A black hole is an object so heavy that neither matter nor even light can escape

Question

A black hole is an object so heavy that neither matter nor even light can escape the influence of its gravitational field. Since no light can escape from it, it appears black. Suppose a mass approximately the size of the Earth’s mass 6.09 × 1024 kg is packed into a small uniform sphere of radius r. Use: The speed of light c = 2.99792 × 108 m/s . The universal gravitation constant G = 6.67259 × 1011Nm2/kg2 . Hint: The escape speed must be the speed of light.

a. Based on Newtonian mechanics, determine the limiting radius r0 when this mass (approximately the size of the Earth’s mass) becomes a black hole. Answer in units of m.

b. Using Newtonian mechanics, how much would a mass of 3.63 g weigh at the surface of this super-dense sphere? Answer in units of N.

Explanation / Answer

c = sqrt(2GM/r0

ro = 2 * G M /c^2 = (2*6.67*10^-11*6.09*10^24)/(9*10^16) = 9.022673333e?3 m = 9.022mm

b) W = m*g = m*G* M/ro^2 = (6.67*10^-11*6.09*10^24*3.63*10^-6)/((9.022*10^-3)^2) = 1.8115e+13km

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