ASTR 230 Problem Set 02: Distances, Magnitudes, and Stellar Structure/Energy Generation

Problem set for Unit 2.

Problems

1. Parallax to distance 15 points

Altair has a measured parallax of 194.95 mas. Compute its distance in parsecs and in light-years (1 pc = 3.26 ly).

2. Distance modulus 15 points

Altair's apparent magnitude is V = 0.77. Using your distance from Problem 1, compute Altair's distance modulus and absolute magnitude.

3. Mass defect and energy release 15 points

Compute the mass defect (in atomic mass units) and the energy released (in MeV) for the fusion of four hydrogen-1 nuclei (each 1.007825 u) into one helium-4 nucleus (4.002602 u), using E = Δmc² with 1 u = 931.494 MeV/c².

4. Textbook problem: solar neighborhood 15 points

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 19, Figuring for Yourself, Exercise 19.31 (verify that 1 pc = 3.09 × 10¹³ km and 3.26 ly): show the unit-conversion derivation and confirm it against the parsec-to-light-year conversion you used in Problem 1.

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 19.1-19.2 (distances and magnitudes) and Chapter 15.4-15.5, 16.1-16.2 (stellar structure and energy generation).

References and Data Sources