Physics hero Issac Newton believed in alchemy, young earth creationism, and made end-of-the-world predictions. That doesn't make everything Newton ever wrote to be wrong or uncitable, however. People can cite Newton without believing his other stuff. He believed in that other stuff, yet is somehow called the 'greatest physcist to have ever lived'. Vijaya is referencing something because he thinks it's correct.
By your posting you appear to be saying that you believe that this paper debunks you, and so you need to somehow discredit the author. And, desperately, you are telling us about something that someone
else believes, who is not the author, that is unrelated to astronomy.
You can find several celestial mechanics experts calling perturbation theory to be based on epicycles as well -
https://wiki.tfes.org/Astronomical_Prediction_Based_on_Patterns Gravitation Vs. Relativity
Charles Lane Poor, Ph.D.
Professor Emeritus of Celestial Mechanics,
Columbia University
Motion of the Planets p.132
“ The deviations from the “ideal” in the elements of a planet’s orbit are called “perturbations” or “variations”.... In calculating the perturbations, the mathematician is forced to adopt the old device of Hipparchus, the discredited and discarded epicycle. It is true that the name, epicycle, is no longer used, and that one may hunt in vain through astronomical text-books for the slightest hint of the present day use of this device, which in the popular mind is connected with absurd and fantastic theories. The physicist and the mathematician now speak of harmonic motion, of Fourier’s series, of the development of a function into a series of sines and cosines. The name has been changed, but the essentials of the device remain. And the essential, the fundamental point of the device, under whatever name it may be concealed, is the representation of an irregular motion as the combination of a number of simple, uniform circular motions. ”