Module 1 Concept Map

How the Pieces Fit Together

Visual diagrams showing the connections between observables, tools, and inferences in Module 1.
Author

Dr. Anna Rosen

How to Use These Maps

These diagrams visualize the connections you’ve built throughout Module 1. Use them to:

  • Before studying: Get the big picture of how topics relate
  • During review: Trace the logic from what we observe to what we learn
  • Before the exam: Verify you understand each connection (not just each box)
TipActive Learning

Try covering part of a diagram and predicting what connects where. If you can trace the reasoning aloud, you understand the material.

The Observable → Model → Inference Framework

This is the course thesis: astronomers measure a few things directly and infer everything else.

flowchart LR
    subgraph observe["🔭 OBSERVABLES<br/><i>What we measure directly</i>"]
        direction TB
        O1["<b>Brightness</b><br/>How much light?"]
        O2["<b>Position</b><br/>Where in the sky?"]
        O3["<b>Wavelength</b><br/>What color/spectrum?"]
        O4["<b>Timing</b><br/>How long? How often?"]
    end

    subgraph model["⚙️ PHYSICAL MODELS<br/><i>The physics that connects them</i>"]
        direction TB
        M1["Inverse-Square Law"]
        M2["Kepler's Laws"]
        M3["Wien's Law<br/>Stefan-Boltzmann"]
        M4["Atomic Transitions<br/>Kirchhoff's Laws"]
        M5["Doppler Effect"]
        M6["Newton's Gravity"]
    end

    subgraph infer["💡 INFERENCES<br/><i>What we learn about the universe</i>"]
        direction TB
        I1["<b>Distances</b>"]
        I2["<b>Orbital Properties</b>"]
        I3["<b>Temperatures</b><br/>Luminosities"]
        I4["<b>Chemical Compositions</b>"]
        I5["<b>Radial Velocities</b>"]
        I6["<b>Masses</b>"]
    end

    O1 --> M1 --> I1
    O2 --> M2 --> I2
    O3 --> M3 --> I3
    O3 --> M4 --> I4
    O3 --> M5 --> I5
    O4 --> M6 --> I6

    style observe fill:#e0f2fe,stroke:#0369a1,stroke-width:2px
    style model fill:#fef3c7,stroke:#b45309,stroke-width:2px
    style infer fill:#dcfce7,stroke:#15803d,stroke-width:2px

NoteKey Insight

Notice that wavelength connects to three different inferences (temperature, composition, velocity). This is why spectroscopy is the astronomer’s most powerful tool — a single spectrum encodes multiple properties simultaneously.

Module 1 Lecture Progression

Each lecture added a new capability to your toolkit. The arrows show dependencies — each topic builds on what came before.

flowchart TB
    subgraph week1["<b>FOUNDATION</b><br/>Weeks 1-2: What Can We Observe?"]
        direction LR
        L1["<b>L1: Four Observables</b><br/>Course thesis"]
        L2["<b>L2: Math Tools</b><br/>Unit conversion, ratios"]
        L3["<b>L3: The Sky</b><br/>Coordinates, seasons"]
        L4["<b>L4: Moon</b><br/>Phases, eclipses"]
    end

    subgraph week2["<b>GRAVITY</b><br/>Weeks 3-4: How Things Move"]
        direction LR
        L5["<b>L5: Kepler</b><br/>Empirical patterns"]
        L6["<b>L6: Newton</b><br/>Physical explanation"]
    end

    subgraph week3["<b>LIGHT</b><br/>Weeks 4-5: What Light Tells Us"]
        direction LR
        L7["<b>L7: EM Spectrum</b><br/>Light as information"]
        L8["<b>L8: Blackbody</b><br/>Temperature from color"]
        L9["<b>L9: Lines</b><br/>Composition"]
        L10["<b>L10: Doppler</b><br/>Motion from shifts"]
    end

    subgraph week4["<b>SYNTHESIS</b><br/>Week 6: Apply the Toolkit"]
        direction LR
        L11["<b>L11: Solar System</b><br/>All tools together"]
        L12["<b>L12: Exoplanets</b><br/>Finding other worlds"]
        L13["<b>L13: Life</b><br/>Drake Equation"]
    end

