Question

Black holes are suspected when a visible star is being noticeably
invisible partner that is more than 3 times as massive as the sun. a)
visible star is being noticeably pulled by an
giant (a dying star) is gravitationally accelerated at 0.075 m/s toward an
object that is 9.4 X 1010 m away, how large a mass must the unseen body
possess? b) How many times more massive is the object than the sun?
(Ms = 1.99 x 1030 kg)

Answer 1

a) The mass of the black hole is $9.94\cdot 10^{30} kg$

b) The black hole is 5 times more massive than the sun

Explanation:

a)

The magnitude of the gravitational force between the black hole and the star is:

$F=G\frac{m M}{r^2}$

where :

$G=6.67\cdot 10^{-11} m^3 kg^{-1}s^{-2}$ is the gravitational constant

m is the mass of the star

M is the mass of the black hole

r is the separation between the objects

According to Newton's second law, the force acting on the star can be also written as

$F=ma$

where a is the acceleration

Combining the two equations,

$a=\frac{GM}{r^2}$

where:

$r=9.4 \cdot 10^{10} m$ is the distance between the two objects

$a=0.075 m/s^2$ is the acceleration of the star

Solving for M, we find the mass of the black hole:

$M=\frac{ar^2}{G}=\frac{(0.075)(9.4\cdot 10^{10})^2}{6.67\cdot 10^{-11}}=9.94\cdot 10^{30} kg$

b)

The mass of the Sun is:

$M_s = 1.99\cdot 10^{30} kg$

while the mass of the black hole in this problem is

$M=9.94\cdot 10^{30} kg$

Therefore, the mass of the black hole written in terms of the solar mass is:

$\frac{M}{M_s}=\frac{9.94\cdot 10^{30}}{1.99\cdot 10^{30}}=5$

So, the black hole is 5 times more massive than the sun.

Learn more about gravitational force:

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