Hyperbolic trajectory
Under standard assumptions a body traveling along this trajectory will coast to infinity, arriving there with hyperbolic excess velocity relative to the central body. Similarly to parabolic trajectory 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.
Contents
Hyperbolic excess velocity
See also: Characteristic energy
Under standard assumptions the body traveling along hyperbolic trajectory will attain in infinity an orbital velocity called hyperbolic excess velocity () that can be computed as:- is standard gravitational parameter,
- is the negative semi-major axis of orbit's hyperbola.
Velocity
Under standard assumptions the orbital velocity () of a body traveling along a hyperbolic trajectory can be computed as (Vallado):- is standard gravitational parameter,
- is radial distance of orbiting body from central body,
- is the negative semi-major axis.
Angle between approach and departure
Let the angle between approach and departure (between asymptotes) be .- and
- is the orbital eccentricity, which is greater than 1 for hyperbolic trajectories.
Distance of closest approach
The distance of closest approach, also called the periapse distance and the focal distance, is given byEnergy
Under standard assumptions, specific orbital energy () of a hyperbolic trajectory is greater than zero and the orbital energy conservation equation for this kind of trajectory takes form:- is orbital velocity of orbiting body,
- is radial distance of orbiting body from central body,
- is the negative semi-major axis,
- is standard gravitational parameter.
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