Final answer:
The difference in gravitational force between a system near the center of the Milky Way and one near the edge is influenced by the central mass and the presence of dark matter. Near the center, the force is stronger due to the combined mass of stars and a supermassive black hole, while the edge experiences a weaker force but is kept in orbit by the gravitational effects of dark matter.
Step-by-step explanation:
The force of gravity on a system close to the center of the Milky Way compared to one near the outside of the galaxy's disk differs due to several factors. Near the center, the collective mass of stars, including the mass of the supermassive black hole, acts as if it were concentrated at a point in the center, exerting a strong gravitational pull. By contrast, a system near the edge of the Milky Way disk experiences a weaker force of gravity from the central mass.
However, observations reveal that stars in the outer regions orbit at unexpectedly high speeds, which cannot be explained by the gravitational pull from the visible matter alone. This discrepancy suggests the presence of a halo of dark matter surrounding the galaxy, with its gravitational influence keeping those outer stars in rapid orbit. Without the dark matter, the stars would likely escape the galaxy's gravitational hold due to insufficient gravitational force from the visible mass alone.
Therefore, while the gravitational force near the center is directly related to the visible mass and the central black hole, the gravitational force on the outskirts of the Milky Way is significantly influenced by dark matter, which is spread throughout the halo and adds to the galaxy's total mass, keeping the stars bound in their orbits.