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Black Holes
An evocative name. These are bodies with an escape velocity greater than that of light.
They swallow up matter- increasing in mass themselves. However if anti matter falls into a
black hole then its mass decreases and eventually the black hole fills up and disappears in
a burst of radiation.
For a black hole vE = c = [2GM/R]1/2
where vE is the velocity of escape, c the speed of light, G the gravitational constant, M the
mass of the star and R its radius.
The diagram (Figure 1) represents the gravitational fields outside a large star and then a
black hole. The depth of the gravitational vortex is much greater for the black hole than for
a heavy star – the escape velocity being the speed of light.
Actually only stars much heavier than the Sun will form black holes. The Sun will become a
red giant and then shrink away to a white dwarf and finally a black dwarf.
Large star
Gravitational Potential curves
Figure 1
Black Hole
The escape velocity of a body obviously increases the closer to the body that you go, for
example for the Earth the escape velocity at the surface of the planet is 11.3 km per
second 10 000 km above the surface this will have fallen to just under 7 km per second.
Clearly for a Black Hole there will be a distance from the centre of the Black hole where its
escape velocity will be equal to that of light – closer you fall in and can never escape,
beyond that distance you could theoretically escape if you have a space ship that could
travel fast enough.
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Although the Sun is too light to form a Black Hole the theoretical "radius" of its event
horizon would be just less than 3 km!
Example problem
Calculate the 'radius' of a black hole formed from a star 50 times the mass as the Sun
collapsing to form a black hole:
Mass = 100x1030 kg
c = [2GM/R]1/2 and so R = 2GM/c2 = [2x6.7x10-11x1032]/9x1016 = 1.5x105 m
R = 150 km
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