The reason why objects within a galaxy, such as stars, generally spin around its center at a relatively constant speed, regardless of their distance from the center, can be explained by the concept of angular momentum and gravitational forces.
Angular momentum is a property of rotating objects and is defined as the product of an object's moment of inertia and its angular velocity. In the case of a galaxy, the stars and other celestial bodies within it possess angular momentum due to their rotation around the galactic center.
Gravity plays a crucial role in this scenario. According to Newton's law of universal gravitation, every object with mass exerts an attractive force on every other object with mass. In a galaxy, the total mass, including the dark matter component, is concentrated towards the center. As a result, the gravitational force is strongest closer to the center of the galaxy.
As the stars and matter within a galaxy orbit the central region, they experience the gravitational pull of the combined mass in the galaxy. Due to conservation of angular momentum, as the distance from the center increases, the rotational speed of objects must decrease to compensate for the increased moment of inertia. In other words, the stars farther from the center must move more slowly to maintain their angular momentum.
This phenomenon is often described by the concept of "Keplerian rotation curves." In many galaxies, the observed rotation curves remain relatively flat or show only a modest decline with increasing distance from the center. This suggests that the mass distribution within galaxies, particularly the presence of dark matter, plays a crucial role in maintaining the uniform rotation of objects at different distances from the center.
In contrast, the solar system has a different mass distribution. Most of the mass is concentrated in the Sun, and the planets are relatively much less massive. As a result, the gravitational forces experienced by planets within the solar system are primarily due to the Sun. This leads to a different pattern of orbital speeds, where planets closer to the Sun move faster and those farther away move slower. The mass distribution in the solar system does not exhibit the same concentration towards the center as in a galaxy, leading to distinct orbital dynamics.
It's important to note that while the overall rotation in a galaxy tends to be relatively constant, there can still be variations and deviations from this pattern due to various factors such as interactions with neighboring galaxies, tidal forces, and non-uniform mass distributions. Nonetheless, the general trend of relatively constant rotation in galaxies is a result of the combination of angular momentum and gravitational forces acting on the stellar and matter components within them.