tailieunhanh - Basic Theoretical Physics: A Concise Overview P5

Basic Theoretical Physics: A Concise Overview P5. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | 32 6 Motion in a Central Force Field Kepler s Problem Kepler s Three Laws of Planetary Motion They are 1 The planets orbit the central star . the sun on an elliptical path where the sun is at one of the two foci of the ellipse. 2 The vector from the center of the sun to the planet covers equal areas in equal time intervals. 3 The ratio T2 a3 where T is the time period and a the major principal axis of the ellipse is constant for all planets of the solar system . In his famous interpretation of the motion of the moon as a planet orbiting the earth . the earth was considered as the central star Newton concluded that this constant parameter is not just a universal number but proportional to the mass M of the respective central star. As already mentioned Kepler s second law is also known as the law of equal areas and is equivalent to the angular momentum theorem for relative motion because for relative motion1 dL r x F dt . 0 for central forces . if F r. In fact we have L r x p m r2f ez . Here m is the reduced mass appearing in Newton s equation for the relative motion of a two-particle system such as planet-sun where the other planets are neglected this reduced mass m 1 m 1 M is practically identical to the mass of the planet since m C M. The complete law of gravitation follows from Kepler s laws by further analysis which was first performed by Newton himself. The gravitational force F which a point mass M at position RM exerts on another point mass m at r is given by F r -y m M r - Rm 6 2 I 3 . . r - Rm I3 The gravitational force which acts in the direction of the line joining r and Rm is i attractive since the gravitional constant 7 is 0 ii k m M and iii as Coulomb s law in electromagnetism inversely proportional to the square of the separation. i We do not write down the many sub-indices rei. which we should use in principle. Newtonian Synthesis From Newton s Theoryof Gravitation to Kepler 33 As has already been mentioned the principle of .