When I was a freshman at UF taking an honors physics class I thought, gee, why are we learning Newtonian physics when Einsteinian physics is more than half a century old? When I graduated with a PhD many years later and went to work analyzing rocket trajectories for the Star Wars program, I learned that I didn't learn Newtonian physics in the University, I learned what we can call rudimentary physics.
Since the time of Newton classical physics has consisted of the analysis of differential equation models of physical systems. Since differential equations are an advanced topic in calculus, physics is necessarily taught at the U for two years ! without differential equations.
Unfortunately, once you've taken a course in differential equations, the real difficulty with Newtonian physics presents itself, that is, most differential equations are unsolvable.
Thus Kepler's Problem, which Newton (and Kepler) solved (numerically using Kepler's equation) is not taught in University. To see how difficult the analytic solution is, check wiki Freefall to see the analytic solution in 1-D, an infinite series solution.
From Thornton's Classical Physics - "Edmond Halley is generally given the credit for bringing Newton's work of gravitational and central forces to the attention of the world. After observing the comet personally in 1682 Halley became interested. Partly because of a bet between Christopher Wren and Robert Hooke. Halley asked Newton in 1684 what paths the planets must follow if the Sun pulled them with a force inversely proportional to their distances. To the astonishment of Halley, Newton replied "Why, in ellipses, of course." Newton had worked it out 20 years previously, but had not published the result. With painstaking effort Halley was able in 1705 to predict the next occurrence of the comet now bearing his name, to be 1758."
As I learned working on Star Wars, orbit problems are easy to solve numerically (from the laws of motion and gravity), i.e. simulate, and that's the way it's done in engineering today. For details see ... The Coming Revolution in Physics Education ...
https://www.academia.edu/42129766/The_Coming_Revolution_in_Physics_Education