Question

A stellar black hole may form when a massive star dies. The mass of the star collapses down to a single point. Imagine an astronaut orbiting a black hole having six times the mass of the Sun. Assume the orbit is circular.

(a) Find the speed of the astronaut if his orbital radius is r = 1 AU.

(b) Find his speed if his orbital radius is r = 8.9 km.

(c) Compare your answers to the speed of light in a vacuum. What would the astronaut's orbital speed be if his orbital radius were smaller than 8.9 km?

Answer 1

a) Orbital velocity V= sqrt(GM/r)
   given mass is six times the mass of sun = 6*2*10^30 kg
       radius r = 1 A U = 149597871 km , G = 6.67 X 10-11 N m2/ kg2
       substituting the values we get orbitalspeed i s
       v= sqrt(6.67 X 10-11*12*10^30/149597871*10^3)
       = 7.314*10^8 m/s = 2.438 c
b) if r= 8.9 km = 8900 m
v= sqrt(6.67*10^-11*12*10^30/8900)
           = 8993258426*10^8 m/s
           = 2997752808 c

c) if r is smaller than 8.9 km still the speed would be large