Conics and Beyond: Understanding Trajectories in Multiple Gravitational Fields

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When an object of significant mass travels in space under the influence of a single gravitational field, its trajectory is described by conic sections. However, when affected by two gravitational fields, the trajectory becomes more complex, represented by a higher-degree polynomial equation. The discussion highlights the challenges of the three-body problem, emphasizing that there is generally no analytic solution under Newtonian gravity, with only a few special cases yielding solutions. This complexity arises from the interactions between multiple gravitational fields. Understanding these trajectories is crucial for advanced studies in celestial mechanics and astrodynamics.
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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 ?
 
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