Editing Orbital mechanics (section)

===Hyperbolic orbits===
If <math>e>1</math>, the orbit formula,
:<math>r={{h^2}\over{\mu}}{{1}\over{1+e\cos\theta}}</math>

describes the geometry of the hyperbolic orbit. The system consists of two symmetric curves. The orbiting body occupies one of them; the other one is its empty mathematical image. Clearly, the denominator of the equation above goes to zero when <math>\cos\theta = -1/e</math>. we denote this value of true anomaly
:<math>\theta_\infty = \cos^{-1} \left( -\frac1e \right)</math>
since the radial distance approaches infinity as the true anomaly approaches <math>\theta_\infty</math>, known as the ''true anomaly of the asymptote''. Observe that <math>\theta_\infty</math> lies between 90° and 180°. From the trigonometric identity <math>\sin^2\theta+\cos^2\theta=1</math> it follows that:
:<math>\sin\theta_\infty = \frac1e \sqrt{e^2 - 1}</math>

====Energy====
Under standard assumptions, [[specific orbital energy]] (<math>\epsilon\,</math>) of a [[hyperbolic trajectory]] is greater than zero and the [[orbital energy conservation equation]] for this kind of trajectory takes form:
:<math>\epsilon={v^2\over2}-{\mu\over{r}}={\mu\over{-2a}}</math>
where:
*<math>v\,</math> is the [[orbital speed|orbital velocity]] of orbiting body,
*<math>r\,</math> is the radial distance of orbiting body from [[central body]],
*<math>a\,</math> is the negative [[semi-major axis]] of the [[orbit]]'s [[hyperbola]],
*<math>\mu\,</math> is [[standard gravitational parameter]].

====Hyperbolic excess velocity====
{{See also|Characteristic energy}}

Under standard assumptions the body traveling along a hyperbolic trajectory will attain at <math>r =</math> infinity an [[orbital speed|orbital velocity]] called hyperbolic excess velocity (<math>v_\infty\,\!</math>) that can be computed as:
:<math>v_\infty=\sqrt{\mu\over{-a}}\,\!</math>
where:
*<math>\mu\,\!</math> is [[standard gravitational parameter]],
*<math>a\,\!</math> is the negative [[semi-major axis]] of [[orbit]]'s [[hyperbola]].

The hyperbolic excess velocity is related to the [[specific orbital energy]] or characteristic energy by
:<math>2\epsilon=C_3=v_{\infty}^2\,\!</math>