Final answer:
The age of a star cluster is determined using stellar chronometry, involving the comparison of observed and calculated H-R diagrams and focusing on the main-sequence turnoff point. Spectroscopy is used to acquire data essential for this process.
Step-by-step explanation:
The technique used for finding the age of a cluster of stars is known as stellar chronometry. This method involves comparing the observed Hertzsprung-Russell (H-R) diagrams of real star clusters with calculated H-R diagrams of various ages. Astronomers particularly look at the position at the top of the main sequence, where stars begin to divert from the main sequence to become red giants, known as the main-sequence turnoff point.
This turnoff point serves as an indicator of a cluster's age because more massive stars leave the main sequence sooner than less massive stars. Thus, by determining the luminosity and mass of the most massive stars still on the main sequence, astronomers can estimate the age of the entire cluster.
Spectroscopy is an essential tool in this process, providing data about the stars' composition, temperature, and other characteristics that are crucial for plotting accurate H-R diagrams and determining masses and luminosities of the stars. It is important to note that methods like radiocarbon dating are not used for estimating the age of star clusters, as this technique is primarily used for dating organic materials up to about 60,000 years old, not astronomical objects.