Univ. Bremen
Prof. E. Hackmann
Celestial Mechanics
(S2, elective, 6 ECTS)
Learning Outcomes:
Knowledge and Understanding:
Participants understand the basic principles of orbital motion in Newtonian framework as well as within General Relativity.
Applying Knowledge and Understanding:
PrerequisitesBasic courses in Physics on mechanics, basics in Special and General Relativity.
ProgramAt the beginning a short repetition of Special and General Relativity is given. First, an overview over non-relativistic celestial mechanics is given. This consists in a complete solution of the Kepler problem. Based on that, perturbation theory (Gauß, Lagrange) is described and applied to several perturbation forces like gravitational multipole moments of the gravitating body or air drag. The secular and oscillating parts of the solution are described. Next, the same problem will be carried through within General relativity where first the analytical solutions of the motion in a Schwarzschild and also Kerr space-time will be completely described. Based on that all observable orbital effects like the perihelion shift, the Lense-Thirring effect, as well as the deflection of quasi-hyperbolic motion will be described. Also effects on light as light deflection and gravitational time delay and red shift will be derived. Finally, disturbances based on self-force and the Poynting-Robertson effect will be discussed. The results will be applied to the motion of stars around Black Holes and also to satellites orbiting the Earth. A list of references will be provided at the start of the semester.
Description of how the course is conducted
Description of the didactic methods
Description of the evaluation methods
Adopted TextbooksA list of references will be provided at the start of the semester.
Recommended readings