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Conics and beyond

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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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