    L1 --> L2 --> L3 --> L4
    L4 --> L5 --> L6
    L6 --> L7 --> L8 --> L9 --> L10
    L10 --> L11 --> L12 --> L13

    style week1 fill:#dbeafe,stroke:#1e40af,stroke-width:2px
    style week2 fill:#fed7aa,stroke:#c2410c,stroke-width:2px
    style week3 fill:#bbf7d0,stroke:#15803d,stroke-width:2px
    style week4 fill:#e9d5ff,stroke:#7e22ce,stroke-width:2px

ImportantWhy This Order Matters

The sequence isn’t arbitrary:

  • Geometry first (L1-4) because it’s direct observation
  • Gravity next (L5-6) because orbits reveal mass
  • Light last (L7-10) because spectroscopy reveals everything else
  • Capstone (L11-13) because now you can combine all tools

Kepler → Newton: Pattern to Explanation

The L5 → L6 transition illustrates how science works: observe patterns first, then find the physics that explains them.

flowchart LR
    subgraph kepler["<b>KEPLER (L5)</b><br/><i>Described the patterns</i>"]
        direction TB
        K1["<b>Law 1:</b> Elliptical orbits<br/><i>What shape?</i>"]
        K2["<b>Law 2:</b> Equal areas<br/><i>How does speed vary?</i>"]
        K3["<b>Law 3:</b> P² ∝ a³<br/><i>How do period and distance relate?</i>"]
    end

    subgraph transition["<b>THE QUESTION</b>"]
        Q["<b>WHY?</b><br/>What force causes<br/>these patterns?"]
    end

    subgraph newton["<b>NEWTON (L6)</b><br/><i>Explained the physics</i>"]
        direction TB
        N1["<b>Gravity:</b> F = GMm/r²<br/><i>Force law</i>"]
        N2["<b>Centripetal:</b> F = mv²/r<br/><i>Orbital mechanics</i>"]
        N3["<b>Newton-Kepler:</b> M = 4π²a³/GP²<br/><i>Mass from orbits!</i>"]
    end

    kepler --> transition --> newton

    style kepler fill:#fef3c7,stroke:#b45309,stroke-width:2px
    style transition fill:#fee2e2,stroke:#dc2626,stroke-width:2px
    style newton fill:#dbeafe,stroke:#1e40af,stroke-width:2px

WarningExam Connection

This is a common exam topic: “Explain the difference between Kepler’s empirical laws and Newton’s physical explanation.”

Kepler could predict where planets would be. Newton could explain why — and that explanation lets us measure mass.

The Light Lectures: One Phenomenon, Many Tools

L7-L10 show how starlight encodes multiple types of information.

flowchart TB
    LIGHT["🌟 <b>STARLIGHT ARRIVES</b><br/>A single beam carries all this information"]

    subgraph analysis["How we decode it"]
        direction TB

        subgraph L7box["<b>L7: What IS light?</b>"]
            EM["Electromagnetic waves<br/>λ, ν, E relationships<br/>Full spectrum radio → γ"]
        end

        subgraph L8box["<b>L8: Continuous Spectrum</b>"]
            BB["Blackbody radiation<br/><b>Wien:</b> T from peak λ<br/><b>Stefan-Boltzmann:</b> L from T, R"]
        end

        subgraph L9box["<b>L9: Discrete Lines</b>"]
            SL["Absorption & emission<br/><b>Kirchhoff's Laws</b><br/>OBAFGKM sequence"]
        end

        subgraph L10box["<b>L10: Line Positions</b>"]
            DOP["Wavelength shifts<br/><b>Doppler effect</b><br/>Δλ/λ = v/c"]
        end
    end

    subgraph results["What we learn"]
        direction TB
        TEMP["🌡️ <b>Temperature</b>"]
        LUM["💡 <b>Luminosity</b>"]
        COMP["🧪 <b>Composition</b>"]
        MOT["🚀 <b>Velocity</b>"]
    end

