Total mass of galaxy, circular acceleration and gravity

[Maiia]

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

 

[chrisk]

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.

 

[Maiia]

? I thought I did use that distance to calculate the tangential velocity of the sun...