Answer:
age of the cluster is 3.125 × 10⁸ years
Explanation:
Given that;
stars at the turnoff point in a star cluster have masses of about 4 solar masses
Age of the cluster?
we know that the main sequence lifetime of a star in solar lifetime(t) is related to the mass of the star in solar masses(M). expressed as
ζ = M^(-5/2)
our M is 4, so we substitute
ζ = 4^(-5/2)
ζ = 0.03125 solar lifetime
now convert the lifetime of star cluster into years
ζ = 0.03125 solar lifetime × (10¹⁰ years / 1 solar lifetime)
ζ = 312,500,000 ≈3.124 × 10⁸ years
therefore age of the cluster is 3.125 × 10⁸ years
