The molecular clouds circling the active nucleus of the galaxy m106 orbit at a speed of about 1000 km/s, with an orbital radius of 0.49 light-year = 4.8×1015 meters. part a use the orbital velocity law mr=r×v2g to calculate the mass of the central black hole. give your answer in kilograms.

The mass of the central black hole is

Explanation:

The Universal law of gravitation shows the interaction of gravity between two bodies:

 (1)

Where G is the gravitational constant, M and m are the masses of the two objects and r is the distance between them.

For this particular case M is the mass of the central black hole and m is the mass of the molecular cloud. Since it is a circular motion the centripetal acceleration will be:

 (2)

Then Newton's second law () will be replaced in equation (1):

By replacing (2) in equation (1) it is gotten:

(3)

Therefore, the mass of the central black hole can be determined if M is isolated from equation (3):

(4)

Equation 4 it is known as the orbital velocity law.

Where M is the mass of the central black hole, r is the orbital radius, v is the orbital speed and G is the gravitational constant.

Before replacing the orbital speed in equation 4 it is necessary to make the conversion from kilometers to meters:

⇒

Then, equation 4 can be finally used:

Hence, the mass of the central black hole is

truck y has a greater velocity than truck x.