ABSTRACT
The historical basis for central force problems comes from Kepler’s three laws of planetary motion. These also go by the names of law of equal areas, law of ellipse and law of harmonics. Kepler announced the first two laws in 1609 while the third was stated in 1619 to get an insight into the behavior of the then known planets orbiting around the Sun. This chapter focuses on the general class of central force problems noting the distinction between inertial and gravitational mass and the related issue of the principle of equivalence. It discusses the properties and equations of orbits. A study of the general class of power law potentials is the next point of inquiry in which the stability condition of the entire class of power law potentials and mapping of the general class of potentials is examined. The specific cases of the Coulomb and isotropic potentials are illustrated and finally a treatment of Laplace–Runge–Lenz vector is given.
