PH I - 15 - Zweikörperproblem, Kepler'sche Gesetze

Introduction to Physics I Associate Professor Dr. Dr. h.c. Paul Wagner Faculty of Physics University of Vienna ---- Timeline: 0:00:33 - Recap: Newton's Law of Gravitation (also vector-wise) 0:06:05 - Consideration of Potential Energy: Force can be written as the negative gradient of a potential Gravity: conservative force field 0:14:24 - Graphical Representation of Potential Energy: Definition of the 'infinite range' of a force: The potential does not decay faster than 1/r. Reference point of the potential energy is usually at infinity 0:24:20 - Transition to the Two-Body Problem 0:26:06 - Two-Body Problem: Geometry of Problem 2 coupled equations of motion. Introduction of relative velocity 0:36:50 - Definition of reduced mass, reducing the two-body problem to the motion of a body with reduced mass. Brief discussion of three- and multi-body problems 0:43:48 - Discussion of a special case: one mass much larger than the second mass: e.g., Sun – Earth 0:46:50 - Planetary motion as a central body problem. Conservation of angular momentum, since there is no external torque present. Conclusion: Motion in an orbital plane Calculation of the areas swept out by the radius vector 0:55:50 - Kepler's second law: the radius vector sweeps out the same areas in equal times; this applies to all central forces 0:58:30 - Two further Kepler laws apply to the law of gravitation (without derivation): Kepler 1: Planetary orbits are ellipses, with the Sun at one focus. Kepler 3: Squares of the orbital periods are proportional to the cubes of the semi-major axes 1:02:00 - Reference to Mercury's orbit/General Relativity 1:04:37 - Moving reference frames: Consideration of an inertial frame as a reference frame and another arbitrarily moving system relative to it (translation, acceleration, rotation) 1:09:00 - Translation of systems: uniformly moving reference frame. Transformation of position coordinates Galilean Transformation ----