Module 2: Discovering the HR Diagram

Weeks 4–7 | From photons to physical properties

Why this module matters

You now have the foundational tools — dimensions, gravity, and light. This module puts them to work on the central question of observational astronomy: how do we learn about objects we can never touch?

Starting from nothing but the photons that reach our telescopes, you will measure stellar distances, luminosities, temperatures, compositions, and masses. Each lecture adds one link to the inference chain, and by the end of the module you will have built the Hertzsprung–Russell diagram — the single most important map in stellar astrophysics.

Learning objectives

By the end of this module, you will be able to:

  • Measure stellar distances using parallax geometry and define the parsec
  • Derive and apply the inverse-square law to infer luminosity from flux and distance
  • Connect color to temperature via Wien’s law and infer radius via Stefan-Boltzmann
  • Interpret stellar spectra to determine temperature and composition
  • Apply the HR diagram to classify stars and understand their evolutionary states
  • Measure stellar velocities from Doppler shifts and determine masses from binary orbits

Lectures

Lecture 1: Distance & Parallax

February 12, 2026

Parallax, the inverse-square law, and the measurement chain from angular shift to luminosity.

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Lecture 2: Surface Flux and Colors

February 12, 2026

Color-temperature inference, Stefan-Boltzmann scaling, blackbody demo, ultraviolet catastrophe, and HR diagram radius intuition.

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Spectra & Composition

February 17, 2026

Every element has a unique spectral fingerprint. By spreading starlight into a rainbow, we decode composition, temperature, and velocity — from a single observation.

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Lecture Readings

Lecture 1: Distance & Parallax

February 12, 2026

Measuring distance is the fundamental problem in astronomy. This lecture introduces parallax, derives the inverse-square law, and shows how distance unlocks luminosity — the vertical axis of the HR diagram.

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Lecture 2: Surface Flux & Colors of Stars

February 12, 2026

Given that we can measure a star’s total luminosity (from Lecture 1) and its color, we ask: what can we learn about temperature and physical size? We apply blackbody radiation (Lecture 4 (Module 1)) to solve one of astronomy’s central inference problems — how Stefan-Boltzmann and Wien’s laws connect observable color to physical properties of stars.

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Lecture 3: Spectra & Composition

February 17, 2026

Every element has a unique spectral fingerprint. By spreading starlight into a rainbow and analyzing dark absorption lines, we can determine what atoms are present in a star’s atmosphere and how fast it is moving toward or away from us. This lecture connects atomic physics to cosmic inference — and shows how the same physics explains Earth’s climate.

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Solutions

Solutions are posted for practice problems after homework deadlines. Use them to study and to check your reasoning.

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Required Textbook Reading

  • Chapter 2 (pp. 9–14): Angular Size, Parallax, and the Parsec
  • Chapter 3 (pp. 15–24): Stellar Flux, Luminosity, and Distance
  • Chapter 4 (pp. 25–30): Blackbody Radiation and Wien’s Law
  • Chapter 5 (pp. 28–35): Stellar Spectra and Classification
  • What causes the solar abundance problem? Helioseismology and spectroscopy give different answers for the Sun’s composition.
  • Why do stellar models struggle with convection? We still use mixing-length theory from the 1950s because convection is so hard to model.
  • Are there stars older than the universe? Some age estimates exceed 13.8 Gyr — systematic errors or new physics?