Editing Hyperbolic trajectory (section)

===Semi-major axis, energy and hyperbolic excess velocity===
{{see also|Characteristic energy}}

The semi major axis (<math>a\,\!</math>) is not immediately visible with a hyperbolic trajectory but can be constructed as it is the distance from periapsis to the point where the two asymptotes cross. Usually, by convention, it is negative, to keep various equations consistent with elliptical orbits.

The semi major axis is directly linked to the [[specific orbital energy]] (<math>\epsilon\,</math>) or [[characteristic energy]] <math>C_3</math> of the orbit, and to the velocity the body attains at as the distance tends to infinity, the hyperbolic excess velocity (<math>v_\infty\,\!</math>). 
:<math>v_{\infty}^2=2\epsilon=C_3=-\mu/a</math>  or <math>a=-{\mu/{v_\infty^2}}</math>
where: <math>\mu=Gm\,\!</math> is the [[standard gravitational parameter]] and <math>C_3</math> is characteristic energy, commonly used in planning interplanetary missions

Note that the total energy is positive in the case of a hyperbolic trajectory (whereas it is negative for an elliptical orbit).