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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. This is a hyperbolic orbit with semi-minor axis = 0 and eccentricity = 1.
A spacecraft that is leaving the central body on a hyperbolic trajectory has more than enough energy to escape: = | | > where = is the standard gravitational parameter, is the semi-major axis of the orbit's hyperbola (which may be negative in some convention).
Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola , as can be seen when graphed on a Minkowski diagram whose coordinates represent a suitable inertial (non-accelerated) frame.
Astronomers have been discovering weakly hyperbolic comets that were perturbed out of the Oort Cloud since the mid-1800s. Prior to finding a well-determined orbit for comets, the JPL Small-Body Database and the Minor Planet Center list comet orbits as having an assumed eccentricity of 1.0. (This is the eccentricity of a parabolic trajectory ...
ʻOumuamua's hyperbolic trajectory over the Solar System. ʻOumuamua appears to have come from roughly the direction of Vega in the constellation Lyra . [ 50 ] [ 51 ] [ 56 ] [ 57 ] Its incoming direction of motion is 6° from the solar apex (the direction of the Sun's movement relative to local stars), the most likely direction from which ...
If the body has a velocity greater than escape velocity then its path will form a hyperbolic trajectory and it will have an excess hyperbolic velocity, equivalent to the extra energy the body has. A relatively small extra delta- v above that needed to accelerate to the escape speed can result in a relatively large speed at infinity.
2I/Borisov's trajectory is extremely hyperbolic, having an orbital eccentricity of 3.36. [ 3 ] [ 4 ] This is much higher than the 300+ known weakly hyperbolic comets , with heliocentric eccentricities just over 1, and even ʻOumuamua with an eccentricity of 1.2.
Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the ...