Instructor: William H. Jefferys
RLM 15.218 (471-3302)
Office Hours: MWF 2-3
Email:
TA: Magnus Gustafsson
RLM 13.134 (471-1311)
Office Hours: TTh 1-2:30
E-mail:
Prerequisite: Upper Division Standing or Consent of Instructor
Textbooks:
Danby, Fundamentals of Celestial Mechanics, Second Edition.
Meeus, Astronomical Algorithms.
The Personal Astrolabe, Modern Edition--(Look for this in School Supplies Section of Coop).
Recommended Background:
This is a course for science and engineering majors. It is particularly designed for astronomy majors and for those in allied fields such as physics, mathematics, and aerospace engineering who would like to have an astronomy course at an upper-division level that covers astrometry and dynamical astronomy. We will assume that students have a knowledge of astronomy at the level of AST 307. Students should also have taken Mathematics 427K or its equivalent, or be taking it concurrently. A course at the level of Physics 315 or its equivalent would also be useful.
Course Contents:
This course covers the basics of positional, dynamical and kinematical astronomy. Topics include: Spherical astronomy; Astronomical reference frames and corrections for effects such as precession, nutation, etc; Time; Analysis of observations, including linear and nonlinear estimation; Astrometry; Discussion of two-body problem; Lunar, planetary, and double star orbits; Restricted Three-body Problem and basic perturbation theory; Kinematics and dynamics of stars in the Galaxy; Structure of the Galaxy; Expansion of the Universe. A more detailed syllabus follows.
1) Celestial Sphere and Coordinate Systems, and Time (5 lectures)
Equatorial, horizon (alt-azimuth) and ecliptic coordinate systems. Solar, sidereal and universal time. Equation of time. Analog devices for calculating astronomical phenomena. Establishment of time scales, i.e., solar time, sidereal time, atomic time, dynamical time. Effects of earth rotation and polar motion on time and position. Global Positioning System (GPS).
2) Spherical Trigonometry and Coordinate Transformations (3 lectures)
Geometry of a spherical surface. Definition of the spherical triangle. Establishment of the fundamental formulae. Small angle and right angle special cases. Solution of simple problems. Matrix and quaternion methods. Application to astronomical coordinate systems.
3) Positions in the Sky (4 lectures)
Topocentric, geocentric, heliocentric and barycentric reference frames. Geometric, mean, true, and apparent place. Refraction, precession, nutation, aberration, parallax and proper motion. Correction of star positions for these effects.
4) Elements of data and error analysis (3 lectures)
Theory of errors. Maximum likelihood and least-squares analysis. Normal equations. Nonlinear least squares and differential corrections.
5) Astrometric techniques (5 lectures)
Classical optical instruments and their application to photographic and CCD astrometry. Transit instruments and impersonal astrolabes. Radar and laser ranging as an astrometric technique. Very long baseline interferometry. Radio and optical interferometry. Space-based astrometry.
6) The 2-Body Problem (6 lectures)
Set up and solve Newton's laws of motion for the two-body problem. Energy and angular momentum integrals; Kepler's laws. The orbit in time. Kepler's equatioand numerical techniques for solving it.
7) The Restricted 3-Body Problem (3 lectures)
Set up Newton's laws of motion for the restructed three-body problem. Single-particle trajectories. Jacobi's Integral and zero-velocity surfaces. Lagrangian points. The Roche lobe and its implications for the evolution of binary stars.
8) Perturbation theory (2 lectures)
The basic theory of perturbations of two-body orbits, understood from a graphical and physically intuitive point of view.
9) The Determination of Orbits (3 lectures)
Determination of preliminary orbital elements from observational data. Differential correction of orbits.
10) Binary stars (2 lectures)
Elements of the orbit of a binary star. Visual and spectroscopic binary orbits. Theory of determination of orbits of binary stars. Astrophysical information obtainable from analysis of the orbits of binary stars.
11) Galactic kinematics and dynamics (3 lectures)
Motion of stars in the galaxy. Oort's constants. Statistical parallax. Kinematics of stellar orbits. Structure of the galaxy.
12) Fundamental Methods of Distance Determination (3 lectures)
The determination of distances to objects outside the solar system. Secular and statistical parallax, moving cluster parallax, binary stars, cosmological distance scale.
Course Grade:
Your course grade will be based on homework and on two exams. One exam will be given at the end of the first half of the course and the other on the last class day of the course. Each will cover only the half of the course that immediately preceeds it. Together they will count for 60% of your final grade. There will be frequent homework assignments and together they will count for 40% of your final grade. The first and second halves of the course will count equally towards your final grade. There will be no term papers, projects, or laboratory exercises. There will be no final exam.
Numerical Grade Letter Grade
90.00 to 100.0 A 80.00 to 89.99 B 70.00 to 79.99 C 60.00 to 69.99 D 00.00 to 59.99 F