Final answer:
An initially blue star cluster dominated by the light of an O star would appear blue from a distance. Over 10 billion years, its color may shift to red as the O and A stars die off and the cooler G and M stars dominate the luminosity.
Step-by-step explanation:
When observing a star cluster from a large distance, the overall light we see is a combination of the light emitted by individual stars within the cluster. The type of stars that would dominate the light in a new cluster consisting of one O star, 10 A stars, 100 G stars, and 1000 M stars would be the O star. This is because O stars are much more luminous than the other types of stars listed, despite there being fewer of them. Thus, initially the cluster would appear blue, the characteristic color of an O star.
After a significant amount of time, such as 10 billion (1010) years, the color of the cluster would likely change as the more massive O and A stars evolve off the main sequence and become red giants or supernovae, leaving the cooler and longer-lived G and M stars. Over time, as the initial O and A stars have ended their life cycles, the light from the cluster would be dominated by G and M stars, making the cluster appear redder due to these stars' cooler temperatures.
Stars come in various masses and temperatures, with their luminosities and colors providing clues about their stages in life. When analyzing a star cluster, it's not just the number of each type of star that matters but also the individual luminosity and temperature that determines the overall light emission and color observed from a distance.