Compute mass of black hole, gravitational and circular acceleration

AI Thread Summary
To determine the mass of the black hole at the center of our galaxy, the semi-major axis of the star S0-19's orbit, which is 1720 AU, is used as the orbital radius since the problem assumes a circular orbit. The orbital period of S0-19 is 37 years, and the calculations require converting AU into a suitable unit for mass determination, specifically solar masses (Msun). It's clarified that AU is a distance measurement, not a time unit, which simplifies the calculations. The problem can also be approached using elliptical orbit equations, but the circular assumption streamlines the process. Understanding these concepts is crucial for accurately computing the black hole's mass.
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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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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.
 
oh i see... thanks for your help!
 

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