[Alamo-Girl]

To the extent that these might affect the apparent motion of the Sun as viewed from the Earth at all, the effect is negligible compared to the apparent motion of the Sun due to the Earth's rotation. For the purposes of our thought experiment, we can consider the Sun to be stationary WRT an inertial frame.

Newtonian physics works quite nicely within our solar system, but when we examine the universe, Special and General Relativity are necessary. Ditto at the quantum level, Quantum Mechanics or Quantum Field Theory is necessary.

IOW, one may postulate the Sun as a hypothetically stationary object for his thought experiment and the math will work. He may transform coordinates.

But CMB measurements from the 1960's forward confirm that the Sun is not stationary. Nothing in the universe is stationary. Space/time itself is expanding.

[betty boop]

...one may postulate the Sun as a hypothetically stationary object for his thought experiment....

But Zero Sum's postulation would not "entail" that the Sun must "agree" to stand still, so to accommodate his/her thought experiment.

So what's the point of the thought experiment?

As it stands, it has no "stationary object," no anchor or criterion according to which its phenomena can be compared and judged. JMHO FWIW