Newton's equations, known as Newtonian mechanics, and Einstein's equations, specifically his theory of general relativity, are two different frameworks that describe the behavior of physical systems. While Newtonian mechanics works well in describing the motion of objects at everyday speeds and scales, it is not consistent with certain phenomena observed at extreme speeds or in the presence of strong gravitational fields.
Einstein's theory of general relativity, on the other hand, provides a more comprehensive and accurate description of gravity, including the effects of space, time, and mass on the curvature of spacetime. It has been successful in explaining phenomena such as the bending of light around massive objects and the prediction of black holes.
In situations where gravitational effects are weak and speeds are much smaller compared to the speed of light, Newtonian mechanics is a good approximation and is simpler to use than the more complex equations of general relativity. Newtonian mechanics can be seen as an approximation of general relativity in the limit of low speeds and weak gravitational fields.
However, when dealing with extreme conditions, such as near the speed of light or in strong gravitational fields, Newtonian mechanics fails to accurately describe the observed phenomena, and Einstein's equations of general relativity become necessary. In such cases, the predictions of general relativity have been confirmed by numerous experimental tests and observations.
Overall, while Newtonian mechanics and general relativity have different scopes of applicability, they can both be useful and consistent within their respective domains of validity.