Editing Hyperbolic trajectory (section)

===Speed===

Under standard assumptions the [[orbital speed]] (<math>v\,</math>) of a body traveling along a '''hyperbolic trajectory''' can be computed from the [[vis-viva equation|''vis-viva'' equation]] as:
:<math>v=\sqrt{\mu\left({2\over{r}}+{1\over{a}}\right)}</math><ref>Orbital Mechanics & Astrodynamics by Bryan Weber: https://orbital-mechanics.space/the-orbit-equation/hyperbolic-trajectories.html</ref>
where:
*<math>\mu\,</math> is [[standard gravitational parameter]],
*<math>r\,</math> is radial distance of orbiting body from [[central body]],
*<math>a\,\!</math> is the absolute value (distance) of the [[semi-major axis]].

Under standard assumptions, at any position in the orbit the following relation holds for [[Kinetic energy|orbital velocity]] (<math>v\,</math>), local [[escape velocity]] (<math>{v_{esc}}\,</math>) and hyperbolic excess velocity (<math>v_\infty\,\!</math>):
:<math>v^2={v_{esc}}^2+{v_\infty}^2</math>

Note that this means that a relatively small extra [[delta-v|delta-''v'']] above that needed to accelerate to the escape speed results in a relatively large speed at infinity. For example, at a place where escape speed is 11.2&nbsp;km/s, the addition of 0.4&nbsp;km/s yields a hyperbolic excess speed of 3.02&nbsp;km/s.
:<math>\sqrt{11.6^2-11.2^2}=3.02</math>

This is an example of the [[Oberth effect]]. The converse is also true - a body does not need to be slowed by much compared to its hyperbolic excess speed (e.g. by atmospheric drag near periapsis) for velocity to fall below escape velocity and so for the body to be captured.