Modern light on ancient feud: Robert Hooke and Newton's graphical method

The feud between Robert Hooke and Isaac Newton, over whether Newton should have acknowledged Hooke's influence on his graphical method of constructing planet orbits, the celebrated Proposition 1, Theorem 1 of the Principia, has remained ongoing among their respective supporters, even after 300 years. The drama has escalated in recent decades, with a claim that Hooke may have used the same method and obtained an elliptical orbit for a linear force, a feat that some considered Newton never did for the inverse-square force. Modern understanding of Newton's graphical method as a symplectic integrator can now shed light on whether this claim is creditable.