Classical Mechanics Level pending

If the mass of an object, specifically a sphere, were to be compressed to a sphere of a certain radius, the escape velocity on the surface of that sphere would be equal to the speed of light. This radius is called Schwarzschild radius.

Given that the escape velocity, $$v_e = \sqrt{ \dfrac{2GM}R }$$, where $$G$$ is the Gravitiational constant, $$M$$ is the mass of the sphere and $$R$$ is the radius, deduce the expression for Schwarzschild radius, $$R_\text{Sch}$$ and find out the Schwarzschild radius of Hercules-Corona Broealis Great Wall (largest known structure in the observable universe).

Details and Assumptions:

• $$G = 6.67408 \times 10^{-11} \text{ m}^3 \text{kg}^{-1} \text{s}^{-2}$$.

• $$M = 3.9782 \times10^{49}\text{ kg}$$.

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