Final answer:
Newton's shell theorem is applied in astrophysics to estimate the mass of galaxies, such as our Milky Way, and assess the presence of dark matter, using Kepler's third law and calculating orbital speeds and distances.
Step-by-step explanation:
When considering which of Newton's shell theorems applies to a galaxy, we refer to the principle that if you have matter evenly distributed in the shape of a sphere, the gravity it exerts on an object just outside is as if all the matter were concentrated at a point in the center.
For galaxies, this allows us to simplify complex systems for practical calculations. In the case of our galaxy, the Milky Way, it can be assumed that all the mass within the Sun's orbit is concentrated at the center. By applying Kepler's third law, as modified by Newton, we can estimate the mass of the galaxy and assess the presence of dark matter through orbital velocity observations.
Additionally, this principle plays a role in estimating the mass of a black hole at the galaxy's center by examining the orbital speed and distance of stars close to the center. The mass of the Milky Way Galaxy, deduced to be about 100 billion times the mass of the Sun, and the evidence for dark matter have both been obtained through the application of these calculations. Thus, it's evident that Kepler's third law, as informed by Newton's insights, plays a crucial role in modern astrophysics.