Stellar parallax in the Neo-Tychonian planetary system

The recent paper published in European Journal of Physics [1] aimed to demonstrate the kinematical and dynamical equivalence of heliocentric and geocentric systems. The work is performed in the Neo-Tychonian system, with key assumption that orbits of distant masses around the Earth are synchronized with the Sun's orbit. Motion of Sun and Mars have been analysed, and the conclusion was reached that the very fact of the accelerated motion of the Universe as a whole produces the so-called "pseudo-potential" that not only explains the origin of the pseudo-forces, but also the very motion of the celestial bodies as seen from the static Earth. After the paper was published, the question was raised if that same potential can explain the motion of the distant stars that are not affected by the Sun's gravity (unlike Mars), and if it can be used to reproduce the observation of the stellar parallax. The answer is found to be positive.