    LIGHT --> L7box
    L7box --> L8box --> TEMP & LUM
    L7box --> L9box --> COMP
    L9box --> L10box --> MOT

    style LIGHT fill:#fef08a,stroke:#ca8a04,stroke-width:2px
    style L7box fill:#e0e7ff,stroke:#4338ca,stroke-width:1px
    style L8box fill:#fef3c7,stroke:#b45309,stroke-width:1px
    style L9box fill:#dcfce7,stroke:#15803d,stroke-width:1px
    style L10box fill:#fce7f3,stroke:#be185d,stroke-width:1px
    style results fill:#f0fdf4,stroke:#166534,stroke-width:2px

Capstone: Everything Connects

L11-L13 demonstrated that the toolkit works together. Here’s how each capstone lecture used multiple tools:

flowchart TB
    subgraph tools["<b>YOUR TOOLKIT</b>"]
        direction LR
        T1["⚖️ <b>Newton</b><br/>Mass from orbits"]
        T2["🌡️ <b>Wien</b><br/>T from peak λ"]
        T3["🧪 <b>Spectroscopy</b><br/>Compositions"]
        T4["🚀 <b>Doppler</b><br/>Velocities"]
    end

    subgraph L11box["<b>L11: Solar System</b><br/><i>Why is our solar system arranged this way?</i>"]
        direction TB
        SS1["Frost line → rocky vs. gas"]
        SS2["Planet masses from moons"]
        SS3["Compositions from spectra"]
    end

    subgraph L12box["<b>L12: Exoplanets</b><br/><i>How do we find planets around other stars?</i>"]
        direction TB
        EX1["<b>Transit:</b> R from depth"]
        EX2["<b>RV:</b> M from wobble"]
        EX3["Combined → density → rocky?"]
    end

    subgraph L13box["<b>L13: Are We Alone?</b><br/><i>What do we actually know?</i>"]
        direction TB
        DR1["Which Drake terms are known?"]
        DR2["R★, fp, ne: constrained"]
        DR3["fl, fi, fc, L: unknown"]
    end

    T1 --> SS2 & EX2
    T2 --> SS3
    T3 --> SS3
    T4 --> EX2

    SS1 & SS2 & SS3 --> L12box
    L12box --> L13box

    style tools fill:#f0fdf4,stroke:#166534,stroke-width:2px
    style L11box fill:#dbeafe,stroke:#1e40af,stroke-width:2px
    style L12box fill:#fed7aa,stroke:#c2410c,stroke-width:2px
    style L13box fill:#e9d5ff,stroke:#7e22ce,stroke-width:2px

Quick Reference: Observable → Tool → Inference

What You Observe Which Tool What You Learn Key Equation
Peak wavelength of spectrum Wien’s Law Temperature \(T = b/\lambda_{peak}\)
Total brightness at known distance Stefan-Boltzmann Luminosity \(L = 4\pi R^2 \sigma T^4\)
Brightness at unknown distance Inverse-square law Distance \(F = L/4\pi d^2\)
Orbital period + distance Kepler’s Third Law Mass (of central object) \(P^2 = 4\pi^2 a^3/GM\)
Absorption line wavelengths Kirchhoff + atomic physics Chemical composition Line patterns = elemental fingerprints
Wavelength shift of lines Doppler effect Radial velocity \(v = c \cdot \Delta\lambda/\lambda_0\)
Transit depth + RV amplitude Combined methods Density → rocky vs. gas \(\rho = M/V\)

Self-Test: Can You Trace the Logic?

NoteTry This

For each inference below, trace backward through the diagram:

  1. “That star is 6000 K” — What did we observe? What model did we apply?
  2. “That planet has mass 0.5 M♃” — What observations were needed? What physics connects them?
  3. “That exoplanet is rocky” — What two methods were combined? What did each contribute?

If you can answer these without looking, you’ve mastered Module 1.

What’s Next?

In Module 2: Stars, we apply this same toolkit to understand stellar evolution:

  • How stars are born (gravity + gas clouds → protostars)
  • Why they shine (nuclear fusion in the core)
  • How they evolve (main sequence → giants → endpoints)
  • What determines their fate (mass is destiny!)

The Observable → Model → Inference framework continues — we’re just adding new physics.