= Patched conic approximation
The <patched conic approximation> models different portions of a spacecraft trajectory by separate two-body <Kepler orbits>, matching <position> and <velocity> where one attracting body gives way to another. For a surface departure from a nonrotating planet, <conservation of energy> gives $u^2=v_e^2+w^2$, where $u$ is surface launch <speed>, $v_e$ is the planet's surface <escape speed>, and $w$ is the planet-relative <hyperbolic excess speed>. Adding that excess <velocity> vector to the planet's orbital <velocity> supplies the heliocentric initial condition. It neglects the simultaneous full gravitational action of both bodies near the matching region.
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