8.284 | Spring 2006 | Undergraduate

Modern Astrophysics


Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Course Description

This course explores the applications of physics (Newtonian, statistical, and quantum mechanics) to fundamental processes that occur in celestial objects. The list of topics includes Main-sequence Stars, Collapsed Stars (White Dwarfs, Neutron Stars, and Black Holes), Pulsars, Supernovae, the Interstellar Medium, Galaxies, and as time permits, Active Galaxies, Quasars, and Cosmology. Observational data is also discussed.


Students must have previously completed Quantum Physics I (8.04) and Quantum Physics II (8.05) with a grade of C or higher. No prior knowledge of astronomy is required.


There is no single text for this course. All of the assigned readings come from the following texts:

Bohm-Vitense, Erika. Introduction to Stellar Astrophysics. 3 vols. New York, NY: Cambridge University Press, 1989. ISBN: 9780521344029.

Binney, James, and Scott Tremaine. Galactic Dynamics. Princeton, NJ: Princeton University Press, 1987. ISBN: 9780691084442.

Clayton, Donald D. Stellar Evolution and Nucleosynthesis. Chicago, IL: University of Chicago Press, 1983. ISBN: 9780226109534.

Hansen, Carl J., and Steven D. Kawaler. Stellar Interiors: Physical Principles, Structure, and Evolution. New York, NY: Springer, 2004. ISBN: 9780387200897.

Mihalas, Dimitri, and James Binney. Galactic Astronomy. San Francisco, CA: W.H. Freeman, 1981, chapter 2. ISBN: 9780716712800.

Press, William H. Introduction to Astrophysics

Shu, Frank H. The Physical Universe. Mill Valley, CA: University Science Books, 1982. ISBN: 9780935702057.

Schechter, Paul. 8.902 Notes on Cosmology (PDF)

Although these are not part of the required readings, students may also find the following books useful:

Binney, James, and Michael Merrifield. Galactic Astronomy. Princeton, NJ: Princeton University Press, 1998. ISBN: 9780691004020.

Gray, David F. The Observation and Analysis of Stellar Photospheres. New York, NY: Cambridge University Press, 2005. ISBN: 9780521851862.

Harwit, Martin. Astrophysical Concepts. New York, NY: Springer, 1998. ISBN: 9780387949437.

Longair, Malcolm S. Galaxy Formation. New York, NY: Springer, 1998. ISBN: 9783540637851.

Osterbrock, Donald E. The Astrophysics of Gaseous Nebulae and Active Galactic Nuclei. Sausalito, CA: University Science Books, 2006. ISBN: 9781891389344.

Ostlie, Dale A., and Bradley W. Carroll. An Introduction to Modern Astrophysics. Reading, MA: Addison-Wesley Publishing, 1996. ISBN: 9780201547306.

Peebles, P. J. E. Physical Cosmology. Princeton, NJ: Princeton University Press, 1971. ISBN: 9780691081083.

———. Principles of Physical Cosmology. Princeton, NJ: Princeton University Press, 1993. ISBN: 9780691074283.

Schwarzschild, Martin. Structure and Evolution of the Stars. New York, NY: Dover Publications, 1977. ISBN: 9780486614793.

———. The Physics of Astrophysics. 2 vols. Mill Valley, CA: University Science Books, 1991. ISBN: 9780935702644.

Silk, Joseph. The Big Bang. New York, NY: W.H. Freeman, 2001. ISBN: 9780716742463.

Spitzer, Lyman. Physical Processes in the Interstellar Medium. New York, NY: Wiley, 1978. ISBN: 9780471022329.

Unsold, Albrecht. The New Cosmos. New York, NY: Springer, 2001. ISBN: 9783540678779.

Weinberg, Steven. The First Three Minutes. New York, NY: Basic Books, 1993. ISBN: 9780465024377.

———. Gravitation and Cosmology. New York, NY: Wiley, 1972. ISBN: 9780471925675.

Problem Sets

There are 11 problem sets. Approximately one set is due per week. Solutions will be provided four days after the due date.


There will be one in-class midterm exam. There will also be a comprehensive final exam, scheduled by the Registrar and held during the final exam period.

Grading Policy

Midterm exam 20%
Problem sets 40%
Final exam 40%




Equatorial coordinates and sidereal time


Galactic coordinates

Distances to stars

3 Magnitudes (apparent and absolute) and color indices Problem set 1 due

Spectral classification

The Kepler problem

5 Parametric solution to Kepler  

Masses of stars

Mass radius relation

7 Mass measurements for exoplanets and our black hole Problem set 2 due
8 Telescopes  
9 Polytropic stars  

Classical and quantum statistics

The Saha equation


Equations of state

Application of Lane-Emden solution: White dwarfs

Problem set 3 due
12 Simple results for the sun and other stars  
13 Radiative transport  


Scaling laws


Problem set 4 due

Energy generation

Coulomb penetration factor

16 Nuclear “burning” in the sun and other stars  
17 Evolution of stars of low, intermediate and high mass Problem set 5 due
18 Stellar atmospheres  
19 Lines in stellar atmospheres  
20 In-class exam Problem set 6 due
21 Introduction to the interstellar medium  
22 Photoionized nebulae (H II regions and planetaries)  
23 Supernovae and shocks  
24 Adiabatic supernova shocks Problem set 7 due
25 Galaxy morphology  

Quantifiable properties of galaxies

Collisional relaxation times

27 Collisionless Boltzmann equation (cartesian) and its moments Problem set 8 due
28 Boltzmann and the 4 jeans equations (spherical)  
29 Galaxy disks: Rotation and epicyclic motion  
30 Galaxy models: Potentials, orbits, and distribution functions Problem set 9 due
31 Clusters of galaxies  

Evidence for the expansion and homegeneity of the universe

Newtonian derivation of Friedmann universe

33 Galaxy formation Problem set 10 due
34 Friedman-Robertson-Walker metric  
35 Friedman equation with radiation and other stuff  
36 Supernovae and cosmic acceleration Problem set 11 due
37 Recombination and helium production  
38 Fluctuations in the cosmic microwave background  
  Final exam  

Course Info

As Taught In
Spring 2006
Learning Resource Types
Problem Sets