than that of a large one, and of course the differential of gravitational field strength is much higher too.
Note that spaghettification is a function of three things: the rate of change of gravitational field strength, how well a body is held together, and the size of the body. So gaseous planets, stars, etc are probably easier to spaghettify than your average hapless astronaut...:whistle:.
...That's probably a enough nerdicises for now... I need some clear sky!:rolleyes::whistle:
Al.