Astronomical data show that the perihelion of Mercury advances about 574 seconds of an arc per century. Newtonian theory does not predict any advance in the perihelion, but relativity theory does a very good job of predicting this effect. Your project is to learn about basic perturbation methods for 2nd order differential equations, then use these techniques to explain the advance of the perihelion of Mercury. Describe why the theory of relativity succeeds, where Newtonian mechanics fails. A good starting reference for this subject is Frederic Wan’s Mathematical Models and Their Analysis, pp. 35f. Additional material can be found on the web such as these websites:
The last of the websites gives a detailed Maple account of your project, so you would have to expand on both the modeling and the mathematical theory behind your project.