 4

Use a circular Earth orbit of radius $a$ about the Sun, neglect Earth's rotation, the other planets and atmospheric drag, and treat the launch as an initial impulse followed by unpowered flight of constant mass. DefineIn the patched conic approximation, a surface launch at speed $u$ leaves Earth's gravitational field with Earth-relative hyperbolic excess speed $w$, whereThus the necessary solar-orbit change must be supplied in addition to escaping Earth's gravity; simply adding the two escape speeds is incorrect. The asymptotic departure direction can be chosen to minimize $w$. Representative values are $v_E\simeq 29.78\mathrm{km}{\mathrm{s}}^{-1}$ and $v_{e,E}\simeq 11.186\mathrm{km}{\mathrm{s}}^{-1}$.^[ref]