Hello fellow PF-goers As part of my high school curriculum I am required to write an extended essay on an academic field of my choice. I plan on doing a physics paper about the free-fall landing times of objects from high altitudes in a classical newtonian potential. My plan is to seperate my paper into these parts 1.Analyse free-fall landing times of initially stationary objects, expand the newtonian force in a power series and analyse the issue in zeroth, first, second and third order. (F=-g+ar+br^2+cr^3+..). I will be using mathematica to solve for the second and third order results. 2.Analyse free-fall landing times for objects with a non-zero initial angular velocity. I will switch to the lagrangian formulation for this and repeat the same power expansion method as before. 3.Tally the data, and compare to "exact" results given by mathematica. Compare the inaccuracies as a I increase the order of the taylor expansion. Advice?