How can you use orbital properties to learn about the mass of the galaxy?

Answer 1

The gravitational influence of mass contained within an orbit of a particular size determines the speed (and therefore period) of that orbit. So by measuring the period and size of the orbit, we can determine the mass inside the orbit. This concept works equally well for the orbits of stars and gas within spiral galaxies. By looking at the mass inside the orbit of stars or gas at different distances from the center of the galaxy, the mass of a galaxy as a function of radial distance from the center the mass of a galaxy inside radius r obtained from the rotation curve of the galaxy.

What have we learned?

In discussing the orbits of planets around a star, or the orbits of stars around the center of the galaxy, the mass inside the orbit determines, via gravity, the properties of the orbit. The difference here is that if you look at a bigger orbit (farther from the center), the mass inside that orbit is bigger than the mass inside the smaller orbit. We have to remember that the mass of the planets is insignificant compared to the mass of the star. I as well learned the expression for the mass enclosed within an orbit of radius r is M = v2r/G, where G is Newton's gravitational constant (and v is the orbital speed of a star at distance r. This formula is essentially another way of writing Kepler's Law Porb2 = constant * r3.)