Editing Hyperbolic trajectory (section)

=== Eccentricity and angle between approach and departure===
With a hyperbolic trajectory the [[orbital eccentricity]] (<math>e\,</math>) is greater than 1. The eccentricity is directly related to the angle between the asymptotes. With eccentricity just over 1 the hyperbola is a sharp "v" shape. At <math>e=\sqrt 2</math> the asymptotes are at right angles. With  <math>e>2</math> the asymptotes are more than 120° apart, and the periapsis distance is greater than the semi major axis. As eccentricity increases further the motion approaches a straight line.

The angle between the direction of periapsis and an asymptote from the central body is the [[true anomaly]] as distance tends to infinity (<math>\theta_\infty\,</math>), so <math>2\theta_\infty\,</math> is the external angle between approach and departure directions (between asymptotes). Then

:<math>\theta{_\infty}=\cos^{-1}(-1/e)\,</math> or <math>e=-1/\cos\theta{_\infty}\,</math>