orbital precession
A planet's orbit is an ellipse, but the ellipse itself does not have to stay still. Imagine the long oval of the orbit slowly rotating in its own plane, like the petals of a flower drawn one slightly turned from the last, so the point of closest approach drifts a little further around with every loop. That slow turning of the orbit is orbital precession.
Precession happens whenever the force is not a perfect, isolated inverse-square pull. In a pure two-body Newtonian orbit the ellipse is fixed and closes on itself exactly. But the tugs of other planets, the slight flattening of the central body, and relativistic effects all break that perfection and make the orbit's orientation creep forward (or backward). The drift is usually tiny — measured in tiny fractions of a degree per century — but it accumulates relentlessly over many orbits.
Precession is famous for a historic surprise. Mercury's orbit precesses by about 574 arcseconds per century, and Newtonian gravity, accounting for all the other planets, explained all but 43 arcseconds of it. That stubborn leftover defied explanation until 1915, when Einstein's general relativity predicted exactly that extra 43 arcseconds per century from the curvature of spacetime near the Sun. The precession of Mercury thus became one of the first triumphs of general relativity and a clear signpost of where Newton's picture must give way.
The 43-arcseconds-per-century anomaly in Mercury's perihelion — a drift so slow it takes thousands of years to add up to a single degree — was the discrepancy that general relativity erased exactly, with no fudge factor.
A tiny, stubborn drift became a decisive test of a new theory of gravity.
Most of Mercury's precession is ordinary Newtonian physics from the other planets and the choice of coordinate frame; only the small 43-arcsecond residue is relativistic. It is easy to overstate the relativistic part, which is real but a tiny slice of the whole.