A planet having mass equal to that of the earth `(M = 6 xx10^(24)kg)` has radius R such that a particle projected from its surface at the speed of light `(c=3xx10^(8)ms^(-1))` just fails to escape. Assuming Newton’s Law of gravitation to be valid calculate the radius and mass density of such a planet. Are the numbers realistic? Note: The radius that you calculated is known as Schwarzschild radius. Actually we need to use theory of general relativity for solving this problem.

Answer

R = 8.9 mm: `d=2xx10^(30)kgm^(-3)`