Total mass of galaxy, circular acceleration and gravity

AI Thread Summary
The discussion revolves around estimating the mass of the Milky Way galaxy contained within the Sun's orbit, which is approximately 26,000 light-years away from the central black hole. The user attempts to calculate the mass using the formulas for distance, velocity, and gravitational mass but encounters discrepancies with their teacher's answer. Key points include the correct conversion of time and distance units, as well as the proper calculation of the Sun's tangential velocity. A critical error noted is the misunderstanding of the speed of light as the Sun's tangential velocity. The conversation emphasizes the importance of accurate unit conversions in astrophysical calculations.
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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
 
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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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