Hyperbolic trajectory | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-10-03

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Hyperbolic_trajectory


00:01:02 1 Parameters describing a hyperbolic trajectory
00:01:44 1.1 Semi-major axis, energy and hyperbolic excess velocity
00:04:21 1.2 Eccentricity and angle between approach and departure
00:06:45 1.3 Impact parameter and the distance of closest approach
00:10:31 2 Equations of motion
00:10:41 2.1 Position
00:14:05 2.2 Flight path angle
00:14:55 2.3 Velocity
00:18:16 3 Radial hyperbolic trajectory
00:18:46 4 Relativistic two-body problem
00:19:02 5 See also
00:19:34 6 References



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SUMMARY
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In astrodynamics or celestial mechanics, a hyperbolic trajectory is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola. In more technical terms this can be expressed by the condition that the orbital eccentricity is greater than one.
Under simplistic assumptions a body traveling along this trajectory will coast towards infinity, settling to a final excess velocity relative to the central body. Similarly to parabolic trajectories, all hyperbolic trajectories are also escape trajectories. The specific energy of a hyperbolic trajectory orbit is positive.
Planetary flybys, used for gravitational slingshots, can be described within the planet's sphere of influence using hyperbolic trajectories.