According to Newtonian laws and often considered counter-intuitive bodies of different mass are accelerated by gravitation differently: A heavy body  falls faster to earth than a lighter one, as gravitational force equals mass times acceleration meaning the more mass you have the faster the velocity becomes.

How can it be derived in Newtonian physics that the path of a moving body across the sky is NOT bent depending on its mass? Is the formula of gravitational deviation that differs from "radial acceleration" empirically found and cannot be derived from Newton's laws on force, mass and impulse? 

Then, in relativistic physics, there is the principle of equivalence of energy and mass. A photon that has no rest mass but has energy should be accelerated and bent by gravitational force according to its energy thus wavelenght.

However, the formula on the angle of bending and on  the shift of frequency show that both angle of curvature of path and change of wavelength/frequency (redshift/blueshift) do not depend on the energy/wavelength/frequency/relativistic mass of the photon.

Why do mass and  energy "cancel out"? 

Related:

["Does 'special relativity + newtonian gravity' predict gravitational bending of light?][1]

The Newtonian deflection angle is: θ=2GM/rc2.


  [1]: https://physics.stackexchange.com/questions/425890/does-special-relativity-newtonian-gravity-predict-gravitational-bending-of-l