Editing Sub-orbital spaceflight (section)

==Orbit==
During [[freefall]] the trajectory is part of an [[elliptic orbit]] as given by the [[orbit equation]]. The [[perigee]] distance is less than the [[radius of the Earth]] ''R'' including atmosphere, hence the [[ellipse]] intersects the Earth, and hence the spacecraft will fail to complete an orbit. The major axis is vertical, the [[semi-major axis]] ''a'' is more than ''R''/2. The [[specific orbital energy]] <math>\epsilon</math> is given by:

<math display="block">\varepsilon = -{\mu \over {2a}} > -{\mu \over {R}}\,\!</math>

where <math>\mu\,\!</math> is the [[standard gravitational parameter]].

Almost always ''a'' < ''R'', corresponding to a lower <math>\epsilon</math> than the minimum for a full orbit, which is <math>-{\mu \over {2R}}\,\!</math>

Thus the net extra specific energy needed compared to just raising the spacecraft into space is between 0 and <math>\mu \over{2R}\,\!</math>.