Final answer:
Without additional data or assumptions regarding the mass distribution model of the galaxy, we can't accurately determine the total mass within a radius of 4 kpc or the dark matter mass within a radius of 2 kpc. The total mass of the Milky Way is about 2 × 10¹² solar masses, with dark matter comprising up to 95%.
Step-by-step explanation:
To estimate the total mass of the galaxy within a radius of 4 kpc (kilo parsecs), and the mass of dark matter within a radius of 2 kpc, we need to use the provided astronomical data. According to the information given, the total mass of the Milky Way galaxy is about 2 × 10¹² solar masses (M☉), with up to 95% of this mass being dark matter.
We must assume that dark matter is uniformly distributed throughout the Milky Way. The mass within a specific volume can be found by calculating the fraction of the total volume that volume represents and then applying that fraction to the total mass.
The radial distribution of mass in a galaxy typically follows certain profiles which require specific models to describe.
Since we are not given a specific mass distribution model or the exact mass within 4 kpc, we can't provide a precise answer without additional data or assumptions.
Similarly, we lack the details to accurately calculate the dark matter mass within a radius of 2 kpc. Such calculations would typically involve complex astrophysical models that go beyond simple volumetric ratios because dark matter distribution is not uniform and is influenced by a galaxy's overall mass distribution and dynamics.