What are the generalizations of Kepler’s laws of planetary motion?

Generalization of Kepler’s first law expands the class of trajectories along which some cosmic bodies can move in the gravitational field of others. Such orbits can be all possible curves of conic sections, not just ellipses. The second generalized law states that it is not just the modulus of the sector velocity that is constant, but the vector of the sector velocity, from which it also follows that the planets orbits are flat. The third generalized law of planetary motions is more accurate than the law in Kepler’s formulation. This is explained by taking into account the non-inertial nature of the frame of reference associated with the Sun.

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