Question

2. A black hole with a mass equal to 6 billion solar masses (6×109 Msun) lies at the center of the galaxy M87.

a. Calculate the Schwarzschild radius of this supermassive black hole. Express your answer in kilometers (km), where 1 km = 1000 m. (1 point)

b. Compare this Schwarzshild radius with the semi-major axis of Neptune’s orbit, 4.5×109 km. (That is, divide one by the other to determine the ratio.) Is the black hole, as defined by its Schwarzschild radius, larger or smaller than our planetary system (in which Neptune’s orbit is the largest)? (1 point)

c. Calculate the maximum luminosity that the matter falling onto the black hole could produce. (1 point)

d. Compare (using a ratio) this maximum luminosity to the total luminosity of all the stars in the galaxy, about 4×1038 W. (That is, divide one luminosity by the other to determine the ratio.) (1 point)

Answer 1

a) Schwarzschild radius R_s = 2 G M / C²

   G = Gravitational constant

M = Mass

C = Speed of the light

Sun's schwarzschild radius is 2.95 km. So , the given black hole's schwarzchild radius is = 6×10⁹ × 2.95 = 17.7 × 10⁹ km.

b) Compare the neptune's orbit semi major axis with the given blackhole schwarzschild radius.

Neptune semi major axis = 4.5 ×10⁹ km

= 17.7 / 4.5 = 3.93

The blackhole is larger 3.93 times larger than our planetary system. 3.93 : 1