It is the inability to seperate terrestial ballistics from terrestial
ballistics applied to planetary motion which generates this mess.

If you want to adhere to Newton's explanation for planetary motion
through the ballistics agenda you will also adhere to his view in
isolating the solar system from the effects of any other motion
(galactic orbital motion for instance).

"Cor. 2. And since these stars are liable to no sensible parallax from
the annual motion of the earth, they can have no force, because of
their immense distance, to produce any sensible effect in our system.
Not to mention that the fixed stars, every where promiscuously
dispersed in the heavens, by their contrary actions destroy their
mutual actions, by Prop. LXX, Book I."

Because elliptical orbits can vary from being more to less
elliptical,at least I can take the option of considering an influence
generated by the solar system's galactic orbital motion on heliocentric
planetary motion,you want to stay with Newton's view then good for you.

Want to keep the Newtonian Sun around the Earth is the same as the
Earth around the Sun when the motion of the solar system in one
direction around the Milky Way axis ( from a line drawn through the
center of the Sun ) is occuring.

How many avenues would you like to cut off to support the terrestial
ballistics agenda for planetary motion.All this is easy with the
original reasoning of the early heliocentrists for they operated from a
line drawn through the center of the Earth's heliocentric orbital path
which allows additional rotations to be grafted in,in observation and
in principle.Newton shuts it all off.