Compute mass of black hole, gravitational and circular acceleration

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SUMMARY

The discussion focuses on calculating the mass of the black hole at the center of our galaxy using the orbital characteristics of star S0-19. Given an orbital period of 37 years and a semimajor axis of 1720 AU, the mass can be determined by applying Kepler's Third Law of planetary motion. The semimajor axis serves as the orbital radius in this scenario, simplifying the calculation. The conversion of AU to seconds is unnecessary for this specific calculation, as AU is a distance measurement, not a time unit.

PREREQUISITES
  • Understanding of Kepler's Third Law of planetary motion
  • Knowledge of astronomical units (AU) and their significance
  • Familiarity with circular orbital mechanics
  • Basic skills in unit conversion and dimensional analysis
NEXT STEPS
  • Research the application of Kepler's Third Law in astrophysics
  • Learn about the calculation of mass using orbital parameters
  • Explore the differences between circular and elliptical orbits
  • Study the significance of astronomical units in astrophysical calculations
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in black hole dynamics and orbital mechanics will benefit from this discussion.

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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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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