Final answer:
Astronomers have concluded that dark matter exists within and between galaxies in a cluster by observing that the total mass of a cluster, inferred from the movements of galaxies, is much higher than the mass of observable matter.
Step-by-step explanation:
By analyzing the motion of galaxies within a cluster, astronomers have determined that the total mass of a galaxy cluster greatly exceeds the combined mass of the visible matter it contains, including both the individual galaxies and the hot intracluster gas.
In the given example, the mass of the galaxy cluster is determined to be 800 MMW based on the movement of galaxies, while the visible matter within the cluster (galaxies and intracluster gas) totals only 120 MMW (40 MMW from galaxies and 80 MMW from gas).
This significant discrepancy suggests that a large proportion of the cluster's mass is made up of dark matter, which is not observable by conventional means but whose presence is inferred from gravitational effects on visible objects.
The comparison of the cluster's total mass with that of the visible matter implies that dark matter exists between galaxies in the cluster as well as within individual galaxies themselves, confirming that dark matter is distributed across the universe and plays a crucial role in the structure and evolution of galaxy clusters.