Central Conservative Forces and Orbits beyond Conic Sections

The well-known characteristics of orbitals of classic central conservative force stems from the forces in proportion to the inverse square distance. In this article the authors extend the scope of the interest to central forces that are in proportion to algebraic integer powers of distance. Specifically, we investigate cases where the power of the distance varies between -2 to 4. Within this range the classic conic sections are associates with n = -2. The equation of motion leading to the orbitals only for n = I and -2 are analytically solvable. The remaining cases are analytically unsolvable nonlinear differential equations. Utilizing Computer Algebra System （CAS） we solve these equations numerically. For certain values of n numeric solutions are conducive to unseen trajectories.