Final answer:
The age of a star cluster is determined by using the H-R diagram to identify the main-sequence turnoff point, combined with theoretical models, to estimate the age of the cluster. Younger clusters display a range of positions for stars, whereas in older globular clusters, the absence of luminous blue stars is a key indicator of age. Improved stellar models and satellite data have refined these estimates significantly.
Step-by-step explanation:
The age of a star cluster is determined by comparing the observed Hertzsprung-Russell (H-R) diagram with theoretical models. Astronomers look for the main-sequence turnoff point, which is the stage where the most massive stars in a cluster move off the main sequence to become red giants. The position and luminosity of these stars are critical for estimating the cluster's age. For younger clusters, such as open clusters and associations, stars of different masses are found in distinct positions on the H-R diagram. This distribution allows scientists to estimate the time since the stars condensed from an interstellar cloud. On the other hand, globular clusters, generally older, are dated by the absence of luminous blue stars and by using improved models of the stars' interiors and more precise distance measurements from satellites, indicating that they are around 12-13 billion years in age.