Patched Conics

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The method of patched conics is a means of generating interplanetary trajectories for spacecraft by patching together the conic section trajectories for each sphere of influence.

For example: On an Earth to Mars transfer, a hyperbolic trajectory is required to escape the gravity well of the Earth, and an elliptical trajectory is required to transfer from Earth's sphere of influence to that of Mars. By patching these two conic sections together the appropriate mission trajectory can be found.