Answer to Question #131133 in Mechanics | Relativity for Khethiwe

Question

How much should the Earth be compressed without losing any material in order for it to become a blackhole. (note : The mass of Earth is 5.9 x 1024 kg and the gravitational constant is 6.67 x 10-11 N m2 kg-2 (Hint: Use Schwarzschild radius)

Answer 1

Explanations & Calculations

• Any object to attain the blackhole status is defined by a concept of Schwarzschild radius.
• Any object reduced beyond volume of a sphere of a Schwarzschild radius, is expected to behave as a blackhole.
• Schwarzschild radius is given by $r_s = \frac{2GM}{c^2}$ where M & c are the mass of the object and the speed of light respectively.
• Therefore,

$\qquad\qquad \begin{aligned} \small r_s &= \small \frac{2( 6.67\times10^{-11}Nm^2kg^{-2}) ( 5.9\times 10^{24}kg)}{(3\times 10^8ms^{-1})^2}\\ \small &= \small 8.745\times10^{-3}m=8.745 mm \end{aligned}$

• Therefore, the Earth should be compressed down to a sphere of radius 8.745 mm.