Newtonian physics -- like any scientific paradigm -- was abandoned when it could no longer explain physical reality. Newton's theories on the nature of light was abandoned when it could not explain interference. His ideas of gravity were shown to be only an approximation when it was shown it could not explain the bending of star light near a large mass. And his basic ideas of space and time have also been shown to be not in accord with experiment.
Newtonian Mechanics
Newtonian physics and relativity differ in their treatment of motion and gravity. Newtonian physics describes motion and gravity based on absolute space and time, while relativity considers them as relative and interconnected. Additionally, relativity accounts for the effects of high speeds and strong gravitational fields, which are not addressed in Newtonian physics.
Newtonian and Quantum
Newtonian physics....etc.
Classical (or Newtonian) and Quantum.
Gravitational Physics is Newtonian Physics! Quaternion Gravity will be an advance, when Gravitational Energy is recognized to be: E = Newtonian Energy (-mu/r) and vector Energy (mcV) = -mu/r + mcV.
Typically, there are considered two forms of physics. Newtonian and modern. Newtonian relates to Newton-era mechanics and E&M. Modern physics loosely refers to post-newton physics. Modern physics primarily refers to 20th century physics as it incorporates relativity and quantum theory.
Newtonian physics, also called classical or pre-relativistic physics refer to the physics after Aristotelian physics and before the 1920s when the theory of relativity was formed. They distinctly differ from Aristotelian physics in that they cover the physics of motion, scientific method, describe contact and non-contact forces such as magnetism
Newtonian physics fails to explain motion correctly in extreme conditions such as at speeds approaching the speed of light or in the presence of very strong gravitational fields where the effects of relativity become significant. Additionally, at the quantum level, where particles behave in ways that cannot be predicted using classical physics, Newtonian physics also breaks down.
Newtonian, or classical physics applies to physical, every day things, while quantum physics is a type of theoretical physics that does not apply to any physical things.
The solutions will be extremely similar to what you would get for equations in Newtonian physics. At everyday speeds the deviation from Newtonian mechanics is negligible.
Yes, many physical phenomena can be accurately described and predicted using Newtonian physics, particularly for objects with speeds much slower than the speed of light and on scales larger than atoms. However, when dealing with very small scales (like quantum mechanics) or very high speeds (like near the speed of light), Newtonian physics may not provide accurate predictions.