ASTR 410 Problem Set 03 Solutions: The Rotation Curve and the Missing Mass and Spiral Structure, Bars, and Galactic Resonances: quantitative reasoning

Instructor solution key

Scoring overview

Problems 1–4 are worth 25 points each. Award credit for correct reasoning, units, reproducibility, and interpretation; separate arithmetic slips from conceptual errors.

Problem 1

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: M(<8.2 kpc)=Rv^2/G = 1.0262e+11 solar masses.

Problem 2

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: The result must include a labeled plot, a sensitivity comparison, and a provenance statement. A numerical answer without those elements is incomplete.

Problem 3

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: The result must include a labeled plot, a sensitivity comparison, and a provenance statement. A numerical answer without those elements is incomplete.

Problem 4

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: The result must include a labeled plot, a sensitivity comparison, and a provenance statement. A numerical answer without those elements is incomplete.

Common errors