Editing Hyperbolic trajectory (section)

===Position===

In a hyperbolic trajectory the [[true anomaly]] <math>\theta</math> is linked to the distance between the orbiting bodies (<math>r\,</math>) by the [[orbit equation]]:

:<math>r = \frac{\ell}{1 + e\cdot\cos\theta}</math>

The relation between the true anomaly {{mvar|θ}} and the [[eccentric anomaly]] ''E'' (alternatively the hyperbolic anomaly ''H'') is:<ref>{{Cite web|url=http://control.asu.edu/Classes/MAE462/462Lecture05.pdf|title=Spacecraft Dynamics and Control|last=Peet|first=Matthew M.|date=13 June 2019}}</ref>

:<math>\cosh{E} = {{\cos{\theta} + e} \over {1 + e \cdot \cos{\theta}}} </math> &nbsp; &nbsp; or &nbsp; &nbsp; <math> \tan \frac{\theta}{2} = \sqrt{\frac{e+1}{e-1}} \cdot \tanh \frac{E}{2}</math> &nbsp; &nbsp; or &nbsp; <math> \tanh \frac{E}{2} = \sqrt{\frac{e-1}{e+1}} \cdot \tan \frac{\theta}{2}</math>

The eccentric anomaly ''E'' is related to the [[mean anomaly]] ''M'' by [[Kepler's equation]]:

:<math> M = e \sinh E - E </math>

The mean anomaly is proportional to time

:<math>M=\sqrt{\frac{\mu}{-a^3}}.(t-\tau),</math> where ''μ'' is a [[Standard gravitational parameter|gravitational parameter]]  and ''a'' is the [[semi-major axis]] of the orbit.