Total mass of galaxy, circular acceleration and gravity

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SUMMARY

The discussion focuses on estimating the total mass of the Milky Way galaxy based on the Sun's orbit around the central black hole. The calculations involve using the equations for distance, velocity, and gravitational mass, specifically applying the formula V^2(r)/G to derive the mass. The user calculated the mass to be approximately 1.75 x 10^41 kg, but encountered discrepancies with their teacher's answer. Key points include the importance of correctly interpreting the distance of a light-year and the tangential velocity of the Sun.

PREREQUISITES
  • Understanding of gravitational physics and orbital mechanics
  • Familiarity with the equations of motion, specifically d=vt and v=2π(r)/T
  • Knowledge of gravitational constant (G) and its application in mass calculations
  • Basic understanding of astronomical units, particularly light-years
NEXT STEPS
  • Review the concept of gravitational mass and its calculation using V^2(r)/G
  • Study the implications of orbital mechanics in astrophysics, focusing on galactic dynamics
  • Learn about the methods of estimating mass in celestial bodies, including the use of Kepler's laws
  • Explore the significance of light-years in astronomical measurements and calculations
USEFUL FOR

Astronomy students, astrophysicists, and educators involved in teaching gravitational physics and galactic dynamics will benefit from this discussion.

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Homework Statement


The Sun orbits the black hole in the center of the Milky Way galaxy. It takes approx 225million years for the Sun to make one revolution, and the Sun is approx 26,000 light-years away. Estimate the mass of the galaxy contained inside the Sun's orbit. If there is roughly 5 times more mass in the Milky Way galaxy outside of the Sun's orbit than inside, estimate the total mass galaxy.

could someone please check my work on this problem? I don't seem to be getting the same answer as my teacher did.

Homework Equations


d=vt
v=2pi(r)/T
V^2(r)/G= mass of galaxy

The Attempt at a Solution


1. d=vt
v=speed of light= 3 * 10^8m/s
t=1yr converted to sec * 26,000 yrs= 8.19936*10^11 sec
substituting numbers: d=radius= 2.459808*10^20 m

2. v=2pi(r)/T
where r= answer in 1. and T=225mill years conv to seconds=7.0956 * 10^15sec
plugging in, I get: 217817.1792m/s

3. v^2(r)/G= mass galaxy
plugging in v as answer to 2. and r as answer to 1, I get: mass total galaxy= 1.75 * 10^41kg
 
Physics news on Phys.org
A light year is a unit of distance, not time. It's the distance light will travel in vacuum for one year. Use this distance to calculate the tangential velocity of the sun. Your approach states the tangential velocity of the sun is the speed of light.
 
? I thought I did use that distance to calculate the tangential velocity of the sun...
 

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