Final answer:
The comparison to "merry-go-rounds" helps visualize the varied rotational velocities of galaxies in a cluster, affected by their positions and the cluster's mass including dark matter. It's an analogy to demonstrate the impact of mass distribution on revolution speeds, aligning with Kepler's third law.
Step-by-step explanation:
The author compares galaxy clusters to "merry-go-rounds" to illustrate a concept in astrophysics pertaining to the dynamics within galaxy clusters. Just as children at different distances from the center of a merry-go-round move at different speeds, galaxies positioned at various distances from the center of a cluster revolve with velocities that depend on their positions and the overall mass of the cluster, which includes substantial amounts of dark matter. This analogy helps readers visualize the rotation and revolution of galaxies, which is governed by laws such as Kepler's laws of planetary motion and the principles of gravitation.
Using the merry-go-round comparison, the author does not emphasize the speed at which galaxies rotate (Option 1) or the continuous nature of their movement (Option 2). Neither does the author use the comparison to denote the commonality of rotating clusters (Option 4). Instead, the focus of the comparison to merry-go-rounds lies in explaining the impact of weight (mass) and positional factors on the revolution speeds of the galaxies within the cluster (Option 3). Kepler's laws, particularly the third law that relates the orbital period to the distance from the center of mass, are relevant in understanding why objects (like stars and galaxies) further out take longer to complete an orbit than those nearer the center.
The author compares galaxy clusters to merry-go-rounds to show how weight and position affect revolution speed (Option 3).