A stellar black hole may form when a massive star dies. The mass of the star col

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 five times the mass of the Sun. Assume the orbit is circular. Find the speed of the astronaut if his orbital radius is r = 1 AU Find his speed if his orbital radius is r = 7.4 km. m/s CHECK and THINK: 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 7.4 km?

Explanation / Answer

mass of black hole = 5 M = 5 x 1.989 x 10^30 kg = 9.945 x 10^30 kg

r = 1 AU = 1.496 x 10^11 m

For circular orbit,

G (5M ) (m) / r^2 = m v^2 / r

(6.67 x 10^-11)(9.945 x 10^30) / r = v^2

v = sqrt[ (6.67 x 10^-11)(9.945 x 10^30) / (1.496 x 10^11)]

v = 66588.54 m/s

b) when r = 7.4 x 10^3 m

v = sqrt[ (6.67 x 10^-11)(9.945 x 10^30) / (7.4 x 10^3)]

v = 2.994 x 10^8 m/s

c) this speed is just equal to the speedof light.

if radius is smaller than this then oribital speed needed will be more than speed of light (that is not possible hence particle will not to be able to orbit and it will collapse into black hole)

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