Columbia University 
Astronomy and Astrophysics

Astronomy C2002
Introduction to Astrophysics, II
Hours: 2:40-3:55PM Tuesday/Thursday
Classroom: Pupin 1332


Arlin Crotts
Associate Professor of Astronomy
Phone number: 854-7899
Office: Pupin 1012
Office hours: Tuesday 4:00-5:30 P.M.
Instructor's home page.

Bulletin description

Course summary:

The topic of this course is galaxies and their place in the Universe. In particular we will cover interstellar material in our own Galaxy, the structures and motion within our Galaxy, types of normal galaxies, more exotic "active" galaxies, galactic cores, "dark matter" within galaxies, the larger structures in which galaxies are contained, the expansion of the Universe, gravitation's effects on the Universe, dark energy and the acceleration of Universal expansion, the Big Bang, the creation of matter and the chemical elements in the early Universe, dark matter in the Universe, the evolution of the Universe and current trends in trying to understand how the Universe was created and how it evolves. We will explore many of the recent discoveries made by the Hubble Space Telescope and other space observatories, and novel studies from the surface of the Earth of dark matter and large scale structure in the Universe. This is an exciting field where much is still unknown, but where significant progress is currently being made. This progress involves the application of well-established principles of physics in order to discover new ones capable of explaining how the Universe and the objects within it came to be. We will be using mathematics and basic physics to explain many of the concepts of the course.

Our text will be a very readable work by Carroll and Ostlie, An Introduction to Modern Astrophysics. There will be a weekly reading of about 35 pages from the book, plus about a half-dozen, usually simple writing or calculational exercises. Grading will consist of 50% weekly exercises, 25% final exam, 15% midterm exam and 10% class participation. The lowest three exercise grades (15% of the course grade) or the equivalent on the exams will be dropped in computing the final grade.


None. The level of mathematics required is basic algebra and a working knowledge of calculus, both of which we will use extensively. THE STUDENT IS URGED TO BE REALISTIC IN JUDGING WHETHER HER/HIS MASTERY OF MATHEMATICS ARE SUFFICIENT AND FRESH.

The level of difficulty of mathematics involved in the course encompasses:

exponential notation: 300000 = 3×105, 0.00025 = 2.5×10-4, etc.

logarithms, roots, exponentiation: log xn = n log x, x0.5 = , etc.

basic trigonometry: (sin x)/(cos x)=tan x, sin 2x = 2 sin x cos x, etc.

differential calculus: d(xn) = n xn-1, d(sin y)/dx = (cos y) (dy/dx), etc.

integral calculus: x2 dx = x3/3 = 7/3, dx/x = ln (x), etc.

It is also assumed that students remember physical concepts from the first part of the course, including Newton's basic laws of moving objects, the wave nature and propagation of light, classical laws of gravitation, angular momentum and gravitational orbits, the virial theorem, thermal radiation, the basic structure of atoms and atomic nuclei, the chemical elements, and the production of spectral lines. Any student who is not familiar with these concepts should consult the instructor during office hours.


Second semester of introductory, calculus-based physics course taken concurrently (or already completed).

Course Syllabus and Assignments

Required texts:

An Introduction to Modern Astrophysics by Bradley W. Carroll and Dale A. Ostlie (1996, Addison-Wesley, available for $93.99 from ISBN 0-201-54730-9, hardcover, 1325 pages).

Department of Astronomy home page.

Columbia University home page.

2003 January 10