In astrodynamics, the patched conic approximation or patched two-body approximation[1][2] is a method to simplify trajectory calculations for spacecraft in a multiple-body environment.
The simplification is achieved by dividing space into various parts by assigning each of the n bodies (e.g. the Sun, planets, moons) its own sphere of influence.
Although this method gives a good approximation of trajectories for interplanetary spacecraft missions, there are missions for which this approximation does not provide sufficiently accurate results.
On an Earth-to-Mars transfer, a hyperbolic trajectory is required to escape from Earth's gravity well, then an elliptic or hyperbolic trajectory in the Sun's sphere of influence is required to transfer from Earth's sphere of influence to that of Mars, etc.
By patching these conic sections together—matching the position and velocity vectors between segments—the appropriate mission trajectory can be found.