This is a working draft for Leslie's review. The dependency edges below are a first pass — the diagram and the prerequisite table are the parts to check hardest, since they drive hold-vs-advance decisions.
The course map shows the eight units as a spine — the turning sky first, the search for life last. But the real prerequisite structure isn't a straight line: it's a directed graph. Astronomy is more strictly cumulative than most subjects — the history of astronomy needs the motion of the sky, stellar physics needs light and spectra, cosmology needs the distance ladder the stars provide. A weak concept early doesn't just lower one grade, it cascades into everything downstream that needs it. This page is the map a guide uses to find the concept that's actually blocking a stuck student.
An arrow means “must be mastered first.” Units 05, 06, and 08 each pull from two upstream units — those are the cascade points where one soft prerequisite quietly breaks several later units.
Prerequisite gating
A unit unlocks when its prerequisites are mastered — demonstrated, not merely seen. "Covered in class" is not the gate; a cleared rubric is. The difference matters most at the cascade points, where a soft prerequisite quietly breaks two or three later units.
| Unit | Must have mastered first |
|---|---|
| 01 The Sky & Celestial Motion | — (entry point) |
| 02 The History of Astronomy | 01 (the old models make no sense until you can read the sky’s daily and yearly motion) |
| 03 Light, Telescopes & Spectra | 02 (the telescope-and-spectroscope era grows straight out of the historical arc) |
| 04 The Solar System | 02 (the Copernican–Keplerian revolution is what put the Sun at the center) |
| 05 The Sun & the Stars | 03 (spectra decode a star) + 04 (the Sun is our nearest star) |
| 06 Galaxies & the Milky Way | 03 (redshift & spectra) + 05 (stars are what galaxies are built from) |
| 07 Cosmology & the Big Bang | 05 (Cepheids & standard candles — the distance ladder rests on stellar physics) |
| 08 Space Exploration & Life in the Universe | 06 (galactic scale) + 07 (the expanding, evolving universe) |
Gap-cascade diagnosis
When a student stalls late, the visible symptom is rarely the real problem — the broken concept is usually upstream. Trace the arrows backward. Common cascades:
| Late symptom | Upstream concept to check first |
|---|---|
| Cosmic distances and the expanding universe don’t add up (Unit 07) | The Sun & the Stars from Unit 05 — the distance ladder is built on Cepheids and stellar brightness. |
| Galaxy classification and redshift fall apart (Unit 06) | Light & spectra from Unit 03 — a redshift is a spectrum read for motion, not a galaxy fact. |
| Habitable-zone and exoplanet reasoning stalls (Unit 08) | Stellar type and luminosity from Unit 05 — a star’s output sets where life could sit. |
| Stellar spectra and the H–R diagram go wrong (Unit 05) | Where the light is read — Unit 03, light, telescopes & spectra. |
Using the graph to plan a re-attempt
The graph turns a "not yet" into a targeted re-attempt instead of a whole-unit re-teach. When a student fails a downstream demonstration:
- Trace backward to the upstream node the symptom points to.
- Re-attempt the upstream concept first — close the gap at its source, not where it surfaced.
- Then re-run the downstream demonstration. Often it passes without any re-teaching of the downstream unit at all, because the cascade is resolved.
This is also where the integration guide matters: some astronomy concepts depend on an applied-math idea — logarithms for the magnitude scale, ratios for the period-luminosity law, parallax geometry for distance — from another spoke. When the upstream astronomy node looks solid but the student still stalls, check the cross-disciplinary dependency before re-teaching the astronomy.