Galaxy Rotation Curves
Name: ________________________________ Section: __________ Date: __________
Station: __________ Group members: ________________________________________________
Goal: explain why flat galaxy rotation curves imply missing mass (or modified gravity) beyond visible stars and gas.
Station card: Galaxy Rotation (12-15 minutes) Artifact: one radial profile table + one interpretation claim.
- Start with No dark matter and note the outer slope from $30$ to $50\,{\rm kpc}$.
- Switch to Milky Way-like and compare $V_{\rm total}$ and $V_{\rm Kep}$ at the same radius.
- Increase halo mass and describe how the outer curve changes.
- Switch to mass mode and identify where $M_{\rm dark}$ first exceeds $M_{\rm vis}$.
- Record the baryon fraction at $R=50\,{\rm kpc}$ and compare to $f_{b,\rm cosmic}=0.157$.
- Toggle MOND and compare curve shape agreement at galaxy scale.
- Run one mystery challenge (predict -> check -> explain), then use Copy challenge evidence.
| Case | $R$ (kpc) | $V_{\rm total}$ (km/s) | $V_{\rm Kep}$ (km/s) | $V_{\rm MOND}$ (km/s) | $M_{\rm total}(<R)$ ($10^{10}M_\odot$) | $M_{\rm vis}(<R)$ ($10^{10}M_\odot$) | $M_{\rm dark}(<R)$ ($10^{10}M_\odot$) | $M_{\rm dark}/M_{\rm vis}$ | $f_b$ |
|---|---|---|---|---|---|---|---|---|---|
| Snapshot | |||||||||
| $R=2$ | |||||||||
| $R=5$ | |||||||||
| $R=10$ | |||||||||
| $R=15$ | |||||||||
| $R=20$ | |||||||||
| $R=30$ | |||||||||
| $R=40$ | |||||||||
| $R=50$ |
Claim prompt
- At what radius does dark matter become dominant in your run?
- What does your $f_b(50\,{\rm kpc})$ value suggest about where most mass resides?
- One sentence: why is “galaxy behaves like solar system” not a good default model here?