A \"black hole\" is created when a star collapses to such a small radius that th

Question

A "black hole" is created when a star collapses to such a small radius that the gravitational force at its surface becomes so strong that not even light can escape. This radius is called the Schwarzchild radius in honor of Karl Schwarzchild who first solved the equations of General Relativity and showed that black holes could exist, at least in theory. Although the proper calculation requires knowledge of General Relativity (Einsteinian Gravity), interestingly we can derive the correct Schwarzchild radius by doing a calculation using classical physics (Newtonian Gravity). That is, you'll use the equation we derived in class and solve for the Schwarzchild radius assuming that the escape speed equals the speed of light.

What is the Schwarzchild radius for a star of mass M = 1.90 x 1030kg? (this star is comparable in mass to our Sun).

m

Find the density of such a black hole

kg/m3

Explanation / Answer

We know that

Schwarzchild radius rs =2GM/c2

rs is the schwarzschild radius of the graviting central body

G is the gravitational constant=6.67*10-11 m3 kg-1 s-2

M is the mass of the object

c is the speed of the light

A)

Given that that the mass of the star M = 1.90 x 1030kg

Now rs =2*6.67*10-11 m3 kg-1 s-2 * 1.90 x 1030kg/(3*108m/s)2 =2.816*103m =2816m

B)

The density of such a black hole is given by p =m/Vs

Vs =(4/3)pirs3 =1.33*3.14*(2816)3 =9.325*1010m3

Now the density is p =m/Vs =1.90 x 1030kg/9.325*1010m3=2.037*1019kg/m3

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