I have the following problem:
"The Sun has an orbital speed of about 220 km s−1 around the center of the Galaxy, whose distance is 28 000 light years. Estimate the total mass of the Galaxy in solar masses."
I know how to solve it in two different ways, considering the galaxy mass as the total mass inside the sphere that the sun is orbiting:
using that the gravitational force is equal to the centripetal force;
by Kepler's third law
But, in both cases, what I get is the total mass of the Galaxy, in kilograms. To estimate this mass in solar masses, I need to know the solar mass - which is easily found, but it's not given in this problem - and then I divide the value that I find by it.
The question is: is there a way I can obtain this ratio without knowing somehow the solar mass? Is there a way that I can get directly an expression with the ratio M(galaxy)/M(sun) and not depending on the value of the last one?