Hyperbolic trajectory

In <a href="/facts/Astrodynamics/oB3tqNG9">astrodynamics</a> or <a href="/facts/Celestial_mechanics/FA3uR78J">celestial mechanics</a>, a hyperbolic trajectory or hyperbolic orbit (from <a href="/facts/Newton%2527s_law_of_universal_gravitation/F6qH2XC3">Newtonian theory</a>: <a href="/facts/Hyperbola/6R6ER0mY">hyperbola</a> shape) is the trajectory of any object around a <a href="/facts/Central_body/PzvXx42a">central body</a> with enough speed to escape the central object's gravitational rotational force; expressed as <a href="/facts/Orbital_eccentricity/WGlB4NBn">orbital eccentricity</a> (
 
 
 
 e
 
 
 
 {\displaystyle e\,}
 
) designated by any number more than 1.
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 <a href="/facts/Parabolic_trajectory/vDNtF83E">parabolic trajectories</a>, all hyperbolic trajectories are also <a href="/facts/Escape_trajectory/vDNtF83E">escape trajectories</a>. The <a href="/facts/Specific_orbital_energy/TvB2yk8a">specific energy</a> of a hyperbolic trajectory orbit is positive.
Planetary flybys, used for <a href="/facts/Gravity_assist/4sqIByot">gravitational slingshots</a>, can be described within the planet's <a href="/facts/Sphere_of_influence_(astrodynamics)/L3r5zYMo">sphere of influence</a> using hyperbolic trajectories.

Hyperbolic trajectory open-in-new

Hyperbolic trajectory