Problem set for Unit 3.
Cloud A has T = 10 K and n = 10⁵ molecules/cm³. Cloud B has T = 100 K and n = 10² molecules/cm³. Using the qualitative Jeans-criterion dependence (collapse favored by low T, high n), state which cloud is more likely to be collapsing to form stars, and explain your reasoning.
Using L = M^3.5 and t = 10 Gyr × M^-2.5, compute the main-sequence lifetime of a 6 M☉ star. Compare it to the lifetime of a 2 M☉ star and state the ratio.
An open cluster's main-sequence turnoff mass is measured to be 5 M☉. Compute the cluster's age in millions of years.
OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 22, Figuring for Yourself, Exercise 22.34-22.35 (estimating cluster ages from the luminosity of the most massive main-sequence star): using the mass-luminosity relation, identify the mass of a star with luminosity 10⁴ L☉ and compute the implied cluster age using this problem set's t = 10 Gyr × M^-2.5 formula.
Submit a clear solution with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without visible work receives partial credit at most.
OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 20.1-20.2 (interstellar medium) and Chapter 22.1-22.3 (post-main-sequence evolution, star clusters).
materials/ASTR230/data/ where referenced above.