Curved spacetime tells matter how to move. GR has so far withstood all experimental tests. Spacetime curvature changes as Mercury gets closer to the sun on its orbit. Gives the orbit a little twist. Bending of Starlight Light travels on the shortest path through spacetime.
Gravity bends light passing a massive object.
Data are from the 1922 Total Solar Eclipse. Loss of energy from Gravity Waves should make the pulsars orbit closer. Are mathematically much simpler. So we continue to use and teach Newtonian physics, leaving the more complex General Relativity for when the full treatment is required. The values quoted above for the observed and predicted precession of the perihelion of Mercury's orbit differ a great deal from those given in Seed's book, and require some comment.