Which theory supersedes Newton's laws at speeds close to light speed?

Special relativity supersedes Newton’s laws as the more accurate theory for motion at speeds close to the speed of light. Newtonian mechanics remains an excellent approximation when speeds are much smaller than light speed.

Albert Einstein published special relativity in 1905 in his paper “On the Electrodynamics of Moving Bodies.” The theory begins with two postulates: the laws of physics are the same in all inertial frames, and light in a vacuum has the same speed for every inertial observer.

Near light speed, Newton’s assumptions about absolute time and simple velocity addition fail. Time intervals and lengths depend on the observer’s motion, simultaneity becomes relative, and momentum takes the relativistic form involving the Lorentz factor. A massive object can approach, but never reach, light speed because the energy required rises without limit.

Special relativity does not make Newton’s laws useless. It reproduces Newtonian results in the low-speed limit, just as Newtonian mechanics remains useful for ordinary vehicles, projectiles, and planets when relativistic effects are negligible. General relativity is needed when gravity or strongly curved spacetime is central.