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Repulsing objects by photons

Base radiation pressure or light pressure phenomenon, the the particle photon with stationary mass zero has a momentum which can be transfered to an object. The good example is a light mill.
The light radiation and objects repulsion must be follow by law of momentum conservation. The figure1 shows repulsing two identical objects with mass m. After a period of time the objects are utilizing photons momentums and start conduct a translational motion. If laser system has identical ray intensity in both directions then objects will have translational momentums P with same value.

Other words, the objects with same mass m will have same velocities v1.

The laser system with identical ray intensity in both directions has zero net momentum.

However, the objects will utilize less photon momentums when these objects increase it's own velocities relatively to laser. The speed of light is constant. However, base on Doppler effect the photons will increase wavelength which reduce photons momentum.


Other words, the objects linear velocities will gain in non-linear mode.

How photons will repulse objects if one of them is rotating?
The figure2 shows repulsing objects by photons where one of them conducts rotation around it's own center of mass.



In this case, this objects will utilize photon momentum differently. After some period of time, the non-rotated object will utilize photons momentums on velocity v. However, the rotated object will utilize photons momentums on velocity v+wR. Base on Doppler effect the rotated object will utilize photons momentums less then non-rotated object. Therefore, after some period of time the rotated and non-rotated objects will have different translational velocities v1 and v2.

Will it work into air environment ?
The goal of this article is transfer translational momentum without mass transfer. Would it possible to do it into air environment? What if transfer momentums to objects through air wave? The Doppler effect for rotated object will be a plus.


Conclusion
Base on Doppler effect and particles(photons) with zero stationary mass, the repulsed objects may have different translational velocities by value inside isolated system.