Compute mass of black hole, gravitational and circular acceleration

In summary, the task is to determine the mass of the black hole at the center of our galaxy using the orbital period and semimajor axis of star S0-19. The problem assumes a circular orbit and the semimajor axis is equivalent to the orbital radius. The answer should be expressed in solar masses, without the need for converting AU into seconds.
  • #1
Maiia
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Homework Statement


Determine the mass of the black hole lurking at the center of our galaxy. Conveniently, Nature has arranged for a number of stars to be orbiting the black hole. Star S0-19 has an orbital period of 37 years, and a semimajor axis of 1720 AU. Assume circular orbit and compute the mass of the black hole. Express your answer in solar masses, Msun.

What I'm confused about in this problem is if the semi-major axis is the same as the orbital radius? and do I have to convert AU into seconds for solar masses?
 
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  • #2
The problems states to assume a circular orbit. So, the radius is the semimajor axis in this case. It simplifies the problem but is can be solved using an elliptical orbit. AU is astronomical unit and is equal to the mean distance between our sun and the earth; it is not a unit of time.
 
  • #3
oh i see... thanks for your help!
 

1. How is the mass of a black hole computed?

The mass of a black hole is computed by measuring the gravitational effects it has on its surroundings, such as the orbits of nearby stars and gas clouds. Scientists use the equations of general relativity to calculate the mass based on these observations.

2. What is the significance of the gravitational acceleration of a black hole?

The gravitational acceleration of a black hole is the force that causes objects to fall towards it. This acceleration is incredibly strong near the event horizon of a black hole, leading to the extreme distortion of space and time around it.

3. How does circular acceleration differ from gravitational acceleration?

Circular acceleration is the acceleration of an object moving in a circular path, while gravitational acceleration is the force of gravity acting on that object. In the case of objects orbiting a black hole, circular acceleration is caused by the gravitational pull of the black hole.

4. How does the mass of a black hole affect its gravitational and circular acceleration?

The greater the mass of a black hole, the stronger its gravitational pull and the higher the circular acceleration of objects orbiting it. This is why supermassive black holes, with masses billions of times that of our Sun, have such strong gravitational and circular acceleration.

5. Can the mass of a black hole change over time?

Yes, the mass of a black hole can change over time as it accretes matter from its surroundings. This occurs when gas and dust are pulled into the black hole's event horizon and add to its mass. However, the mass of a black hole can also decrease over time through a process called Hawking radiation.

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