Explain how and why the turnoff point on the H-R diagram of a cluster is related to the cluster's age.

Question: Explain the relationship between the turnoff point on the H-R diagram of a star cluster and the cluster's age. Answer: The turnoff point on the H-R diagram of a star cluster is the point at which stars in the cluster evolve off the main-sequence phase, indicating the end of their hydrogen fusion lifetimes. This point helps to estimate the cluster's age, as clusters with turnoff points toward high-mass stars are younger, while those with turnoff points towards low-mass stars are older. The main-sequence lifetime of stars is crucial in determining the age of the cluster, with more massive stars having shorter lifetimes, evolving off the main-sequence first, while less massive stars continue their main-sequence phase longer.