There is no great mystery behind the lingo called frame of reference as it originally applied to astronomy insofar as there is really no choice in astronomy when it comes to perspectives, especially how planets and moons move relative to a moving Earth including the difference between our own moon and moons of other planets.

Yesterday I posted a link to Hamilton's notion of space and time as this is where mathematicians began to enter the weird world that eventually became relativity but the 20th century people did so by reworking Newton's so-called 'definitions' at variance with what he was actually doing with space,time(keeping) and planetary motions.


Newton invented apparent/true motion based on a notion that in the Earth frame of reference the observer sees the planets move direct/retrograde but in the frame of reference of the Sun the motions appear direct only -

"For to the earth planetary motions appear sometimes direct, sometimes
stationary, nay, and sometimes retrograde. But from the sun they are
always seen direct,..." Newton

That statement is astronomical and intellectual no-man's land even though it became the point of departure where mathematicians entered astronomy and ultimately the fantasy of spacetime.

Contemporaries don't need the fictitious apparent/true motions, they assign proof of a moving Earth and other planets around the Sun by dividing perspectives to faster/slower motion or whether the circumference is greater than the Earth's or smaller as in the case of Venus and Mercury.

https://apod.nasa.gov/apod/ap011220.html

https://encrypted-tbn0.gstatic.com/i...xEhUCr9rw4P7wE

A astronomer should rightly be able to see the astronomical view and also how mathematicians make themselves look ridiculous or careless with the celestial arena while mathematicians generally do not have a feel for astronomy outside magnification. From experience, they have no interest in the roots of empirical involvement in astronomy other than a vague notion that experimental sciences and astronomy can be directly scaled up instead of using experimental sciences as analogies with limitations attached.