Final answer:
Stars at the outer edges of galaxies orbit faster than expected from Newtonian gravity without dark matter, but their speeds do not exceed their escape velocities. The high orbital speeds indicate the presence of dark matter providing additional gravitational pull.
Step-by-step explanation:
Stars at the outer edges of galaxies, such as the Milky Way, orbit faster than expected from Newtonian gravity when only the visible matter is considered. However, this does not imply that these stars exceed their escape velocity, which is larger by a factor of √2 (about 1.41) times the circular orbital velocity. The observed high speeds indicate that there is an additional source of gravity, attributed to a halo of dark matter that surrounds galaxies, causing the orbital speeds to not decrease as expected with distance from the center of the galaxy. While these stars are orbiting faster than would be predicted by the visible matter present, it is not accurate to claim that their speeds are over 41.4% higher than expected; they do not exceed the escape velocity but are higher than what Newtonian dynamics would predict without the presence of dark matter.
Historical measurements by astronomers such as Vera Rubin and Fritz Zwicky revealed that stars' velocities remain high even at large distances from the galactic center, leading to the theory that galaxies contain significant amounts of unseen mass, or dark matter, in a halo that extends beyond the visible galactic disc. This mass is crucial in providing the gravitational pull necessary to keep the stars in their rapid orbits and prevent them from escaping the galaxy's gravitational field.