Conics and Beyond: Understanding Trajectories in Multiple Gravitational Fields

[Jhenrique]

When a object of mass non insignificant is traveling in space and is sob influence of one gravitational field, the trajectory described by this object is a conics (Ax²+Bxy+Cy²+Dx+Ey+F=0), but and if the object is sob influence of two gravitational fields, so the equation the described this object is this kind: Ax³+Bx²y+Cxy²+Dy³+Ex²+Fxy+Gy²+Hx+Iy+J=0 ?

 

[UltrafastPED]

In general, there is no analytic solution to the "three body problem" under Newtonian gravity; there are a few special cases with solutions.

See https://en.wikipedia.org/wiki/Three-body_problem