Question

A black hole has an event horizon radius of 8.00×103 m .

Part A) What is its mass?

Part B) Determine the gravitational acceleration it produces at a distance of 8.01×10³ m from its center.

Part C) Determine the escape speed at a distance of 8.01×10³ m from its center. ANSWER IS NOT 2.1 x 10^8

Answer 1

Given Data

Radius of the black hole, R = 8.0 *10^3 m

A) The mass of the black hole can be calculated from

the Schwarzschild radius R

                   R = 2 GM / c^2

Here G is the Gravitational constant , G = 6.67 *10^-11 Nm^2/kg^2

And c = 3*10^8 m/s

                    M = (8.0 *10^3 m) ( 3*10^8 m/s)^2 / 2(6.67 *10^-11 Nm^2/kg^2)

                    M = 5.4 *10^30 kg

B) Distance from the center, r = 8.01 *10^3 m

          Gravitational acceleration, g = GM / r^2

                              g = ((6.67 *10^-11 Nm^2/kg^2)( 5.4 *10^30 kg)/ ( 8.01 *10^3 m)^2

                              g = 5.61 *10^12 m/s^2

c) Escape speed , v_esc = √ (2 GM / r)

                                    = √ [2*(6.67 *10^-11 Nm^2/kg^2)( 5.4 *10^30 kg) / ( 8.01 *10^3 m) ]

                             v_esc = 2.998 *10^8 m/s