Determining the exact mass of the Milky Way galaxy is a complex task due to the vastness and complexity of the galaxy itself. Scientists use various methods and observations to estimate the mass of the Milky Way, but the estimates can vary depending on the techniques and assumptions used. Here's an overview of the methods and estimated mass ranges:

1. Galaxy Rotation Curve: This method measures the rotation speeds of stars and gas in different regions of the galaxy. By analyzing the rotation curve, astronomers can infer the distribution of mass within the galaxy. Estimates based on the rotation curve suggest a total mass of the Milky Way in the range of (5.8 - 6.5) x 10^11 solar masses.

2. Gravitational Lensing: Gravitational lensing occurs when the light from distant objects is distorted by the gravitational field of massive objects, such as galaxies. By studying the distortions in the light of background galaxies, astronomers can estimate the mass of the intervening galaxy. Estimates using this method suggest a mass range for the Milky Way between (0.9 - 1.9) x 10^12 solar masses.

3. Satellite Galaxy Dynamics: The Milky Way has several satellite galaxies, such as the Magellanic Clouds, that orbit it. By studying the motions and dynamics of these satellite galaxies, astronomers can infer the mass of the Milky Way. This method suggests a mass range of (0.7 - 1.0) x 10^12 solar masses.

4. Jeans Equation Analysis: The Jeans equation relates the velocity dispersion of stars in a galaxy to its mass. By measuring the velocity dispersion of stars in different parts of the Milky Way, astronomers can estimate the local density and hence the total mass of the galaxy. Estimates using this method suggest a mass range of (4.5 - 6.0) x 10^11 solar masses.

5. Dark Matter Halo Models: Dark matter is a hypothetical form of matter that does not emit or reflect light but is believed to make up a significant portion of the universe's mass. The presence of dark matter in the Milky Way is inferred from various observations, and its distribution can be modeled to estimate the total mass of the galaxy. Models suggest a total mass, including dark matter, of the order of (1 - 2) x 10^12 solar masses.

It's important to note that these mass estimates can vary depending on the assumptions and techniques used, and there is still some uncertainty in determining the exact mass of the Milky Way. Furthermore, the Milky Way's mass is not uniformly distributed, with most of its mass concentrated in the central region, including the supermassive black hole at its core.