Description
Covers radiative processes, blackbody radiation, spectra, hydrostatic equilibrium, gravitational potentials, two-body motion, tidal effects, virial arguments, and the physical interpretation of astronomical measurements. This is the first of the upper-division astrophysics core courses (ASTR 310/330/410/420) and is deliberately more mathematically demanding than ASTR 101/120/210/230: results are derived from first principles (the Planck function, the hydrostatic-equilibrium force balance, the reduced two-body problem, the virial theorem, tidal expansion, the Eddington luminosity) rather than presented as applied formulas, and every worked example uses real, precisely measured astronomical data (principally the Alpha Centauri AB binary system, whose orbital elements and stellar parameters were independently live-verified for this course; see reference-log.md).
Learning Outcomes
- Derive the Stefan-Boltzmann and Wien laws as limits/integrals of the Planck function, and apply them to recover a real star's luminosity from its measured radius and temperature.
- Derive the radiative transfer equation's exponential attenuation law and explain the Boltzmann/Saha equations' joint role in setting observed spectral-line strengths.
- Derive the hydrostatic-equilibrium equation and the scalar virial theorem from force balance and mechanics, and use both to estimate a star's central pressure/temperature and a star cluster's dynamical mass.
- Derive escape velocity and the generalized (two-body) Kepler's third law from Newtonian gravity, and apply the latter to determine the total mass of a real binary star system from its orbit alone.
- Derive the tidal-acceleration and Roche-limit formulas and apply them to real solar-system tidal phenomena (the Earth-Moon system, Io's tidal heating).
- Derive the vis-viva equation and the Eddington luminosity, and combine radiative and dynamical methods to cross-check independent physical measurements of the same real star system.
Textbook and Materials
Primary reading: OpenStax Astronomy 2e (free, openly licensed; local extracted reference copy under references/openstax-astronomy-2e-extracted.txt and problem index under references/source-indexes/), Chapter 3 (orbits and gravity), Chapter 5 (radiation and spectra), and Chapter 15-18 (the Sun and stellar properties). Chapter/section citations use the OpenStax Astronomy 2e native chapter numbering, verified against the local extracted text's own embedded figure/table numbering per the ASTR 230 precedent (the generated problem index under references/source-indexes/ uses an internal numbering offset by −1 relative to the published edition). Because ASTR 310 is an upper-division course, several core topics (the Planck-function derivation of Stefan-Boltzmann/Wien, the Boltzmann/Saha equations, the hydrostatic-equilibrium force balance, the virial theorem, the reduced two-body problem, tidal-force derivation, the vis-viva equation, and the Eddington luminosity) go beyond OpenStax Astronomy 2e's introductory treatment; each lecture's slides and notes state explicitly where this course extends beyond the assigned introductory reading.
Assessment
| Component | Weight |
|---|---|
| Problem sets (7) | 30% |
| Labs (7) | 30% |
| Midterm exam (Lectures 1–7) | 15% |
| Final exam (cumulative, emphasis Lectures 8–14) | 20% |
| Participation and reading checks | 5% |
Lecture, Lab, and Problem-Set Cadence
The course runs 14 lectures, 7 labs, and 7 problem sets — a matched 1:1 biweekly cadence in which each lab and its paired problem set both follow the same two-lecture unit. This cadence choice follows the ASTR 210 precedent of a similarly credit-weighted (4-credit) 14-lecture course, but ASTR 310 pairs each lab/problem-set with its own two-lecture unit (the ASTR 230 matched-cadence pattern) rather than ASTR 210's uneven capstone-synthesis cadence, because ASTR 310's units build a single cumulative toolkit (radiation, then hydrostatic/virial equilibrium, then two-body orbital mechanics, then tidal/orbital-energy refinements, then radiation pressure) that culminates in one capstone lab and problem set (Lab/PS 07) rather than requiring an uneven number of technical-report-style labs throughout. A matched cadence also lets each lab and problem set reinforce the immediately preceding lecture pair's derivation while the mathematics is still fresh, which is especially important given this course's higher derivation load relative to ASTR 101/120/210/230.
| Unit | Lectures | Lab | Problem Set | Topic |
|---|---|---|---|---|
| 1 | 1–2 | Lab 01 | PS 01 | Radiative fundamentals and the blackbody radiation law |
| 2 | 3–4 | Lab 02 | PS 02 | Radiative transfer, optical depth, and spectral-line formation |
| 3 | 5–6 | Lab 03 | PS 03 | Hydrostatic equilibrium and the virial theorem |
| 4 | 7–8 | Lab 04 | PS 04 | Gravitational potentials and the two-body Kepler problem |
| 5 | 9–10 | Lab 05 | PS 05 | Binary-star mass determination and tidal effects |
| 6 | 11–12 | Lab 06 | PS 06 | Orbital energy, transfer orbits, and gravitational hierarchy |
| 7 | 13–14 | Lab 07 | PS 07 | Radiation pressure and capstone synthesis |
Revision Policy
High standards apply to all graded work. Problem sets and labs may be revised and resubmitted once for improved credit within one week of return, provided the resubmission includes a short change note identifying what was corrected and why (see each problem set's assessment instructions for full criteria).
Prerequisites Check
ASTR 230 provides the descriptive/quantitative stellar and dynamical foundation (Stefan-Boltzmann and Wien's laws as applied tools, spectral classification, Kepler-type orbital reasoning for black-hole and rotation-curve contexts) that ASTR 310 re-derives from first principles and extends. MATH 251 (Calculus III) supplies the multivariable calculus needed for the Planck-function integral, the shell theorem, and the reduced two-body problem. PHYS 172 supplies the electricity/magnetism and wave background needed for radiation pressure and Thomson scattering in Lecture 13.