The typed question and attempt at it are below:(adsbygoogle = window.adsbygoogle || []).push({});

Question:

The Sun orbits the black hole in the center of the Milky Way galaxy. It takes approximately 225 million years for the sun to make one revolution, and the sun is approximately 26,000 light-years away. Using this information and Kepler's Third Law, estimate the total mass of the galaxy, which would include this black hole. Be sure to use kg, seconds, and meters. How many solar masses is this amount?

Here is a step by step of what I have done so far:

1. Converted light years to meters, and years to seconds:

225 years = 7.10030834 × 10^15 seconds

26,000 light-years = 2.45973739 × 10^20 meters

2. Isolated for M (mass) by plugging the calculated numbers, along with the constant G into Kepler's (third law) equation:

(T = period = 7.10030834 × 10^15 seconds)

(A = 2.45973739 × 10^20 meters)

(G = 6.67 x 10^-11)

(M = Trying to solve for)

(T^2)/(A^3) = (4*(π)^2) / (G*M)

M = (4*(π)^2*A^3) / (G*T^2)

M = (4*(π)^2*(2.5 x 10^20)^3) / (6.67x10^-11*(7.1 x 10 ^15)^2)

M = 1.83 x 10^41

*While talking with a friend he pointed out that I calculated the mass of the black hole not the galaxy. My question is now that I have the mass of the black hole how do I calculate the mass of the galaxy?

(I'm not sure how to determine how many solar masses the given ammount is either...)

Any help would be much appreciated!

Sincerely,

Synchromesh

edit: I spelled "third" wrong, sorry about that...

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# Estimating the total mass of the galaxy (using Kepler's Thid Law)

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