The relationship between dark matter and velocity is primarily described through the concept of galactic rotation curves. Galactic rotation curves refer to the way in which the orbital velocities of stars and other matter within a galaxy change as a function of their distance from the galactic center.
According to our understanding of gravity, the velocity of stars and other celestial objects should decrease with increasing distance from the galactic center. This is because the gravitational force exerted by the visible matter (stars, gas, and dust) within the galaxy decreases as you move away from the center.
However, observations of galactic rotation curves have revealed a puzzling phenomenon: the velocities of stars and gas within galaxies remain relatively constant or even increase with increasing distance from the galactic center. This implies that there must be additional mass present that is not accounted for by the visible matter.
Dark matter is a theoretical form of matter that does not interact with light or other electromagnetic radiation, making it invisible and difficult to detect directly. However, its presence is inferred from its gravitational effects on visible matter. In the case of galactic rotation curves, dark matter is invoked to explain the observed high velocities of stars and gas at large distances from the galactic center.
The additional mass provided by dark matter alters the gravitational field within galaxies, effectively causing stars and gas to move at higher velocities than expected based solely on the visible matter. Dark matter is distributed more widely than visible matter and has a gravitational influence that extends beyond the visible extent of galaxies. This is why it can account for the anomalous rotation curves observed in galaxies.
The exact distribution and nature of dark matter are still open questions in astrophysics and cosmology. Scientists have proposed various theories and models to explain dark matter, such as the presence of weakly interacting massive particles (WIMPs) or modifications to the laws of gravity at large scales. However, direct observational evidence for dark matter remains elusive, and ongoing research and observations aim to shed light on its properties and origins.