Pedal equation and Kepler kinematics

Kepler's laws is an appropriate topic which brings out the significance of pedal equation in Physics. There are several articles which obtain the Kepler's laws as a consequence of the conservation and gravitation laws. This can be shown more easily and ingeniously if one uses the pedal equation of an Ellipse. In fact the complete kinematics of a particle in a attractive central force field can be derived from one single pedal form. Though many articles use the pedal equation, only in few the classical procedure (without proof) for obtaining the pedal equation is mentioned. The reason being the classical derivations can sometimes be lengthier and also not simple. In this paper using elementary physics we derive the pedal equation for all conic sections in an unique, short and pedagogical way. Later from the dynamics of a particle in the attractive central force field we deduce the single pedal form, which elegantly describes all the possible trajectories. Also for the purpose of completion we derive the Kepler's laws.