Researching mechanics without “fixed stars” In the history of humanity, easily observable extra-(Solar System) objects greatly helped understanding certain phenomena inside the Solar System. Importantly, the “precession of the equinox”, and also true periods of heliocentric orbits lying near the ecliptic.
Imagine a system like our Solar System with indigenous astronomers who are unaware of far-away objects (or cannot determine their bearings). How can astronomers possessing some Early Modern technology learn of absolute (inertial) spacial directions then? Ī̲ see several possibilities: looking at highly inclined subsystems (think Uranus with its rings and satellites), noticeably eccentric orbits (such as of Mercury or, occasionally, of comets), or just inclined orbits (think Pallas). But do other reliable references exist?
Say I have a single observatory, and the only things I measure are the times and azimuth angles for the high magnitude solar system bodies (the Sun, Moon, Mercury, Venus, Mars, Jupiter, and Saturn) as they ascend into the sky and descend out of it (for a fixed elevation angle).
If I gather these for a few years, I will have enough data to have an overdetermined system to calculate the latitude of my observatory, the Earth's axial tilt, the Earth's rotation rate, and the orbital elements of all the bodies.
The trick would be to realize that all these bodies (including the Earth) can be approximated by rotating spheres that are revolving around the Sun (with the Moon also revolving around the Earth).  Solar and Lunar eclipses certainly would have helped with this notion.
Though our own ancient astronomers used the relatively fixed locations of the stars as a reference to better track the motions of the planets, they certainly aren't necessary. In fact, perhaps we would have understood the motion in our Solar System sooner in our development if we hadn't been distracted by the rest of the Universe.