## A Simple Derivation of the Angle of Deflection by Transmuting Elliptic into Hyperbolic Orbits

We have seen that the conformal transformation,

$$z=w^2,$$

converts Newton's nonlinear law of gravity into a linear equation of a harmonic oscillator. Here, we will show that it converts elliptical orbits into hyperbolic ones, and in so doing derive the expression for the angle of deflection of light when it grazes a massive body like the sun.