Where does the name hyperbolic trajectory come from?
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.
How is the kinetic energy of a hyperbolic trajectory depicted?
A hyperbolic trajectory is depicted in the bottom-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the hyperbolic trajectory is shown in red. The height of the kinetic energy decreases as the speed decreases and distance increases according to Kepler’s laws.
How is the trajectory of a body determined?
Like an elliptical orbit, a hyperbolic trajectory for a given system can be defined (ignoring orientation) by its semi major axis and the eccentricity. However, with a hyperbolic orbit other parameters may be more useful in understanding a body’s motion.
Is the semi major axis visible in a hyperbolic trajectory?
The semi major axis (a {\\displaystyle a\\,\\!}) is not immediately visible with an hyperbolic trajectory but can be constructed as it is the distance from periapsis to the point where the two asymptotes cross. Usually, by convention, it is negative, to keep various equations consistent with elliptical orbits.
Is the specific energy of a hyperbolic trajectory positive?
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.
Which is an example of a radial hyperbolic trajectory?
A radial hyperbolic trajectory is a non-periodic trajectory on a straight line where the relative speed of the two objects always exceeds the escape velocity. There are two cases: the bodies move away from each other or towards each other.