The Earth rotates (most easily shown by setting up and observing a Foucault's pendulum), and
also orbits around (the common barycentre of!) the Sun. As supported by various such derived details in combination with other observable/calculable measurements (that the distant stars can be shown to be essentially fixed[2]), parellax-proven distances, the more mathematically sound elipsoid orbital definitions[4] of 'local' objects (having common barycentric locii) and the practical experience of sending our own objects into interplanatary space (and, at least tentatively, beyond).
There are always increasingly finer details (the need to account for both forms of relativity in Mercury's orbit, for example, and complications like precession and gravitational resonances) but these are minor instantaneous components. To remove all sense of Earth's orbit and/or rotation from the physical model either defers to an "I am standing upon the Earth and don't
feel the motion" (and clearly have no interest in waiting for Foucault to string up anything) or requires a presumption of increasingly non-Euclidean extents to the local frame to explain how everything 'stationary' is actually apparently whipping around in huge (sometimes compound) arcs around our self-centred universal origin.
The devil is in the details, but we on Earth and the users of the Zog Fortress forum (being hosted on the planet Grog, in orbit around a star in the next galaxy over) could probably both agree about the vaster details of the 'universal background' and yet understand that (as I sit upon this chair in my current room and one of their users reclines against a handy sleeping-surface in their accomodation module) the screen in front of me and the semi-tactile vibratatronic output device in front of them are stationary w.r.t. to our respective selves yet dancing a complex dance of movement respective to the other (dominated mostly by the planetary rotations and the galactic translations, more so than the planetary translations and galactic rotations) if we cared to make the necessary calculations.
[1] The other day I heard a BBC journalist state that someone had 'refuted' some allegations, where they clearly had only 'denied' them (or perhaps 'repudiated') and not even obviously 'rebutted'.
[2] They do have relative motions, notable most easily for
the nearest and most 'drifting' stars, but while this reveals macro-motions (of what they are doing and/or what our Sun is doing) within the galaxy[3], it still establishes a 'baseplate' which can is effectively immobile and can he used to confirm that the far more clearly kindtic daily/annual motions are real and not just entirely a mathematical construct formed of otherwise unestablished assumptions about which frame (and form) of reference we should believe.
[3] And our galaxy vs. other local ones, the local group against the more distant and expanding universe...
[4] As opposed to "crystal spheres upon crystal spheres upon crystal spheres..." that had to be assumed for the planets under prior geocentric assumptions of the structure of the world, and which multiplied the complexity in the name of 'simple and perfect circles'.