Trajectories, equation of motion and forces....

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physics user1
Setting a cartesian system how can i get the equation of the trajectory of an object knowing the forces acting on that object?

Example: If F= GMm/r^2 and let be the sun at the center (point (0,0,0)) of the cartesian system how do i get the equation of an ellipse in this system? ( x^2/a^2 + y^2/b^2 = 1)

Where x and y define the position of the planet in the chosen system centred in the sun
 
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