In what orbits can a cosmic body move if it is in the gravitational field of another cosmic body?

In what orbits can a cosmic body move if it is in the gravitational field of another cosmic body? What are the conditions for the implementation of certain types of movements?

One space body in the gravitational field of another can move along one of five possible trajectories: a straight line, a circle, an ellipse, a parabola or a hyperbola.

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