The imaginary and real velocity of an orbiting body based on different types of conics sections

Abstract

In this paper, I introduce general equation of conics sections based on physical problem on the earth surface in [1]. The conics sections here (hyperbola and ellips) are generated by all maximum points of parabolas. Based on it, I derived them to calculate the velocity and kinetic energy for different types of conics. The main results showed that there is imaginary velocity if type of conics is hyperbola for r=0, but kinetic energy never be imaginary, only be negative value if r=0. Mean while, if types of conics is ellipse, then the velocity is real and kinetic energy always be positive. It is mathematically unique because only imaginary mass based on special relativity that can produce negative energy