Schwarzschild Radius

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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