Euler's method is a numerical approximation technique used to solve differential equations, and it is not typically employed to "debunk" established scientific theories such as Newton's universal gravity or Einstein's theory of general relativity.
Newton's theory of universal gravity, which describes the gravitational force between two objects, has been extensively tested and confirmed by numerous experiments and observations. It accurately predicts the motions of celestial bodies, explains the behavior of falling objects on Earth, and has been the foundation of our understanding of gravity for centuries. While Newton's theory does have limitations (such as its inability to fully explain certain phenomena like the precession of Mercury's orbit), it is still considered a highly accurate and reliable framework for gravitational interactions in many everyday situations.
Einstein's theory of general relativity, on the other hand, provides a more comprehensive and nuanced description of gravity. It extends Newton's theory by incorporating the concept of spacetime curvature, explaining gravity as the curvature of the fabric of the universe caused by mass and energy. General relativity has been extensively tested and confirmed through various observations, such as the bending of starlight around massive objects and the precise predictions of gravitational time dilation.
While it is true that alternative theories or interpretations of gravity exist, scientific progress relies on rigorous testing, experimental validation, and peer-reviewed research. Claims that seek to overturn well-established scientific theories usually require extraordinary evidence to gain acceptance within the scientific community. Without such evidence, it is unlikely that physicists would prioritize teaching or promoting theories that significantly deviate from the established frameworks of Newtonian gravity or Einstein's general relativity.
Regarding the specific work you mentioned, "Newton's time dependent equation" by Roger Anderton, I'm afraid I couldn't find any information about it in my database . It's possible that it may not be widely recognized or accepted within the scientific community, which could be why it isn't taught or promoted by physicists. It's always important to critically evaluate the credibility and scientific consensus surrounding alternative theories before accepting them as replacements for well-established scientific frameworks.