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Black Holes
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Escape speed: The minimum speed required for a projectile to escape
the gravitational effects of an object.
For the earth, the escape speed from the surface is
11 km/sec.
Escape Speed
Interesting piece of information: IF the earth (magic?) could be
collapsed to a radius of 0.008756 m (just about a centimeter)
Some numbers:
From the surface of the earth,
M = 5.97 x 1024 Kg
R = 8.756 x 10-3 m
vescape, earth = 3.0 x 108 m/sec
Hmmmmmmmmmm
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Interesting implication, once the details of General Relativity were
understood:
If the earth were to collapse to a radius of about 1 cm
(a little less, actually), light would not be able to
escape the gravitational pull of the earth.
The trick is that the earth isn’t going to collapse to a
radius of less than 1 cm
However……..
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It is known from physical law that if the starting mass of a star is above 25
solar masses, the core that will remain after the life cycle has been
completed will have a mass greater than 3 solar masses.
There are no known mechanisms in physical law that can overcome gravity
under these circumstances, and the core will continue to collapse
FOREVER
Escape Speed
Recall:
vescape =
1/2
( )
2GM
R
Escape Speed
If you are looking for a circumstance for which the escape speed will
equal the speed of light, then:
vescape = c =
1/2
( )
2GM
R
Or, rearranging,
R=
2G
c2
( )M
or, R  M
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IF a core has a mass greater than 3 solar masses, and gravitation
collapse cannot be stopped, then it is guaranteed that eventually the core
will reach a radius with an escape speed greater than c.
Once this happens, nothing, INCLUDING LIGHT, can escape the large
gravitational pull of the core.
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Schwarzschild Radius – the radius of a celestial object at which
gravitational forces exceed the ability of matter and energy to escape.
Event Horizon – A sphere with a radius equal to the Schwarzschild radius.
Once the radius of the collapsing core goes below the Schwarzschild radius
(ie, the physical object is contained within the event horizon), no form of
information can escape.
Block Hole – A object which has collapsed to a radius smaller that its
Schwarzschild radius.
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Event Horizon
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And from outside, it look like…..
Black Holes
Are we all going to be eaten by
black holes??
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Earth
Sun
Black Holes
Earth
F = G ME M /
r2
Sun
r
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Earth
Sun shrunk to inside
Event Horizon
Black Holes
Earth
r
Sun shrunk to inside
Event Horizon
Black Holes
Earth
F = G ME M /
r2
r
Sun shrunk to inside
Event Horizon
Black Holes
Earth
F = G ME M /
r2
r
Sun shrunk to inside
Event Horizon
The earth will experience no unusual effect
if the sun were to suddenly shrink to
inside of its event horizon !