(First paragraph deleted, according to comments see below,  because erroneously stating that F = m x a applies to gravitation)

Can it be derived from Newtonian laws that the path of a moving photon close to earth is bent not depending on its energy and does not vary according to the wavelength of the photon? How can it be excluded that F = m x a applies to the infraction of a  photon by earth's gravitation? 

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