ASTR 230 Problem Set 07: Large-Scale Structure and Observational Cosmology

Problem set for Unit 7.

Problems

1. Hubble's law prediction 15 points

Using this unit's fitted Hubble constant (H₀ ≈ 71.5 km/s/Mpc, from Lab 07), predict the recession velocity of a galaxy at 250 Mpc.

2. Hubble tension range 15 points

Modern precision measurements place H₀ between about 67 km/s/Mpc (early-universe/CMB-based methods) and 73 km/s/Mpc (local distance-ladder methods) — the “Hubble tension.” Compute the Hubble time implied by each end of this range, and state which is larger.

3. Cluster velocity dispersion and dark matter 15 points

A galaxy cluster has member galaxies with velocities scattered by about 1,000 km/s around the cluster mean. Using the same M ∝ V²R/G logic as the Milky Way's rotation curve (Lecture 10), explain qualitatively why such large velocity dispersions imply a cluster mass far exceeding its visible galaxy mass, and identify one independent line of evidence (not velocity dispersion) that supports the same conclusion.

4. Textbook problem: the cosmic microwave background 15 points

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 29, Review Questions (the cosmic microwave background as evidence for the Big Bang): in 150-250 words, explain why the discovery of the cosmic microwave background by Penzias and Wilson (1965) was considered strong confirmation of the Big Bang model rather than the (then-competing) Steady State model.

Due and Scope

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 Companion Reading

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 28.3-28.5 (dark matter and large-scale structure) and Chapter 29.1-29.3 (Hubble’s law and the Big Bang).

References and Data Sources