Black Size
How can I solve for the size of a black hole?
A black hole is defined as a region with an infinite density so that not even light can escape it. The threshold scenario admits the speed of light (3*108m/s) as the escape velocity from a black hole. Find the size of a black hole resulted from the collapse of a planet such as our Earth.
How do I do this?
Please helppp
Ans: 9 mm
Help me:(
The escape velocity equation is:
v = √(2GM/r)
... where G is the universal gravitational constant, M is the mass of the object, and r is its radius.
We want to compute r where v is known, 3 x 10^5 km/sec. (Note I changed units here to km/sec).
So let's re-write the equation for r:
v² = 2GM / r
v² / 2GM = 1/r
r = 2GM / v²
Now we know that for the Earth's radius (6378 km), v = 11.2 km/sec. That allows us to compute the 2GM term by one more slight re-write:
2GM = r / v°
so
2GM = 6378 / 11.2²
2GM = 50.845
Now going back to our equation for r, knowing 2GM = 50.845, we have:
r = 50.845 / (3 x 10^5)²
or
r = 50.845 / 9 x 10^10
r = 5.6 x 10^-10 km
which is the same as 5.6 x 10^-7 meters, or 5.6 x 10^-4 mm,
or 5.6 x 10-1 nanometers. So no,
So no, I don't know how 9mm is correct here.
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