Module 1 Exam Prep
Self-Assessment & Review Guide
Exam Logistics
Date: Week 7 (see course schedule for exact date)
Duration: 50 minutes
Format: Closed-book, closed-notes
Allowed: Scientific calculator (no graphing calculators or phones)
Provided: Equation sheet (see below for what’s included)
What’s On the Equation Sheet
You will receive a sheet with these equations — you don’t need to memorize them:
| Equation | What It’s For |
|---|---|
| \(c = \lambda \nu\) | Wave relation |
| \(E = h\nu\) | Photon energy |
| \(\lambda_{peak} = \frac{b}{T}\) | Wien’s Law (temperature from peak λ) |
| \(L = 4\pi R^2 \sigma T^4\) | Stefan-Boltzmann (luminosity) |
| \(F = \frac{L}{4\pi d^2}\) | Inverse-square law |
| \(P^2 = \frac{4\pi^2}{GM} a^3\) | Kepler’s Third Law (Newton’s form) |
| \(\frac{\Delta\lambda}{\lambda_0} = \frac{v}{c}\) | Doppler effect |
| \(b = 2.9 \times 10^6\) nm·K | Wien’s constant |
| \(c = 3 \times 10^8\) m/s | Speed of light |
- Definitions of terms (you need to know these)
- Conceptual explanations (you need to understand these)
- Problem-solving strategies (you need to practice these)
Self-Assessment Checklist
Use this checklist to identify gaps in your understanding. Check each item you can confidently do.
Lecture 1: Spoiler Alerts
Lecture 2: Math Survival Kit
Lecture 3: The Sky Is a Map
Lecture 4: Moon Geometry
Lecture 5: Kepler’s Laws
Lecture 6: Newton’s Gravity
Lecture 7: Light as Information
Lecture 8: Blackbody Radiation
Lecture 9: Spectral Lines
Lecture 10: Doppler Effect
Lecture 11: Solar System
Lecture 12: Exoplanets
Lecture 13: Are We Alone?
Key Concepts to Know (No Equation Needed)
These require conceptual understanding, not calculation:
Observable → Model → Inference — How astronomers extract information from light
Seasons — Caused by axial tilt, not distance from Sun
Moon phases — Caused by illumination geometry, not Earth’s shadow
Kepler vs Newton — Kepler found patterns; Newton explained why
Spectral types (OBAFGKM) — Temperature sequence from hot (O) to cool (M)
Kirchhoff’s Laws — Three types of spectra and when each appears
Frost line — Explains solar system architecture
Detection bias — Transit and RV methods favor certain planet types
Sample Exam Questions
Conceptual Questions
Explain why we can determine the mass of a star that has a planet orbiting it, but we cannot determine the mass of an isolated star with no companions.
Hint: What does Newton’s gravity tell us about orbital motion?
Mass is revealed through gravitational effects on other objects. Newton’s form of Kepler’s Third Law (\(M = 4\pi^2 a^3 / GP^2\)) requires measuring orbital period and distance — which requires something to be orbiting.
An isolated star with no companions has no orbit to measure, so we cannot directly determine its mass. (We can estimate mass from temperature and luminosity using stellar models, but that’s an indirect inference, not a direct measurement.)
Star A and Star B have identical temperatures, but Star A is 16 times more luminous than Star B.
How do their radii compare?
Stefan-Boltzmann: \(L = 4\pi R^2 \sigma T^4\)
If temperatures are equal, luminosity scales as \(R^2\):
\[\frac{L_A}{L_B} = \frac{R_A^2}{R_B^2} = 16\]
\[\frac{R_A}{R_B} = 4\]
Star A has 4 times the radius of Star B.
Calculation Questions
A star’s spectrum peaks at 725 nm.
- What is the star’s surface temperature?
- What spectral type is this star likely to be?
- Would you expect to see strong or weak hydrogen Balmer lines? Explain.
(a) Wien’s Law: \(T = b/\lambda_{peak} = (2.9 \times 10^6)/725 = 4000\) K
(b) K-type or early M-type (cool star, ~4000 K)
(c) Weak hydrogen lines. At 4000 K: - Temperature is too low to excite many electrons to the n=2 level - Fewer atoms ready to absorb Balmer-series photons - Balmer lines peak around 10,000 K (A-type stars)
An astronomer observes the sodium D line (rest wavelength 589.0 nm) in a star’s spectrum and finds it at 589.3 nm.
- Calculate the star’s radial velocity.
- Is the star approaching or receding?
- If the star is also moving across the sky at 50 km/s, does this affect your Doppler measurement? Why or why not?
(a) Doppler formula: \[v = c \cdot \frac{\Delta\lambda}{\lambda_0} = (3 \times 10^5) \cdot \frac{0.3}{589.0} = 153 \text{ km/s}\]
(b) \(\lambda_{obs} > \lambda_0\) → Redshift → Receding
(c) No effect. The Doppler effect measures only the radial (line-of-sight) component of velocity. Motion perpendicular to our line of sight (transverse velocity) does not cause a Doppler shift.
Common Mistakes to Avoid
Wrong: Higher temperature → longer peak wavelength
Right: Higher temperature → shorter peak wavelength (Wien’s Law: \(\lambda \propto 1/T\))
Memory trick: Hot = short (blue). Cool = long (red).
Watch out: \(P^2 = a^3\) only works in solar system units (years, AU) for objects orbiting the Sun.
For other systems, use Newton’s form: \(M = 4\pi^2 a^3 / (GP^2)\)
Luminosity scales as: - \(R^2\) (area effect — linear, squared) - \(T^4\) (temperature effect — very steep!)
A star twice as hot is 16× more luminous (at same radius).
Stellar Doppler shifts are tiny — typically ~0.1 nm for velocities of ~50 km/s. You need a spectrograph to measure them precisely. “Redshift” and “blueshift” refer to the direction of the shift, not visible color change.
- Phases: Happen every month (geometry of illumination)
- Eclipses: Rare (Moon must be near a node during new/full phase)
The Moon’s orbit is tilted 5° relative to the ecliptic — usually the Moon passes above or below Earth’s shadow.
Last-Minute Review Strategy
- Review the Concept Map — see how everything connects
- Go through this checklist — identify weak spots
- Do 2-3 Practice Problems — especially ★★ difficulty
- Get sleep — a rested brain performs better
- Eat breakfast
- Bring: pencil, eraser, scientific calculator
- Read each question carefully before calculating
- Check units on every calculation
- If stuck, move on and return later
You’ve Got This
You’ve spent six weeks building the astronomer’s toolkit. Trust the preparation. The exam is designed to test whether you can apply these tools — and you’ve been practicing exactly that in every lecture reading.
Good luck!