Compare Newtonian and Einsteinian Gravity for a Physics Student

You're a first-year physics student and you need Newton and Einstein side by side, not just one then the other. This compares them conceptually and mathematically: the core assumptions of each, where they agree and where they part ways (Mercury's precession, lensing, GPS), and the leap from action-at-a-distance to curved spacetime. It marks exactly where Newton stops being good enough.

I am a first-year undergraduate physics student. Compare Newtonian gravity and Einstein's general relativity at a conceptual and mathematical level. Cover: (1) the core assumptions of each framework, (2) where they agree and where they diverge (e.g., Mercury's perihelion precession, gravitational lensing, GPS corrections), (3) the key insight of curved spacetime versus action-at-a-distance. Point out what Newtonian gravity gets wrong conceptually, not just numerically, and explain why it is still a useful approximation. Use equations where helpful but explain each one in words.