Date: Tue Dec 16 18:57:02 2003
Posted By: Bryan Mendez, Education and Public Outreach Scientist
Area of science: Astronomy
To answer your questions I will use the formulas derived from General
Relativity for a non-spinning black hole, called a Schwarzchild black hole
after the German physicist who first worked out the formulas.
For a Schwarzchild black hole there is a radius beneath which light cannot
escape it, called the Schwarzchild Radius, RS:
RS = 2GM/c2
Where G is the gravitational constant of the Universe (G = 6.67x10-
11 m3 kg-1 s-2), M is the mass of
the black hole, and c is the speed of light (c = 3x108 m/s).
This formula tells you that the radius of the black hole is directly
proportional to the mass of a black hole, i.e.
the more massive the black hole the larger the radius. Since nothing can
travel faster than light, anything falling beneath this radius is forever
lost. The surface at the Schwarzchild Radius is called the Event
Horizon. It is called this because beyond this surface all events must
be forever unknown.
Now, the circumference, C, of a circle is simply 2*Pi*radius. So the
circumference of a black hole is simply
CS = 4(Pi)GM/c2.
The "surface gravity" or gravitational acceleration, g, of a black hole at
its surface is given by General Relativity as
g = GM/Rs2= c4/4GM.
"One G" is the acceleration due to gravity at Earth's surface (g = 9.8
m/s2). Therefore, if we use this value in the equation above
and solve for the mass of the black hole we get
M = c4/4Gg = (3x108 m/s)4 / 4*
(6.67x10-11 m3 kg-1 s-2)*(9.8
= 3.1x1042 kg = 1.5x1012 Suns
So it would be a black hole with the mass of 1.5 trillion Suns that would
have the same surface gravity as Earth. That's the mass of a dozen Milky
Way Galaxies. This black hole would have a diameter of 9.2x1015
m, which is about 1 light-year!
I hope that was useful to you.
Bryan Méndez, Space Science Laboratory, UC Berkeley
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