# Motions of Bodies—Newton’s Laws

# Motions of Bodies—Newton’s Laws

Chapter 2 covers Newtonian dynamics, Newton’s law of gravitation and the motion of mutually gravitating bodies. The principle of least action is used to provide an alternative approach to Newton’s laws. Motion of several bodies is described. By analogy the same results are used to describe the motion of a single body in three dimensions. The equations of motion are solved for a harmonic oscillator potential. The general central potential is considered. The equations are solved for an attractive inverse square law force and shown to agree with Kepler’s laws of planetary motion. The Michell–Cavendish experiment to determine Newton’s gravitational constant is described. The centre of mass is defined and the motion of composite bodies described. The Kepler 2-body problem is solved and applied to binary stars. The positions of the five Lagrangian points are calculated. Energy conservation in mechanical systems is discussed, and friction and dissipation are considered.

*Keywords:*
Newtonian mechanics, Kepler’s laws, Lagrangian points, inverse square law, centre of mass, Newton’s gravitational constant, Cavendish experiment, action principle, elliptical orbit

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