Hyperbolic trajectory
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In astrodynamics or celestial mechanics a hyperbolic trajectory is an orbit with the eccentricity greater than 1. 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. Specific energy of hyperbolic trajectory orbit is positive.
Hyperbolic excess velocity
Under standard assumptions the body traveling along hyperbolic trajectory will attain in infinity an orbital velocity called hyperbolic excess velocity ([v_\infty\,\!]) that can be computed as:- [v_\infty=\sqrt}\,\!]
- [\mu\,\!] is standard gravitational parameter,
- [a\,\!] is length of semi-major axis of orbit's hyperbola.
- [2\epsilon=C_3=v_^2\,\!]
Velocity
Under standard assumptions the orbital velocity ([v\,]) of a body traveling along hyperbolic trajctory can be computed as:- [v=\sqrt}+}\right)}]
- [\mu\,] is standard gravitational parameter,
- [r\,] is radial distance of orbiting body from central body,
- [a\,\!] is length of semi-major axis.
- [v^2=}^2+^2]
Energy
Under standard assumptions, specific orbital energy ([\epsilon\,]) of a hyperbolic trajectory is greater than zero and the orbital energy conservation equation for this kind of trajectory takes form:- [\epsilon=-}=}]
- [v\,] is orbital velocity of orbiting body,
- [r\,] is radial distance of orbiting body from central body,
- [a\,] is length of semi-major axis,
- [\mu\,] is standard gravitational parameter.
See also
External links
- http://www.cix.co.uk/~sjbradshaw/msc/traject.html
- http://www.go.ednet.ns.ca/~larry/orbits/ellipse.html
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