Univ. Bremen
PD Dr. E. Hackmann
, Dr. M. Scharringhausen
Celestial Mechanics
(S3, elective, 6 ECTS)
Learning Outcomes:Students should get a first introduction into the mathematics underlying General Relativity, and learn the equations of motion for point particles and light rays, the electromagnetic field, and the Einstein equations.
Knowledge and Understanding:
Participants understand the basic principles of orbital motion in Newtonian framework as well as within General Relativity.
Applying Knowledge and Understanding:
PrerequisitesBachelor courses on Theoretical Physics (basic courses in Physics on mechanics, basics in Special and General Relativity).
ProgramThe Kepler problem
– introduction of the Kepler problem
– analysis of the equations of motion, conservation laws
– solution to the general problem, Hamilton Jacobi
The general relativistic Kepler problem
– Short repetition into General Relativity
– geodesic equation in Black Hole space-times (Schwarzschild, Kerr, Schwarzschild-de Sitter)
– conservation laws
– solution of the geodesic equation for massive particles
– solutions off the geodesic equation for light
– effects (Perihelion shift, Lense-Thirring)
Description of how the course is conducted– Contact hours (lecture + exercise): 56 h (4 h x 14 weeks)
– Preparation, learning, exercises: 56 h (4 h x 14 weeks)
– Preparation for exam: 68 h
Total working hours: 180 h
Description of the didactic methods
Description of the evaluation methods
Written exam, oral exam, or study work
Adopted Textbooks– Michael W. Soffel, Wen-Biao Han: Applied General Relativity: Theory and Applications in Astronomy, Celestial Mechanics, and Metrology (Springer Nature Switzerland 2019).
– Sergei Kopeikin, Michael Efroimsky, George Kaplan: Relativistic Celestial Mechanics of the Solar System (Wiley-VCH Verlag, Weinheim, 2011)
Recommended readings