Applying Newton's version of Kepler's third law allows us to determine what about our galaxy?

Applying Newton's version of Kepler's third law enables us to calculate the mass of the Milky Way galaxy within a certain radius by observing the orbital velocities of stars and gas clouds at various distances from the center of the galaxy. Kepler's third law, when adapted by Newton to account for gravity, relates the orbital period of an object to its distance from the center of mass.

In this context, if we can measure the orbital speeds of stars at different distances from the galactic center, we can apply the modified version of the law, which states that the square of the orbital period of an object is directly proportional to the cube of the semi-major axis of its orbit. This relationship allows us to infer the gravitational influence exerted by the mass within that radius.

By integrating these measurements, it becomes possible to estimate the mass contained within a specific radius of the galaxy without needing to know the total mass of the Milky Way galaxy. Consequently, this method is instrumental in understanding the distribution of mass, including dark matter, within the galaxy's structure. The other options do not align with the principles derived from Kepler's laws or are beyond the direct applications of this analysis.