Black holes are the evolutionary
endpoints of stars at least 10 to 15 times as massive as the Sun. If a star
that massive or larger undergoes a supernova
explosion, it may leave behind a fairly massive burned out stellar remnant.
With no outward forces to oppose gravitational
forces, the remnant will collapse in on itself. The star eventually collapses
to the point of zero volume and infinite density,
creating what is known as a " singularity
". As the density increases, the path of light
rays emitted from the star are bent and eventually wrapped irrevocably around
the star. Any emitted photons
are trapped into an orbit
by the intense gravitational field; they will never leave it. Because no light
escapes after the star reaches this infinite density, it is called a black
hole.
But contrary to popular myth, a black hole is not
a cosmic vacuum cleaner. If our Sun was suddenly replaced with a black hole of
the same mass, the only thing that would change would be the Earth's
temperature. To be "sucked" into a black hole, one has to cross
inside the Schwarzschild
radius. At this radius, the escape speed is equal to the speed of
light, and once light passes through, even it cannot escape. The
Schwarzschild radius can be calculated using the equation for escape speed.
vesc
= (2GM/R)1/2
For photons, or objects with no mass, we can substitute c (the speed of light) for Vesc and find the Schwarzschild radius, R, to be
R = 2GM/c2 , where G = 6.67 X 10-11 Nm2/kg2 and c = 3.00 X 108 m/s
If the sun was replaced with a
black hole that had the same mass as the sun, the Schwarzschild radius would be
3 km (compared to the sun's radius of nearly 700,000 km). Hence the Earth would
have to get very close to get sucked into a black hole at the center of our
solar system.
For #11, find out what the Schwarzschild radius would be for an object with the same mass as your foil ball. Use this radius to find the density of a black hole within this volume.
An object with a mass of 25 g would have the following radii to have the same density as these objects: Sun (1 cm), white dwarf (0.15 mm), neutron star ( 4 X 10-5 cm), a black hole (singularity point with infinite density)
For #12, here is the density of
some common objects: Water( 1 g/cm3),
aluminum ( 2.7 g/cm3), Earth ( 5.5 g/cm3), nucleus (1015
g/cm3)